Subgroups — #6822346

Order 512.

1408 conjugacy classes of subgroups.

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

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#39527	C₂	1	1	yes	maximal, characteristic, complemented
2	#39024	C₂	1	1	yes	maximal, characteristic
3	#33268	C₂	1	1	yes	maximal, characteristic, complemented
4	#32643	C₂	1	1	yes	maximal, characteristic, complemented
5	#32556	C₂	1	1	yes	maximal, characteristic, complemented
6	#32063	C₂	1	1	yes	maximal, characteristic, complemented
7	#31733	C₂	1	1	yes	maximal, characteristic, complemented
8	#31676	C₂	1	1	yes	maximal, characteristic
9	#31451	C₂	1	1	yes	maximal, characteristic, complemented
10	#31133	C₂	1	1	yes	maximal, characteristic, complemented
11	#31012	C₂	1	1	yes	maximal, characteristic, complemented
12	#30146	C₂	1	1	yes	maximal, characteristic, complemented
13	#30136	C₂	1	1	yes	maximal, characteristic, complemented
14	#29042	C₂	1	1	yes	maximal, characteristic, complemented
15	#28993	C₂	1	1	yes	maximal, characteristic, complemented
16	#28929	C₂	1	1	yes	maximal, characteristic, complemented
17	#28859	C₂	1	1	yes	maximal, characteristic, complemented
18	#27718	C₂	1	1	yes	maximal, characteristic, complemented
19	#27281	C₂	1	1	yes	maximal, characteristic, complemented
20	#27227	C₂	1	1	yes	maximal, characteristic, complemented
21	#27173	C₂	1	1	yes	maximal, characteristic, complemented
22	#27038	C₂	1	1	yes	maximal, characteristic, complemented
23	#26936	C₂	1	1	yes	maximal, characteristic, complemented
24	#25482	C₂	1	1	yes	maximal, characteristic, complemented
25	#25299	C₂	1	1	yes	maximal, characteristic, complemented
26	#25251	C₂	1	1	yes	maximal, characteristic, complemented
27	#25120	C₂	1	1	yes	maximal, characteristic
28	#23131	C₂	1	1	yes	maximal, characteristic, complemented
29	#22584	C₂	1	1	yes	maximal, characteristic, complemented
30	C₄×#489	C₂	1	1	yes	maximal, characteristic, complemented
31	#21632	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×#489	C₂²	1	1	yes	characteristic
33	C₂×#485	C₂²	1	1	yes	characteristic, complemented
34	C₂×#478	C₂²	1	1	yes	characteristic
35	C₂×#465	C₂²	1	1	yes	characteristic
36	C₂×#464	C₂²	1	1	yes	characteristic
37	C₂×#450	C₂²	1	1	yes	characteristic
38	C₂×#446	C₂²	1	1	yes	characteristic, complemented
39	C₂×#435	C₂²	1	1	yes	characteristic
40	C₂×#418	C₂²	1	1	yes	characteristic
41	#2863	C₂²	1	1	yes	characteristic, complemented
42	#2860	C₂²	1	1	yes	characteristic
43	#2800	—	2	1	no	—
44	#2798	—	2	1	no	—
45	#2774	—	2	1	no	—
46	#2756	—	2	1	no	—
47	#2754	—	2	1	no	—
48	#2735	—	2	1	no	—
49	#2702	—	2	1	no	—
50	#2685	—	2	1	no	—
51	#2648	—	2	1	no	—
52	#2632	—	2	1	no	—
53	#2592	C₂²	1	1	yes	characteristic
54	#2584	C₂²	1	1	yes	characteristic, complemented
55	#2581	C₂²	1	1	yes	characteristic, complemented
56	#2538	C₂²	1	1	yes	characteristic
57	#2529	—	2	1	no	—
58	#2525	—	2	1	no	—
59	#2518	—	2	1	no	—
60	#2500	C₂²	1	1	yes	characteristic
61	#2495	C₂²	1	1	yes	characteristic
62	#2495	C₂²	1	1	yes	characteristic, complemented
63	#2492	C₂²	1	1	yes	characteristic, complemented
64	#2489	C₂²	1	1	yes	characteristic
65	#2485	C₂²	1	1	yes	characteristic
66	#2472	—	2	1	no	—
67	#2441	C₂²	1	1	yes	characteristic, complemented
68	#2439	C₂²	1	1	yes	characteristic
69	#2435	C₂²	1	1	yes	characteristic
