Subgroups — #6692572

Order 512.

1628 conjugacy classes of subgroups.

The subgroup lattice has 1276 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#40028	C₂	1	1	yes	maximal, characteristic, complemented
2	#36215	C₂	1	1	yes	maximal, characteristic
3	#32905	C₂	1	1	yes	maximal, characteristic
4	#32560	C₂	1	1	yes	maximal, characteristic, complemented
5	#32555	C₂	1	1	yes	maximal, characteristic, complemented
6	#32438	C₂	1	1	yes	maximal, characteristic, complemented
7	#32433	C₂	1	1	yes	maximal, characteristic, complemented
8	#31478	C₂	1	1	yes	maximal, characteristic, complemented
9	#31470	C₂	1	1	yes	maximal, characteristic, complemented
10	#31159	C₂	1	1	yes	maximal, characteristic, complemented
11	#31157	C₂	1	1	yes	maximal, characteristic, complemented
12	#30202	C₂	1	1	yes	maximal, characteristic, complemented
13	#29974	C₂	1	1	yes	maximal, characteristic, complemented
14	#27708	C₂	1	1	yes	maximal, characteristic, complemented
15	#27706	C₂	1	1	yes	maximal, characteristic, complemented
16	#27565	C₂	1	1	yes	maximal, characteristic, complemented
17	#27558	C₂	1	1	yes	maximal, characteristic, complemented
18	#26365	C₂	1	1	yes	maximal, characteristic, complemented
19	#26353	C₂	1	1	yes	maximal, characteristic, complemented
20	#26186	C₂	1	1	yes	maximal, characteristic, complemented
21	#26182	C₂	1	1	yes	maximal, characteristic, complemented
22	#26117	C₂	1	1	yes	maximal, characteristic, complemented
23	#26110	C₂	1	1	yes	maximal, characteristic, complemented
24	#24538	C₂	1	1	yes	maximal, characteristic
25	#24538	C₂	1	1	yes	maximal, characteristic
26	#24349	C₂	1	1	yes	maximal, characteristic, complemented
27	#24343	C₂	1	1	yes	maximal, characteristic, complemented
28	#22864	C₂	1	1	yes	maximal, characteristic
29	#22864	C₂	1	1	yes	maximal, characteristic
30	#22297	C₂	1	1	yes	maximal, characteristic, complemented
31	#20873	C₂	1	1	yes	maximal, characteristic
32	C₂×#554	C₂²	1	1	yes	characteristic
33	C₂²×C₄×D₄	C₂²	1	1	yes	characteristic
34	C₂×#479	C₂²	1	1	yes	characteristic, complemented
35	C₂×#475	C₂²	1	1	yes	characteristic, complemented
36	C₂×#461	C₂²	1	1	yes	characteristic
37	C₂×#461	C₂²	1	1	yes	characteristic
38	C₂×#450	C₂²	1	1	yes	characteristic
39	C₂×#450	C₂²	1	1	yes	characteristic
40	C₂×#440	C₂²	1	1	yes	characteristic
41	C₂×#440	C₂²	1	1	yes	characteristic
42	C₂×#428	C₂²	1	1	yes	characteristic
43	C₂×#418	C₂²	1	1	yes	characteristic
44	C₂×#418	C₂²	1	1	yes	characteristic
45	#2857	C₂²	1	1	yes	characteristic
46	#2851	C₂²	1	1	yes	characteristic
47	#2848	—	2	1	no	—
48	#2787	—	2	1	no	—
49	#2770	—	2	1	no	—
50	#2747	—	2	1	no	—
51	#2690	—	2	1	no	—
52	#2655	—	2	1	no	—
53	#2590	—	2	1	no	—
54	#2588	—	2	1	no	—
55	#2582	C₂²	1	1	yes	characteristic, complemented
56	#2581	C₂²	1	1	yes	characteristic, complemented
57	#2580	C₂²	1	1	yes	characteristic
58	#2579	—	2	1	no	—
59	#2570	C₂²	1	1	yes	characteristic, complemented
60	#2566	C₂²	1	1	yes	characteristic
61	#2564	—	2	1	no	—
62	#2552	C₂²	1	1	yes	characteristic, complemented
63	#2514	C₂²	1	1	yes	characteristic, complemented
64	#2511	C₂²	1	1	yes	characteristic, complemented
65	#2499	C₂²	1	1	yes	characteristic
66	#2499	C₂²	1	1	yes	characteristic
67	#2454	C₂²	1	1	yes	characteristic
68	#2452	C₂²	1	1	yes	characteristic
69	#2450	—	2	1	no	—
70	#2449	—	2	1	no	—
71	#2446	C₂²	1	1	yes	characteristic, complemented
72	#2446	C₂²	1	1	yes	characteristic, complemented
73	#2442	C₂²	1	1	yes	characteristic
74	#2440	C₂²	1	1	yes	characteristic
75	#2437	—	2	1	no	—
76	#2437	—	2	1	no	—
77	#2362	C₂²	1	1	yes	characteristic
78	#2362	C₂²	1	1	yes	characteristic
79	#2349	C₂²	1	1	yes	characteristic
80	#2349	C₂²	1	1	yes	characteristic
81	D₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
82	D₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
83	D₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
84	#2336	—	2	1	no	—
85	C₄×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
86	#2296	C₂²	1	1	yes	characteristic
87	C₂×#385	—	2	1	no	—
88	#2101	C₂²	1	1	yes	characteristic, complemented
89	#2101	C₂²	1	1	yes	characteristic, complemented
90	#2101	C₂²	1	1	yes	characteristic, complemented
91	#2101	C₂²	1	1	yes	characteristic, complemented
92	#2100	C₂²	1	1	yes	characteristic, complemented
93	#2100	C₂²	1	1	yes	characteristic, complemented
94	#2100	C₂²	1	1	yes	characteristic, complemented
95	#2099	C₂²	1	1	yes	characteristic, complemented
96	#2097	C₂²	1	1	yes	characteristic, complemented
97	#2095	C₂²	1	1	yes	characteristic, complemented
98	#2088	C₂²	1	1	yes	characteristic, complemented
99	#2088	C₂²	1	1	yes	characteristic, complemented
100	#2088	C₂²	1	1	yes	characteristic, complemented
101	#2087	C₂²	1	1	yes	characteristic, complemented
102	#2086	C₂²	1	1	yes	characteristic, complemented
103	#2086	C₂²	1	1	yes	characteristic, complemented
104	#2074	C₂²	1	1	yes	characteristic, complemented
105	#2074	C₂²	1	1	yes	characteristic, complemented
106	#2074	C₂²	1	1	yes	characteristic, complemented
107	#2073	C₂²	1	1	yes	characteristic
108	#2073	C₂²	1	1	yes	characteristic
109	#2072	C₂²	1	1	yes	characteristic, complemented
110	#2071	C₂²	1	1	yes	characteristic
111	#2071	C₂²	1	1	yes	characteristic
112	#2068	C₂²	1	1	yes	characteristic, complemented
113	#2066	C₂²	1	1	yes	characteristic, complemented
114	#2059	C₂²	1	1	yes	characteristic, complemented
115	#2059	C₂²	1	1	yes	characteristic, complemented
116	#2059	C₂²	1	1	yes	characteristic, complemented
117	#2057	C₂²	1	1	yes	characteristic, complemented
118	#2055	C₂²	1	1	yes	characteristic
119	#2055	C₂²	1	1	yes	characteristic
120	#2055	C₂²	1	1	yes	characteristic
121	#2055	C₂²	1	1	yes	characteristic
122	#2043	C₂²	1	1	yes	characteristic, complemented
123	#2043	C₂²	1	1	yes	characteristic, complemented
124	#2026	C₂²	1	1	yes	characteristic, complemented
125	#2026	C₂²	1	1	yes	characteristic, complemented
126	#2026	C₂²	1	1	yes	characteristic, complemented
127	#2024	C₂²	1	1	yes	characteristic, complemented
128	#1993	C₂²	1	1	yes	characteristic, complemented
129	#1992	C₂²	1	1	yes	characteristic, complemented
130	#1985	C₂²	1	1	yes	characteristic, complemented
131	#1985	C₂²	1	1	yes	characteristic, complemented
132	#1968	C₂²	1	1	yes	characteristic
133	#1968	C₂²	1	1	yes	characteristic
134	#1949	C₂²	1	1	yes	characteristic, complemented
135	#1948	C₂²	1	1	yes	characteristic, complemented
136	#1939	C₂²	1	1	yes	characteristic, complemented
137	#1939	C₂²	1	1	yes	characteristic, complemented
138	#1936	C₂²	1	1	yes	characteristic
139	#1936	C₂²	1	1	yes	characteristic
140	#1935	C₂²	1	1	yes	characteristic, complemented
141	#1935	C₂²	1	1	yes	characteristic, complemented
142	#1933	C₂²	1	1	yes	characteristic, complemented
143	#1933	C₂²	1	1	yes	characteristic, complemented
144	#1925	C₂²	1	1	yes	characteristic
145	#1925	C₂²	1	1	yes	characteristic
146	#1921	C₂²	1	1	yes	characteristic, complemented
147	#1920	C₂²	1	1	yes	characteristic, complemented
148	#1917	C₂²	1	1	yes	characteristic, complemented
149	#1917	C₂²	1	1	yes	characteristic, complemented
150	#1916	C₂²	1	1	yes	characteristic, complemented
151	#1916	C₂²	1	1	yes	characteristic, complemented
152	#1894	C₂²	1	1	yes	characteristic
153	#1894	C₂²	1	1	yes	characteristic
154	#1894	C₂²	1	1	yes	characteristic
155	#1894	C₂²	1	1	yes	characteristic
156	#1880	C₂²	1	1	yes	characteristic
157	#1880	C₂²	1	1	yes	characteristic
158	#1877	C₂²	1	1	yes	characteristic
159	#1877	C₂²	1	1	yes	characteristic
160	#1877	C₂²	1	1	yes	characteristic
161	#1877	C₂²	1	1	yes	characteristic
162	#1877	C₂²	1	1	yes	characteristic
163	#1877	C₂²	1	1	yes	characteristic
164	#1877	C₂²	1	1	yes	characteristic
165	#1877	C₂²	1	1	yes	characteristic
166	#1877	C₂²	1	1	yes	characteristic
167	#1877	C₂²	1	1	yes	characteristic
168	#1872	C₂²	1	1	yes	characteristic
169	#1872	C₂²	1	1	yes	characteristic
170	#1865	C₂²	1	1	yes	characteristic, complemented
171	#1864	C₂²	1	1	yes	characteristic
172	#1864	C₂²	1	1	yes	characteristic
173	#1864	C₂²	1	1	yes	characteristic
174	#1864	C₂²	1	1	yes	characteristic
175	#1864	C₂²	1	1	yes	characteristic
176	#1864	C₂²	1	1	yes	characteristic
177	#1863	C₂²	1	1	yes	characteristic, complemented
178	#1862	C₂²	1	1	yes	characteristic
179	#1862	C₂²	1	1	yes	characteristic
180	#1862	C₂²	1	1	yes	characteristic