70	#2427	C₂²	1	1	yes	characteristic
71	#2426	C₂²	1	1	yes	characteristic
72	#2423	C₂²	1	1	yes	characteristic
73	#2423	C₂²	1	1	yes	characteristic
74	#2415	C₂²	1	1	yes	characteristic
75	#2415	C₂²	1	1	yes	characteristic
76	#2408	C₂²	1	1	yes	characteristic
77	#2363	C₂²	1	1	yes	characteristic
78	#2362	C₂²	1	1	yes	characteristic, complemented
79	#2346	C₂²	1	1	yes	characteristic
80	D₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
81	#2320	—	2	1	no	—
82	#2312	—	2	1	no	—
83	C₄×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
84	C₄×#124	C₂²	1	1	yes	characteristic
85	C₄×#124	C₂²	1	1	yes	characteristic
86	#2101	C₂²	1	1	yes	characteristic, complemented
87	#2101	C₂²	1	1	yes	characteristic, complemented
88	#2099	C₂²	1	1	yes	characteristic, complemented
89	#2097	C₂²	1	1	yes	characteristic, complemented
90	#2088	C₂²	1	1	yes	characteristic, complemented
91	#2087	C₂²	1	1	yes	characteristic, complemented
92	#2087	C₂²	1	1	yes	characteristic, complemented
93	#2083	C₂²	1	1	yes	characteristic, complemented
94	#2077	C₂²	1	1	yes	characteristic
95	#2077	C₂²	1	1	yes	characteristic
96	#2075	C₂²	1	1	yes	characteristic
97	#2073	C₂²	1	1	yes	characteristic
98	#2072	C₂²	1	1	yes	characteristic, complemented
99	#2071	C₂²	1	1	yes	characteristic
100	#2068	C₂²	1	1	yes	characteristic, complemented
101	#2067	C₂²	1	1	yes	characteristic
102	#2067	C₂²	1	1	yes	characteristic
103	#2066	C₂²	1	1	yes	characteristic, complemented
104	#2065	C₂²	1	1	yes	characteristic
105	#2065	C₂²	1	1	yes	characteristic
106	#2058	C₂²	1	1	yes	characteristic, complemented
107	#2056	C₂²	1	1	yes	characteristic, complemented
108	#2055	C₂²	1	1	yes	characteristic
109	#2055	C₂²	1	1	yes	characteristic
110	#2042	C₂²	1	1	yes	characteristic
111	#2042	C₂²	1	1	yes	characteristic
112	#2042	C₂²	1	1	yes	characteristic
113	#2036	C₂²	1	1	yes	characteristic
114	#2036	C₂²	1	1	yes	characteristic
115	#2036	C₂²	1	1	yes	characteristic, complemented
116	#2034	C₂²	1	1	yes	characteristic
117	#2033	C₂²	1	1	yes	characteristic
118	#2033	C₂²	1	1	yes	characteristic
119	#2026	C₂²	1	1	yes	characteristic, complemented
120	#2025	C₂²	1	1	yes	characteristic
121	#2023	C₂²	1	1	yes	characteristic
122	#2015	C₂²	1	1	yes	characteristic
123	#2001	C₂²	1	1	yes	characteristic
124	#2001	C₂²	1	1	yes	characteristic, complemented
125	#2000	C₂²	1	1	yes	characteristic
126	#1993	C₂²	1	1	yes	characteristic, complemented
127	#1992	C₂²	1	1	yes	characteristic, complemented
128	#1985	C₂²	1	1	yes	characteristic, complemented
129	#1973	C₂²	1	1	yes	characteristic
130	#1973	C₂²	1	1	yes	characteristic
131	#1971	C₂²	1	1	yes	characteristic, complemented
132	#1968	C₂²	1	1	yes	characteristic
133	#1959	C₂²	1	1	yes	characteristic
134	#1958	C₂²	1	1	yes	characteristic
135	#1955	C₂²	1	1	yes	characteristic
136	#1949	C₂²	1	1	yes	characteristic, complemented
137	#1947	C₂²	1	1	yes	characteristic, complemented
138	#1944	C₂²	1	1	yes	characteristic, complemented
139	#1943	C₂²	1	1	yes	characteristic, complemented
140	#1942	C₂²	1	1	yes	characteristic, complemented
141	#1942	C₂²	1	1	yes	characteristic, complemented
142	#1936	C₂²	1	1	yes	characteristic
143	#1936	C₂²	1	1	yes	characteristic
144	#1936	C₂²	1	1	yes	characteristic
145	#1936	C₂²	1	1	yes	characteristic
146	#1936	C₂²	1	1	yes	characteristic