181	#1862	C₂²	1	1	yes	characteristic
182	#1854	C₂²	1	1	yes	characteristic
183	#1854	C₂²	1	1	yes	characteristic
184	#1851	C₂²	1	1	yes	characteristic
185	#1851	C₂²	1	1	yes	characteristic
186	#1835	C₂²	1	1	yes	characteristic, complemented
187	#1834	C₂²	1	1	yes	characteristic, complemented
188	#1825	C₂²	1	1	yes	characteristic
189	#1825	C₂²	1	1	yes	characteristic
190	#1804	C₂²	1	1	yes	characteristic
191	#1804	C₂²	1	1	yes	characteristic
192	#1802	C₂²	1	1	yes	characteristic
193	#1802	C₂²	1	1	yes	characteristic
194	#1802	C₂²	1	1	yes	characteristic
195	#1802	C₂²	1	1	yes	characteristic
196	#1797	C₂²	1	1	yes	characteristic
197	C₄×#102	C₂²	1	1	yes	characteristic
198	C₄×#102	C₂²	1	1	yes	characteristic
199	#1753	C₂²	1	1	yes	characteristic
200	#1753	C₂²	1	1	yes	characteristic
201	#1736	C₂²	1	1	yes	characteristic
202	#1728	C₂²	1	1	yes	characteristic
203	C₂³×D₄	C₂³	1	1	yes	characteristic
204	C₂⁴×C₄	—	2	1	no	—
205	C₂²×SD₁₆	C₂³	1	1	yes	characteristic
206	C₂²×SD₁₆	C₂³	1	1	yes	characteristic
207	C₂²×SD₁₆	C₂³	1	1	yes	characteristic
208	C₂²×SD₁₆	C₂³	1	1	yes	characteristic
209	C₂²×M₁₆	C₂³	1	1	yes	characteristic
210	C₂²×M₁₆	C₂³	1	1	yes	characteristic
211	#554	—	4	2	no	—
212	#554	—	4	2	no	—
213	C₂×C₄⋊Q₈	C₂³	1	1	yes	characteristic
214	C₂×C₄⋊Q₈	C₂³	1	1	yes	characteristic
215	C₂×#125	—	2	1	no	—
216	C₂×#125	C₂³	1	1	yes	characteristic
217	C₂×#125	C₂³	1	1	yes	characteristic
218	C₂×C₂²⋊Q₈	—	2	1	no	—
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	D₄	1	1	yes	characteristic
224	C₂×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
225	C₂×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
226	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
227	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
228	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
229	C₂×C₄×D₄	—	2	1	no	—
230	C₂×C₄×D₄	—	2	1	no	—
231	C₂×C₄×D₄	—	4	2	no	—
232	C₂×C₄×D₄	—	4	2	no	—
233	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
234	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
235	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
236	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
237	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
238	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
239	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
240	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
241	C₂×#117	C₂³	1	1	yes	characteristic
242	C₂×#117	C₂³	1	1	yes	characteristic
243	C₂²×C₄⋊C₄	—	2	1	no	—
244	C₂²×C₄⋊C₄	—	2	1	no	—
245	C₂²×C₄⋊C₄	C₂³	1	1	yes	characteristic
246	C₂²×C₂²⋊C₄	—	2	1	no	—
247	C₂²×C₂²⋊C₄	—	2	1	no	—
248	C₂²×C₂²⋊C₄	—	2	1	no	—
249	C₂²×C₄²	C₂³	1	1	yes	characteristic
250	#479	—	4	2	no	—
251	#475	—	4	2	no	—
252	#461	—	4	2	no	—
253	#461	—	4	2	no	—
254	#450	—	2	4	no	—
255	#450	—	2	4	no	—
256	#440	—	4	2	no	—
257	#440	—	4	2	no	—
258	#428	—	4	2	no	—
259	C₂×#107	C₂³	1	1	yes	characteristic
260	C₂×#107	C₂³	1	1	yes	characteristic
261	C₂×#107	C₂³	1	1	yes	characteristic
262	C₂×#107	C₂³	1	1	yes	characteristic
263	C₂×#106	C₂³	1	1	yes	characteristic
264	C₂×#106	C₂³	1	1	yes	characteristic
265	C₂×#106	C₂³	1	1	yes	characteristic
266	C₂×#106	C₂³	1	1	yes	characteristic
267	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
268	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
269	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
270	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
271	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
272	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
273	#418	—	2	4	no	—
274	#418	—	4	2	no	—
275	C₂×#103	C₂³	1	1	yes	characteristic
276	C₂×#103	C₂³	1	1	yes	characteristic
277	C₂×#103	C₂³	1	1	yes	characteristic
278	C₂×#103	C₂³	1	1	yes	characteristic
279	C₂×#103	C₂³	1	1	yes	characteristic
280	C₂×#103	C₂³	1	1	yes	characteristic
281	C₂×#103	C₂³	1	1	yes	characteristic
282	C₂×#103	C₂³	1	1	yes	characteristic
283	C₂×#103	C₂³	1	1	yes	characteristic
284	C₂×#103	C₂³	1	1	yes	characteristic
285	C₂×#103	C₂³	1	1	yes	characteristic
286	C₂×#103	C₂³	1	1	yes	characteristic
287	C₂×#102	C₂³	1	1	yes	characteristic
288	C₂×#102	C₂³	1	1	yes	characteristic
289	C₂×#102	C₂³	1	1	yes	characteristic
290	C₂×#102	C₂³	1	1	yes	characteristic
291	C₂×#102	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×C₂²⋊C₈	C₂³	1	1	yes	characteristic
300	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
301	C₂×#97	C₂³	1	1	yes	characteristic
302	C₂×#97	C₂³	1	1	yes	characteristic
303	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
304	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
305	#401	—	2	1	no	—
306	#400	—	2	1	no	—
307	#400	—	2	1	no	—
308	#400	—	2	1	no	—
309	#400	—	2	1	no	—
310	#400	—	2	1	no	—
311	#400	—	2	1	no	—
312	#400	—	2	1	no	—
313	#400	—	2	1	no	—
314	#399	—	2	1	no	—
315	#399	—	2	1	no	—
316	#398	—	2	1	no	—
317	#398	—	2	1	no	—
318	#398	—	2	1	no	—
319	#398	—	2	1	no	—
320	#398	—	2	1	no	—
321	#398	—	2	1	no	—
322	#398	—	2	1	no	—
323	#398	—	2	1	no	—
324	#398	—	2	1	no	—
325	#397	—	2	1	no	—
326	#397	—	2	1	no	—
327	#397	—	2	1	no	—
328	#397	—	2	1	no	—
329	#396	—	2	1	no	—
330	#396	—	2	1	no	—
331	#396	—	2	1	no	—
332	#396	—	2	1	no	—
333	#395	—	2	1	no	—
334	#395	—	2	1	no	—
335	#393	—	2	1	no	—
336	#393	—	2	1	no	—
337	#391	—	2	1	no	—
338	#391	D₄	1	1	yes	characteristic
339	#391	C₂³	1	1	yes	characteristic
340	#391	C₂³	1	1	yes	characteristic
341	#391	C₂³	1	1	yes	characteristic
342	#391	C₂³	1	1	yes	characteristic
343	#391	C₂³	1	1	yes	characteristic
344	#391	C₂³	1	1	yes	characteristic
345	#391	C₂³	1	1	yes	characteristic
346	#391	C₂³	1	1	yes	characteristic
347	#390	C₂³	1	1	yes	characteristic
348	#390	C₂³	1	1	yes	characteristic
349	#390	C₂³	1	1	yes	characteristic
350	#390	C₂³	1	1	yes	characteristic
351	#389	—	2	1	no	—
352	#389	—	2	1	no	—
353	#389	—	2	1	no	—
354	#389	—	2	1	no	—
355	#389	D₄	1	1	yes	characteristic
356	#389	C₂³	1	1	yes	characteristic
357	#389	C₂³	1	1	yes	characteristic
358	#389	C₂³	1	1	yes	characteristic
359	#389	C₂³	1	1	yes	characteristic
360	#389	C₂³	1	1	yes	characteristic
361	#389	C₂³	1	1	yes	characteristic
362	#389	C₂³	1	1	yes	characteristic
363	#389	C₂³	1	1	yes	characteristic
364	#389	C₂³	1	1	yes	characteristic
365	#389	C₂³	1	1	yes	characteristic
366	#389	C₂³	1	1	yes	characteristic
367	#389	C₂³	1	1	yes	characteristic
368	#388	—	2	1	no	—
369	#388	—	2	1	no	—
370	#388	—	2	1	no	—
371	#388	—	2	1	no	—
372	#387	—	2	1	no	—
373	#387	—	2	1	no	—
374	#387	—	2	1	no	—
375	#387	—	2	1	no	—
376	#387	—	2	1	no	—
377	#387	—	2	1	no	—
378	#387	—	2	1	no	—
379	#387	—	2	1	no	—
380	#387	—	2	1	no	—
381	#387	—	2	1	no	—
382	#387	—	2	1	no	—
383	#387	—	2	1	no	—
384	#387	—	2	1	no	—
385	#387	—	2	1	no	—
386	#387	—	2	1	no	—
387	#387	—	2	1	no	—
388	#387	—	2	1	no	—
389	#387	—	2	1	no	—
390	#387	—	2	1	no	—
391	#387	D₄	1	1	yes	characteristic
392	#387	D₄	1	1	yes	characteristic
393	#386	—	2	1	no	—
394	#386	—	2	1	no	—
395	#386	—	2	1	no	—
396	#386	—	2	1	no	—
397	#385	—	2	1	no	—
398	#385	—	2	1	no	—
399	#385	—	2	1	no	—
400	#385	—	2	1	no	—
401	#385	—	2	1	no	—
402	#385	—	2	1	no	—
403	#385	—	2	1	no	—
404	#385	—	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	C₂³	1	1	yes	characteristic
418	#384	C₂³	1	1	yes	characteristic
419	#384	C₂³	1	1	yes	characteristic
420	#384	C₂³	1	1	yes	characteristic
421	#383	—	2	1	no	—
422	#382	C₂³	1	1	yes	characteristic
423	#382	C₂³	1	1	yes	characteristic
424	#382	C₂³	1	1	yes	characteristic
425	#382	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
433	#380	D₄	1	1	yes	characteristic
434	#380	C₂³	1	1	yes	characteristic
435	#380	C₂³	1	1	yes	characteristic
436	#379	—	2	1	no	—
437	#379	—	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×C₂²⋊C₄	C₂³	1	1	yes	characteristic
448	C₄×C₂²⋊C₄	C₂³	1	1	yes	characteristic
449	C₂×#95	—	2	1	no	—
450	C₂×#95	—	2	1	no	—
451	#340	C₂³	1	1	yes	characteristic
452	#340	C₂³	1	1	yes	characteristic
453	#340	C₂³	1	1	yes	characteristic
454	#340	C₂³	1	1	yes	characteristic
455	#340	C₂³	1	1	yes	characteristic
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	#336	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	C₂⁵	—	2	1	no	—
494	C₂²×Q₈	—	2	1	no	—
495	C₂²×Q₈	C₂×D₄	1	1	yes	characteristic
496	C₂²×Q₈	C₂⁴	1	1	yes	characteristic
497	C₂²×Q₈	C₂⁴	1	1	yes	characteristic