147	#1935	C₂²	1	1	yes	characteristic, complemented
148	#1935	C₂²	1	1	yes	characteristic, complemented
149	#1935	C₂²	1	1	yes	characteristic, complemented
150	#1935	C₂²	1	1	yes	characteristic, complemented
151	#1934	C₂²	1	1	yes	characteristic
152	#1934	C₂²	1	1	yes	characteristic
153	#1933	C₂²	1	1	yes	characteristic, complemented
154	#1927	C₂²	1	1	yes	characteristic, complemented
155	#1926	C₂²	1	1	yes	characteristic
156	#1925	C₂²	1	1	yes	characteristic
157	#1925	C₂²	1	1	yes	characteristic
158	#1924	C₂²	1	1	yes	characteristic
159	#1924	C₂²	1	1	yes	characteristic, complemented
160	#1923	C₂²	1	1	yes	characteristic
161	#1923	C₂²	1	1	yes	characteristic, complemented
162	#1920	C₂²	1	1	yes	characteristic, complemented
163	#1920	C₂²	1	1	yes	characteristic, complemented
164	#1920	C₂²	1	1	yes	characteristic, complemented
165	#1919	C₂²	1	1	yes	characteristic, complemented
166	#1894	C₂²	1	1	yes	characteristic
167	#1894	C₂²	1	1	yes	characteristic
168	#1893	C₂²	1	1	yes	characteristic
169	#1892	C₂²	1	1	yes	characteristic, complemented
170	#1880	C₂²	1	1	yes	characteristic
171	#1878	C₂²	1	1	yes	characteristic, complemented
172	#1877	C₂²	1	1	yes	characteristic
173	#1877	C₂²	1	1	yes	characteristic
174	#1875	C₂²	1	1	yes	characteristic
175	#1875	C₂²	1	1	yes	characteristic
176	#1873	C₂²	1	1	yes	characteristic
177	#1873	C₂²	1	1	yes	characteristic, complemented
178	#1864	C₂²	1	1	yes	characteristic
179	#1863	C₂²	1	1	yes	characteristic, complemented
180	#1863	C₂²	1	1	yes	characteristic, complemented
181	#1862	C₂²	1	1	yes	characteristic
182	#1854	C₂²	1	1	yes	characteristic
183	#1854	C₂²	1	1	yes	characteristic, complemented
184	#1836	C₂²	1	1	yes	characteristic, complemented
185	#1831	C₂²	1	1	yes	characteristic, complemented
186	#1825	C₂²	1	1	yes	characteristic
187	#1825	C₂²	1	1	yes	characteristic, complemented
188	#1809	C₂²	1	1	yes	characteristic
189	#1786	C₂²	1	1	yes	characteristic
190	#1786	C₂²	1	1	yes	characteristic
191	#1762	C₂²	1	1	yes	characteristic
192	C₄×#103	C₂²	1	1	yes	characteristic, complemented
193	C₄×#103	C₂²	1	1	yes	characteristic, complemented
194	C₄×#103	C₂²	1	1	yes	characteristic, complemented
195	C₄×#102	C₂²	1	1	yes	characteristic
196	C₄×#102	C₂²	1	1	yes	characteristic
197	#1753	C₂²	1	1	yes	characteristic
198	#1753	C₂²	1	1	yes	characteristic
199	#1752	C₂²	1	1	yes	characteristic, complemented
200	C₈×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
201	#1735	C₂²	1	1	yes	characteristic, complemented
202	C₄×#97	C₂²	1	1	yes	characteristic, complemented
203	C₂³×D₄	C₂³	1	1	yes	characteristic
204	C₂²×Q₁₆	C₂³	1	1	yes	characteristic
205	C₂²×SD₁₆	C₂³	1	1	yes	characteristic
206	C₂²×SD₁₆	C₂³	1	1	yes	characteristic
207	C₂²×M₁₆	C₂³	1	1	yes	characteristic
208	C₂³×C₈	C₂³	1	1	yes	characteristic
209	C₂×C₄⋊Q₈	C₂³	1	1	yes	characteristic
210	C₂×#126	—	2	1	no	—
211	C₂×#125	C₂³	1	1	yes	characteristic
212	C₂×#124	D₄	1	1	yes	characteristic
213	C₂×#124	C₂³	1	1	yes	characteristic
214	C₂×#124	C₂³	1	1	yes	characteristic
215	C₂×C₂²⋊Q₈	—	2	1	no	—
216	C₂×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
217	C₂×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
218	C₂×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
219	C₂×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
220	C₂×#121	C₂³	1	1	yes	characteristic