498	C₂²×D₄	—	2	2	no	—
499	C₂²×D₄	—	2	2	no	—
500	C₂²×D₄	—	2	1	no	—
501	C₂²×D₄	—	2	2	no	—
502	C₂²×D₄	—	4	1	no	—
503	C₂²×D₄	—	4	1	no	—
504	C₂²×D₄	#41	1	4	yes	—
505	C₂²×D₄	C₂⁴	1	1	yes	characteristic
506	C₂²×D₄	C₂⁴	1	1	yes	characteristic
507	C₂³×C₄	—	2	1	no	—
508	C₂³×C₄	—	2	1	no	—
509	C₂³×C₄	—	2	1	no	—
510	C₂³×C₄	—	2	1	no	—
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	—	4	4	no	—
517	C₂³×C₄	—	8	2	no	—
518	C₂³×C₄	—	8	2	no	—
519	C₂³×C₄	C₂×D₄	1	1	yes	characteristic
520	C₂³×C₄	C₂×D₄	1	1	yes	characteristic
521	C₂³×C₄	C₂⁴	1	1	yes	characteristic
522	C₂×SD₁₆	—	2	2	no	—
523	C₂×SD₁₆	—	2	2	no	—
524	C₂×SD₁₆	—	2	2	no	—
525	C₂×SD₁₆	—	2	2	no	—
526	C₂×SD₁₆	—	2	2	no	—
527	C₂×SD₁₆	—	2	2	no	—
528	C₂×SD₁₆	—	2	2	no	—
529	C₂×SD₁₆	—	2	2	no	—
530	C₂×SD₁₆	—	4	1	no	—
531	C₂×SD₁₆	—	4	1	no	—
532	C₂×SD₁₆	—	4	1	no	—
533	C₂×SD₁₆	—	4	1	no	—
534	C₂×M₁₆	—	2	2	no	—
535	C₂×M₁₆	—	2	2	no	—
536	C₂×M₁₆	—	4	1	no	—
537	C₂×M₁₆	—	4	1	no	—
538	C₂×M₁₆	—	4	1	no	—
539	C₂×M₁₆	—	4	1	no	—
540	C₂²×C₈	C₂⁴	1	1	yes	characteristic
541	C₂²×C₈	C₂⁴	1	1	yes	characteristic
542	C₂²×C₈	C₂⁴	1	1	yes	characteristic
543	C₂²×C₈	C₂⁴	1	1	yes	characteristic
544	C₂²×C₈	C₂⁴	1	1	yes	characteristic
545	C₂²×C₈	C₂⁴	1	1	yes	characteristic
546	C₂²×C₈	C₂⁴	1	1	yes	characteristic
547	C₂²×C₈	C₂⁴	1	1	yes	characteristic
548	C₄⋊Q₈	—	2	2	no	—
549	C₄⋊Q₈	—	4	1	no	—
550	C₄⋊Q₈	—	4	1	no	—
551	C₄⋊Q₈	—	4	1	no	—
552	#125	—	2	2	no	—
553	#125	—	4	1	no	—
554	#125	—	4	1	no	—
555	#125	—	4	1	no	—
556	#125	—	4	4	no	—
557	C₂²⋊Q₈	—	2	2	no	—
558	C₂²⋊Q₈	—	2	2	no	—
559	C₂²⋊Q₈	—	2	2	no	—
560	C₂²⋊Q₈	—	2	2	no	—
561	C₂²⋊Q₈	—	4	2	no	—
562	C₂²⋊Q₈	—	4	4	no	—
563	C₂²⋊Q₈	—	4	4	no	—
564	C₂²⋊Q₈	—	4	4	no	—
565	C₂²⋊Q₈	—	8	2	no	—
566	C₂²⋊Q₈	—	8	2	no	—
567	C₄×Q₈	—	4	1	no	—
568	C₄×Q₈	—	4	1	no	—
569	C₄×Q₈	—	4	1	no	—
570	C₄×Q₈	—	4	1	no	—
571	C₄×Q₈	—	4	1	no	—
572	C₄×Q₈	—	4	1	no	—
573	C₄×D₄	—	2	2	no	—
574	C₄×D₄	—	2	2	no	—
575	C₄×D₄	—	2	2	no	—
576	C₄×D₄	—	2	2	no	—
577	C₄×D₄	—	2	2	no	—
578	C₄×D₄	—	2	2	no	—
579	C₄×D₄	—	2	2	no	—
580	C₄×D₄	—	2	2	no	—
581	C₄×D₄	—	4	1	no	—
582	C₄×D₄	—	4	1	no	—
583	C₄×D₄	—	4	1	no	—
584	C₄×D₄	—	4	1	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	—	4	4	no	—
591	#117	—	2	2	no	—
592	#117	—	2	2	no	—
593	#117	—	4	1	no	—
594	#117	—	4	1	no	—
595	C₂×C₄⋊C₄	—	2	2	no	—
596	C₂×C₄⋊C₄	—	2	1	no	—
597	C₂×C₄⋊C₄	—	2	1	no	—
598	C₂×C₄⋊C₄	—	2	1	no	—
599	C₂×C₄⋊C₄	—	2	1	no	—
600	C₂×C₄⋊C₄	—	2	1	no	—
601	C₂×C₄⋊C₄	—	2	1	no	—
602	C₂×C₄⋊C₄	—	2	1	no	—
603	C₂×C₄⋊C₄	—	2	1	no	—
604	C₂×C₄⋊C₄	—	2	1	no	—
605	C₂×C₄⋊C₄	—	2	1	no	—
606	C₂×C₄⋊C₄	—	2	1	no	—
607	C₂×C₄⋊C₄	—	2	1	no	—
608	C₂×C₄⋊C₄	—	2	1	no	—
609	C₂×C₄⋊C₄	—	2	1	no	—
610	C₂×C₄⋊C₄	—	2	1	no	—
611	C₂×C₄⋊C₄	—	2	1	no	—
612	C₂×C₄⋊C₄	—	2	1	no	—
613	C₂×C₄⋊C₄	—	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	—	4	1	no	—
629	C₂×C₄⋊C₄	—	4	4	no	—
630	C₂×C₄⋊C₄	—	8	2	no	—
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	C₂×D₄	1	1	yes	characteristic
638	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
639	C₂×C₄⋊C₄	C₂×D₄	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×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
651	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
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	—	4	4	no	—
675	C₂×C₂²⋊C₄	—	4	4	no	—
676	C₂×C₂²⋊C₄	—	8	2	no	—
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×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
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	—	4	1	no	—
688	C₂×C₄²	—	4	1	no	—
689	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
690	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
691	C₂×C₄²	C₂⁴	1	1	yes	characteristic
692	C₂×C₄²	C₂⁴	1	1	yes	characteristic
693	C₂×C₄²	C₂⁴	1	1	yes	characteristic
694	C₂×C₄²	C₂⁴	1	1	yes	characteristic
695	C₂×C₄²	C₂⁴	1	1	yes	characteristic
696	C₂×C₄²	C₂⁴	1	1	yes	characteristic
697	#107	—	2	2	no	—
698	#107	—	4	1	no	—
699	#107	—	4	1	no	—
700	#107	—	4	1	no	—
701	#106	—	2	2	no	—
702	#106	—	4	1	no	—
703	#106	—	4	1	no	—
704	#106	—	4	1	no	—
705	C₄⋊C₈	—	4	1	no	—
706	C₄⋊C₈	—	4	1	no	—
707	C₄⋊C₈	—	4	1	no	—
708	C₄⋊C₈	—	4	1	no	—
709	C₄⋊C₈	—	4	1	no	—
710	C₄⋊C₈	—	4	1	no	—
711	#103	—	2	2	no	—
712	#103	—	2	2	no	—
713	#103	—	4	1	no	—
714	#103	—	4	1	no	—
715	#103	—	4	1	no	—
716	#103	—	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	#102	—	2	2	no	—
724	#102	—	2	2	no	—
725	#102	—	2	2	no	—
726	#102	—	2	2	no	—
727	#102	—	2	2	no	—
728	#102	—	2	2	no	—
729	#102	—	2	2	no	—
730	#102	—	2	2	no	—
731	#102	—	2	2	no	—
732	#102	—	2	2	no	—
733	#102	—	4	1	no	—
734	#102	—	4	1	no	—
735	C₂²⋊C₈	—	2	2	no	—
736	C₂²⋊C₈	—	2	2	no	—
737	#97	—	4	1	no	—
738	#97	—	4	1	no	—
739	C₄×C₈	—	4	1	no	—
740	C₄×C₈	—	4	1	no	—
741	#95	—	2	1	no	—
742	#95	—	2	1	no	—
743	#95	—	2	1	no	—
744	#95	—	2	1	no	—
745	#95	—	2	1	no	—
746	#95	—	2	1	no	—
747	#95	—	2	1	no	—
748	#95	—	2	1	no	—
749	#95	—	2	1	no	—
750	#95	—	2	1	no	—
751	#95	—	2	1	no	—
752	#95	—	2	1	no	—
753	#95	—	2	1	no	—
754	#95	—	2	1	no	—
755	#95	—	2	1	no	—
756	#95	—	2	1	no	—
757	#95	—	2	1	no	—
758	#95	—	2	1	no	—
759	#95	—	2	1	no	—
760	#95	—	2	1	no	—
761	#95	—	2	1	no	—
762	#95	—	2	1	no	—
763	#95	—	2	1	no	—
764	#95	—	2	1	no	—
765	#95	—	2	1	no	—
766	#95	—	2	1	no	—
767	#95	—	2	1	no	—
768	#95	—	2	1	no	—
769	#95	—	2	1	no	—
770	#95	—	2	1	no	—
771	#95	—	2	1	no	—
772	#95	—	2	1	no	—
773	#95	—	2	1	no	—
774	#95	—	2	1	no	—
775	#95	—	2	1	no	—
776	#95	—	2	1	no	—
777	#95	—	2	1	no	—
778	#95	—	2	1	no	—
779	#95	—	2	1	no	—
780	#95	—	2	1	no	—
781	#95	C₂×D₄	1	1	yes	characteristic
782	#95	C₂×D₄	1	1	yes	characteristic
783	#95	C₂×D₄	1	1	yes	characteristic
784	#95	C₂×D₄	1	1	yes	characteristic
785	#95	C₂×D₄	1	1	yes	characteristic
786	#95	C₂×D₄	1	1	yes	characteristic
787	#95	C₂×D₄	1	1	yes	characteristic
788	#95	C₂×D₄	1	1	yes	characteristic
789	#95	C₂×D₄	1	1	yes	characteristic
790	#95	C₂×D₄	1	1	yes	characteristic
791	C₂⁴	—	2	1	no	—
792	C₂⁴	—	2	1	no	—
793	C₂⁴	—	2	4	no	—
794	C₂⁴	—	4	2	no	—
795	C₂⁴	—	4	2	no	—
796	C₂⁴	—	4	2	no	—
797	C₂⁴	—	4	2	no	—
798	C₂⁴	—	8	1	no	—
799	C₂⁴	—	8	1	no	—
800	C₂⁴	C₂²×D₄	1	1	yes	characteristic
801	C₂×Q₈	—	2	1	no	—
802	C₂×Q₈	—	2	1	no	—
803	C₂×Q₈	—	2	1	no	—
804	C₂×Q₈	—	2	1	no	—
805	C₂×Q₈	—	2	1	no	—
806	C₂×Q₈	—	2	1	no	—
807	C₂×Q₈	—	2	1	no	—
808	C₂×Q₈	—	2	1	no	—
809	C₂×Q₈	—	2	1	no	—
810	C₂×Q₈	—	2	1	no	—
811	C₂×Q₈	—	2	1	no	—
812	C₂×Q₈	—	2	1	no	—
813	C₂×Q₈	—	4	1	no	—
814	C₂×Q₈	—	4	1	no	—
815	C₂×Q₈	—	4	1	no	—
816	C₂×Q₈	—	4	2	no	—
817	C₂×Q₈	—	8	1	no	—
818	C₂×Q₈	—	8	1	no	—
819	C₂×D₄	—	2	8	no	—
820	C₂×D₄	—	2	4	no	—
821	C₂×D₄	—	2	1	no	—
822	C₂×D₄	—	2	1	no	—
823	C₂×D₄	—	2	1	no	—
824	C₂×D₄	—	2	1	no	—
825	C₂×D₄	—	2	1	no	—
826	C₂×D₄	—	2	1	no	—
827	C₂×D₄	—	2	1	no	—
828	C₂×D₄	—	2	1	no	—
829	C₂×D₄	—	4	4	no	—
830	C₂×D₄	—	4	4	no	—
831	C₂×D₄	—	4	4	no	—
832	C₂×D₄	—	4	2	no	—
833	C₂×D₄	—	4	2	no	—
834	C₂×D₄	C₂×#41	1	2	yes	—
835	C₂×D₄	C₂×#41	1	2	yes	—
836	C₂×D₄	H(5,𝔽₂)	1	2	yes	—
837	C₂×D₄	2₋¹⁺⁴	1	2	yes	—
838	C₂²×C₄	—	2	1	no	—
839	C₂²×C₄	—	2	1	no	—
840	C₂²×C₄	—	2	1	no	—
841	C₂²×C₄	—	2	1	no	—
842	C₂²×C₄	—	2	1	no	—
843	C₂²×C₄	—	2	4	no	—
844	C₂²×C₄	—	2	2	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	1	no	—
852	C₂²×C₄	—	2	1	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	—	4	1	no	—
859	C₂²×C₄	—	4	1	no	—
860	C₂²×C₄	—	4	1	no	—
861	C₂²×C₄	—	4	1	no	—
862	C₂²×C₄	—	4	1	no	—
863	C₂²×C₄	—	4	2	no	—
864	C₂²×C₄	—	4	2	no	—
865	C₂²×C₄	—	4	2	no	—
866	C₂²×C₄	—	4	2	no	—
867	C₂²×C₄	—	4	2	no	—
868	C₂²×C₄	—	4	2	no	—
869	C₂²×C₄	—	4	2	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	—	8	1	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	—	8	1	no	—
886	C₂²×C₄	—	8	1	no	—
887	C₂²×C₄	—	8	1	no	—
888	C₂²×C₄	—	8	1	no	—
889	C₂²×C₄	—	8	16	no	—
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×D₄	1	1	yes	characteristic
899	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
900	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
901	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
902	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
903	C₂²×C₄	C₂×#41	1	2	yes	—
904	C₂²×C₄	2₋¹⁺⁴	1	2	yes	—
905	C₂²×C₄	C₂⁵	1	1	yes	characteristic
906	SD₁₆	—	4	4	no	—
907	SD₁₆	—	4	4	no	—
908	SD₁₆	—	8	2	no	—
909	SD₁₆	—	8	2	no	—
910	M₁₆	—	4	4	no	—
911	M₁₆	—	8	2	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	—	2	1	no	—
925	C₂×C₈	—	2	1	no	—
926	C₂×C₈	—	2	1	no	—
927	C₂×C₈	—	2	1	no	—