221	C₂×#121	C₂³	1	1	yes	characteristic
222	C₂×#120	—	2	1	no	—
223	C₂×C₄×Q₈	—	2	1	no	—
224	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
225	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
226	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
227	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
228	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
229	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
230	C₂×#117	C₂³	1	1	yes	characteristic
231	C₂×#117	C₂³	1	1	yes	characteristic
232	C₂×#117	C₂³	1	1	yes	characteristic
233	C₂²×C₂²⋊C₄	—	2	1	no	—
234	#489	—	2	4	no	—
235	#485	—	4	2	no	—
236	#478	—	4	2	no	—
237	#465	—	2	4	no	—
238	#464	—	4	2	no	—
239	#450	—	4	2	no	—
240	#446	—	4	2	no	—
241	#435	—	4	2	no	—
242	C₂×#107	C₂³	1	1	yes	characteristic
243	C₂×#107	C₂³	1	1	yes	characteristic
244	C₂×#107	C₂³	1	1	yes	characteristic
245	C₂×#107	C₂³	1	1	yes	characteristic
246	C₂×#107	C₂³	1	1	yes	characteristic
247	C₂×#106	C₂³	1	1	yes	characteristic
248	C₂×#106	C₂³	1	1	yes	characteristic
249	C₂×#106	C₂³	1	1	yes	characteristic
250	C₂×#106	C₂³	1	1	yes	characteristic
251	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
252	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
253	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
254	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
255	#418	—	2	4	no	—
256	C₂×#103	C₂³	1	1	yes	characteristic
257	C₂×#103	C₂³	1	1	yes	characteristic
258	C₂×#103	C₂³	1	1	yes	characteristic
259	C₂×#103	C₂³	1	1	yes	characteristic
260	C₂×#103	C₂³	1	1	yes	characteristic
261	C₂×#103	C₂³	1	1	yes	characteristic
262	C₂×#103	C₂³	1	1	yes	characteristic
263	C₂×#103	C₂³	1	1	yes	characteristic
264	C₂×#103	C₂³	1	1	yes	characteristic
265	C₂×#103	C₂³	1	1	yes	characteristic
266	C₂×#103	C₂³	1	1	yes	characteristic
267	C₂×#103	C₂³	1	1	yes	characteristic
268	C₂×#102	C₂³	1	1	yes	characteristic
269	C₂×#102	C₂³	1	1	yes	characteristic
270	C₂×#102	C₂³	1	1	yes	characteristic
271	C₂×#102	C₂³	1	1	yes	characteristic
272	C₂×#102	C₂³	1	1	yes	characteristic
273	C₂×#102	C₂³	1	1	yes	characteristic
274	C₂×#102	C₂³	1	1	yes	characteristic
275	C₂×#102	C₂³	1	1	yes	characteristic
276	C₂×#102	C₂³	1	1	yes	characteristic
277	C₂×#102	C₂³	1	1	yes	characteristic
278	C₂×#102	C₂³	1	1	yes	characteristic
279	C₂×#102	C₂³	1	1	yes	characteristic
280	C₂×#102	C₂³	1	1	yes	characteristic
281	C₂×#102	C₂³	1	1	yes	characteristic
282	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
283	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
284	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
285	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
286	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
287	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
288	C₂×#97	C₂³	1	1	yes	characteristic
289	C₂×#97	C₂³	1	1	yes	characteristic
290	C₂×#97	C₂³	1	1	yes	characteristic
291	C₂×#97	C₂³	1	1	yes	characteristic
292	C₂×#97	C₂³	1	1	yes	characteristic
293	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
294	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
295	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
296	#400	—	2	1	no	—
297	#400	—	2	1	no	—
298	#400	—	2	1	no	—
299	#400	—	2	1	no	—
300	#400	—	2	1	no	—
301	#399	—	2	1	no	—
302	#399	—	2	1	no	—
303	#399	—	2	1	no	—
304	#398	—	2	1	no	—