928	C₂×C₈	—	2	1	no	—
929	C₂×C₈	—	2	1	no	—
930	C₂×C₈	—	2	1	no	—
931	C₂×C₈	—	2	1	no	—
932	C₂×C₈	—	2	1	no	—
933	C₂×C₈	—	2	1	no	—
934	C₂×C₈	—	2	1	no	—
935	C₂×C₈	—	2	1	no	—
936	C₄⋊C₄	—	2	2	no	—
937	C₄⋊C₄	—	2	2	no	—
938	C₄⋊C₄	—	2	2	no	—
939	C₄⋊C₄	—	2	2	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	—	2	1	no	—
956	C₄⋊C₄	—	2	1	no	—
957	C₄⋊C₄	—	2	1	no	—
958	C₄⋊C₄	—	2	1	no	—
959	C₄⋊C₄	—	2	1	no	—
960	C₄⋊C₄	—	2	1	no	—
961	C₄⋊C₄	—	2	1	no	—
962	C₄⋊C₄	—	2	1	no	—
963	C₄⋊C₄	—	4	1	no	—
964	C₄⋊C₄	—	4	1	no	—
965	C₄⋊C₄	—	4	1	no	—
966	C₄⋊C₄	—	4	1	no	—
967	C₄⋊C₄	—	4	1	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	—	4	2	no	—
981	C₄⋊C₄	—	4	2	no	—
982	C₄⋊C₄	—	4	2	no	—
983	C₄⋊C₄	—	4	2	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	—	8	1	no	—
992	C₄⋊C₄	—	8	1	no	—
993	C₄⋊C₄	—	8	1	no	—
994	C₄⋊C₄	—	8	1	no	—
995	C₄⋊C₄	—	8	1	no	—
996	C₄⋊C₄	—	8	1	no	—
997	C₄⋊C₄	—	8	1	no	—
998	C₄⋊C₄	—	8	1	no	—
999	C₄⋊C₄	—	8	1	no	—
1000	C₄⋊C₄	H(5,𝔽₂)	1	2	yes	—
1001	C₂²⋊C₄	—	2	4	no	—
1002	C₂²⋊C₄	—	2	2	no	—
1003	C₂²⋊C₄	—	4	1	no	—
1004	C₂²⋊C₄	—	4	1	no	—
1005	C₂²⋊C₄	—	4	1	no	—
1006	C₂²⋊C₄	—	4	2	no	—
1007	C₂²⋊C₄	—	4	2	no	—
1008	C₂²⋊C₄	—	4	2	no	—
1009	C₂²⋊C₄	—	4	2	no	—
1010	C₂²⋊C₄	—	4	2	no	—
1011	C₂²⋊C₄	—	4	2	no	—
1012	C₂²⋊C₄	—	4	2	no	—
1013	C₂²⋊C₄	—	4	2	no	—
1014	C₂²⋊C₄	—	4	2	no	—
1015	C₂²⋊C₄	—	4	2	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	—	8	1	no	—
1021	C₂²⋊C₄	—	8	1	no	—
1022	C₂²⋊C₄	—	8	1	no	—
1023	C₂²⋊C₄	—	8	1	no	—
1024	C₂²⋊C₄	—	8	1	no	—
1025	C₂²⋊C₄	—	8	1	no	—
1026	C₂²⋊C₄	—	8	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	—	2	1	no	—
1038	C₄²	—	2	1	no	—
1039	C₄²	—	4	1	no	—
1040	C₄²	—	4	1	no	—
1041	C₄²	—	4	2	no	—
1042	C₄²	—	4	2	no	—
1043	C₄²	—	8	1	no	—
1044	C₄²	—	8	1	no	—
1045	C₄²	—	8	1	no	—
1046	C₄²	—	8	1	no	—
1047	C₂³	—	2	1	no	—
1048	C₂³	—	2	1	no	—
1049	C₂³	—	2	2	no	—
1050	C₂³	—	2	2	no	—
1051	C₂³	—	2	1	no	—
1052	C₂³	—	2	2	no	—
1053	C₂³	—	2	1	no	—
1054	C₂³	—	2	1	no	—
1055	C₂³	—	2	1	no	—
1056	C₂³	—	2	2	no	—
1057	C₂³	—	4	8	no	—
1058	C₂³	—	4	8	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	—	8	4	no	—
1070	C₂³	—	8	4	no	—
1071	C₂³	—	8	4	no	—
1072	C₂³	—	8	4	no	—
1073	C₂³	—	8	4	no	—
1074	C₂³	#548	1	2	yes	—
1075	C₂³	C₂³×D₄	1	1	yes	characteristic
1076	Q₈	—	4	1	no	—
1077	Q₈	—	4	1	no	—
1078	Q₈	—	4	1	no	—
1079	Q₈	—	4	1	no	—
1080	Q₈	—	4	1	no	—
1081	Q₈	—	4	1	no	—
1082	Q₈	—	4	1	no	—
1083	Q₈	—	4	1	no	—
1084	Q₈	—	8	2	no	—
1085	Q₈	—	16	2	no	—
1086	D₄	—	2	2	no	—
1087	D₄	—	2	2	no	—
1088	D₄	—	2	2	no	—
1089	D₄	—	2	2	no	—
1090	D₄	—	2	2	no	—
1091	D₄	—	4	8	no	—
1092	D₄	—	4	1	no	—
1093	D₄	—	4	1	no	—
1094	D₄	#539	1	4	yes	—
1095	C₂×C₄	—	2	1	no	—
1096	C₂×C₄	—	2	1	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	1	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	1	no	—
1123	C₂×C₄	—	2	2	no	—
1124	C₂×C₄	—	2	1	no	—
1125	C₂×C₄	—	2	1	no	—
1126	C₂×C₄	—	2	1	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	—	4	4	no	—
1137	C₂×C₄	—	4	1	no	—
1138	C₂×C₄	—	4	1	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	—	4	1	no	—
1176	C₂×C₄	—	4	1	no	—
1177	C₂×C₄	—	4	1	no	—
1178	C₂×C₄	—	8	4	no	—
1179	C₂×C₄	—	8	4	no	—
1180	C₂×C₄	—	8	4	no	—
1181	C₂×C₄	—	8	4	no	—
1182	C₂×C₄	—	8	2	no	—
1183	C₂×C₄	—	8	4	no	—
1184	C₂×C₄	—	8	4	no	—
1185	C₂×C₄	—	8	4	no	—
1186	C₂×C₄	—	16	2	no	—
1187	C₂×C₄	—	16	2	no	—
1188	C₂×C₄	#548	1	2	yes	—
1189	C₂×C₄	#575	1	2	yes	—
1190	C₂×C₄	#577	1	2	yes	—
1191	C₂×C₄	C₂²×#41	1	1	yes	characteristic
1192	C₂×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
1193	C₂×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
1194	C₂×C₄	C₂×2₋¹⁺⁴	1	1	yes	characteristic
1195	C₂×C₄	C₂×2₋¹⁺⁴	1	1	yes	characteristic
1196	C₂×C₄	#585	1	1	yes	characteristic
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	C₈	—	4	1	no	—
1205	C₂²	—	2	2	no	—
1206	C₂²	—	2	4	no	—
1207	C₂²	—	2	2	no	—
1208	C₂²	—	2	2	no	—
1209	C₂²	—	4	2	no	—
1210	C₂²	—	4	1	no	—
1211	C₂²	—	4	2	no	—
1212	C₂²	—	4	1	no	—
1213	C₂²	—	4	2	no	—
1214	C₂²	—	4	2	no	—
1215	C₂²	—	4	1	no	—
1216	C₂²	—	4	2	no	—
1217	C₂²	—	4	2	no	—
1218	C₂²	—	4	1	no	—
1219	C₂²	—	4	2	no	—
1220	C₂²	—	4	2	no	—
1221	C₂²	—	4	2	no	—
1222	C₂²	—	8	16	no	—
1223	C₂²	—	8	1	no	—
1224	C₂²	—	8	1	no	—
1225	C₂²	—	8	1	no	—
1226	C₂²	—	8	1	no	—
1227	C₂²	C₂×#548	1	1	yes	characteristic
1228	C₂²	#3484	1	1	yes	characteristic
1229	C₂²	#3489	1	1	yes	characteristic
1230	C₂²	C₂×#575	1	1	yes	characteristic
1231	C₂²	C₂×#577	1	1	yes	characteristic
1232	C₂²	#3585	1	1	yes	characteristic
1233	C₂²	#3586	1	1	yes	characteristic
1234	C₄	—	2	2	no	—
1235	C₄	—	2	2	no	—
1236	C₄	—	2	2	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	1	no	—
1243	C₄	—	4	1	no	—
1244	C₄	—	4	1	no	—
1245	C₄	—	4	1	no	—
1246	C₄	—	4	2	no	—
1247	C₄	—	4	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	—	8	1	no	—
1255	C₄	—	8	1	no	—
1256	C₄	—	8	1	no	—
1257	C₄	—	8	1	no	—
1258	C₄	—	8	1	no	—
1259	C₄	—	8	1	no	—
1260	C₄	—	8	1	no	—
1261	C₄	C₂×#539	1	1	yes	characteristic
1262	C₄	#3505	1	1	yes	characteristic
1263	C₄	#3535	1	1	yes	characteristic
1264	C₄	#3538	1	1	yes	characteristic
1265	C₂	—	4	2	no	—
1266	C₂	—	4	4	no	—
1267	C₂	—	8	2	no	—
1268	C₂	#37702	1	1	yes	characteristic
1269	C₂	#61318	1	1	yes	characteristic
1270	C₂	#61340	1	1	yes	characteristic
1271	C₂	#61589	1	1	yes	characteristic
1272	C₂	#61610	1	1	yes	characteristic
1273	C₂	#62126	1	1	yes	characteristic
1274	C₂	#62232	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³	C₂³×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁵
prime radical	C₂³×D₄	C₂³
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³ ◁ C₄×C₂²⋊Q₈ ◁ G
LECS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #40028	C₂	semidirect
4. #32560	C₂	semidirect
5. #32555	C₂	semidirect
6. #32438	C₂	semidirect
7. #32433	C₂	semidirect
8. #31478	C₂	semidirect
9. #31470	C₂	semidirect
10. #31159	C₂	semidirect
11. #31157	C₂	semidirect
12. #30202	C₂	semidirect
13. #29974	C₂	semidirect
14. #27708	C₂	semidirect
15. #27706	C₂	semidirect
16. #27565	C₂	semidirect
17. #27558	C₂	semidirect
18. #26365	C₂	semidirect
19. #26353	C₂	semidirect
20. #26186	C₂	semidirect
21. #26182	C₂	semidirect
22. #26117	C₂	semidirect
23. #26110	C₂	semidirect
26. #24349	C₂	semidirect
27. #24343	C₂	semidirect
30. #22297	C₂	semidirect
34. C₂×#479	C₂²	semidirect
35. C₂×#475	C₂²	semidirect
55. #2582	C₂²	semidirect
56. #2581	C₂²	semidirect
59. #2570	C₂²	semidirect
62. #2552	C₂²	semidirect
63. #2514	C₂²	semidirect
64. #2511	C₂²	semidirect
71. #2446	C₂²	semidirect
72. #2446	C₂²	semidirect
88. #2101	C₂²	semidirect
89. #2101	C₂²	semidirect
90. #2101	C₂²	semidirect
91. #2101	C₂²	semidirect
92. #2100	C₂²	semidirect
93. #2100	C₂²	semidirect
94. #2100	C₂²	semidirect
95. #2099	C₂²	semidirect
96. #2097	C₂²	semidirect
97. #2095	C₂²	semidirect
98. #2088	C₂²	semidirect
99. #2088	C₂²	semidirect
100. #2088	C₂²	semidirect
101. #2087	C₂²	semidirect
102. #2086	C₂²	semidirect
103. #2086	C₂²	semidirect
104. #2074	C₂²	semidirect
105. #2074	C₂²	semidirect
106. #2074	C₂²	semidirect
109. #2072	C₂²	semidirect
112. #2068	C₂²	semidirect
113. #2066	C₂²	semidirect
114. #2059	C₂²	semidirect
115. #2059	C₂²	semidirect
116. #2059	C₂²	semidirect
117. #2057	C₂²	semidirect
122. #2043	C₂²	semidirect
123. #2043	C₂²	semidirect
124. #2026	C₂²	semidirect
125. #2026	C₂²	semidirect
126. #2026	C₂²	semidirect
127. #2024	C₂²	semidirect
128. #1993	C₂²	semidirect
129. #1992	C₂²	semidirect
130. #1985	C₂²	semidirect
131. #1985	C₂²	semidirect
134. #1949	C₂²	semidirect
135. #1948	C₂²	semidirect
136. #1939	C₂²	semidirect
137. #1939	C₂²	semidirect
140. #1935	C₂²	semidirect
141. #1935	C₂²	semidirect
142. #1933	C₂²	semidirect
143. #1933	C₂²	semidirect
146. #1921	C₂²	semidirect
147. #1920	C₂²	semidirect
148. #1917	C₂²	semidirect
149. #1917	C₂²	semidirect
150. #1916	C₂²	semidirect
151. #1916	C₂²	semidirect
170. #1865	C₂²	semidirect
177. #1863	C₂²	semidirect
186. #1835	C₂²	semidirect
187. #1834	C₂²	semidirect

Maximal subgroups

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

subgroup	index
#40028	2
#36215	2
#32905	2
#32560	2
#32555	2
#32438	2
#32433	2
#31478	2
#31470	2
#31159	2
#31157	2
#30202	2
#29974	2
#27708	2
#27706	2
#27565	2
#27558	2
#26365	2
#26353	2
#26186	2
#26182	2
#26117	2
#26110	2
#24538	2
#24349	2
#24343	2
#22864	2
#22297	2
#20873	2