305	#398	—	2	1	no	—
306	#398	—	2	1	no	—
307	#397	—	2	1	no	—
308	#397	—	2	1	no	—
309	#397	—	2	1	no	—
310	#397	—	2	1	no	—
311	#397	—	2	1	no	—
312	#397	—	2	1	no	—
313	#397	—	2	1	no	—
314	#397	—	2	1	no	—
315	#396	—	2	1	no	—
316	#396	—	2	1	no	—
317	#396	—	2	1	no	—
318	#396	—	2	1	no	—
319	#396	—	2	1	no	—
320	#395	—	2	1	no	—
321	#395	—	2	1	no	—
322	#394	—	2	1	no	—
323	#394	—	2	1	no	—
324	#394	—	2	1	no	—
325	#394	—	2	1	no	—
326	#394	—	2	1	no	—
327	#394	—	2	1	no	—
328	#394	—	2	1	no	—
329	#394	—	2	1	no	—
330	#394	—	2	1	no	—
331	#394	—	2	1	no	—
332	#393	—	2	1	no	—
333	#393	—	2	1	no	—
334	#393	—	2	1	no	—
335	#392	—	2	1	no	—
336	#391	—	2	1	no	—
337	#391	—	2	1	no	—
338	#391	—	2	1	no	—
339	#391	D₄	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	#390	—	2	1	no	—
347	#390	—	2	1	no	—
348	#390	D₄	1	1	yes	characteristic
349	#390	C₂³	1	1	yes	characteristic
350	#390	C₂³	1	1	yes	characteristic
351	#390	C₂³	1	1	yes	characteristic
352	#390	C₂³	1	1	yes	characteristic
353	#390	C₂³	1	1	yes	characteristic
354	#390	C₂³	1	1	yes	characteristic
355	#389	—	2	1	no	—
356	#389	—	2	1	no	—
357	#389	—	2	1	no	—
358	#389	—	2	1	no	—
359	#389	—	2	1	no	—
360	#389	—	2	1	no	—
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	#389	C₂³	1	1	yes	characteristic
369	#389	C₂³	1	1	yes	characteristic
370	#389	C₂³	1	1	yes	characteristic
371	#389	C₂³	1	1	yes	characteristic
372	#389	C₂³	1	1	yes	characteristic
373	#388	—	2	1	no	—
374	#388	—	2	1	no	—
375	#388	—	2	1	no	—
376	#388	—	2	1	no	—
377	#388	—	2	1	no	—
378	#388	—	2	1	no	—
379	#388	—	2	1	no	—
380	#388	—	2	1	no	—
381	#388	—	2	1	no	—
382	#388	—	2	1	no	—
383	#388	—	2	1	no	—
384	#388	—	2	1	no	—
385	#388	—	2	1	no	—
386	#388	—	2	1	no	—
387	#388	—	2	1	no	—
388	#388	—	2	1	no	—
389	#388	—	2	1	no	—
390	#388	—	2	1	no	—
391	#388	—	2	1	no	—
392	#388	—	2	1	no	—
393	#388	—	2	1	no	—
394	#388	—	2	1	no	—
395	#388	—	2	1	no	—
396	#388	—	2	1	no	—
397	#388	D₄	1	1	yes	characteristic
398	#388	D₄	1	1	yes	characteristic
399	#388	D₄	1	1	yes	characteristic
400	#388	D₄	1	1	yes	characteristic
401	#387	—	2	1	no	—
402	#387	—	2	1	no	—
403	#387	—	2	1	no	—
404	#387	—	2	1	no	—
405	#387	—	2	1	no	—
406	#387	—	2	1	no	—
407	#387	—	2	1	no	—
408	#387	—	2	1	no	—
409	#387	—	2	1	no	—
410	#387	—	2	1	no	—
411	#387	—	2	1	no	—
412	#386	—	2	1	no	—
413	#386	—	2	1	no	—
414	#386	—	2	1	no	—
415	#386	—	2	1	no	—
416	#384	C₂³	1	1	yes	characteristic
417	#384	C₂³	1	1	yes	characteristic
418	#383	—	2	1	no	—
419	#383	—	2	1	no	—
420	#383	—	2	1	no	—
421	#382	—	2	1	no	—
422	#382	—	2	1	no	—
423	#382	D₄	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	C₂³	1	1	yes	characteristic
429	#380	C₂³	1	1	yes	characteristic
430	#380	C₂³	1	1	yes	characteristic
431	#380	C₂³	1	1	yes	characteristic
432	#380	C₂³	1	1	yes	characteristic
433	#380	C₂³	1	1	yes	characteristic
434	#379	—	2	1	no	—
435	#379	—	2	1	no	—
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	C₂³	1	1	yes	characteristic
441	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
442	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
443	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
444	C₄×C₂²⋊C₄	—	2	1	no	—
445	C₄×C₂²⋊C₄	—	2	1	no	—
446	C₄×C₂²⋊C₄	—	2	1	no	—
447	C₄×C₂²⋊C₄	C₂³	1	1	yes	characteristic
448	C₄×C₂²⋊C₄	C₂³	1	1	yes	characteristic
449	C₄×C₂²⋊C₄	C₂³	1	1	yes	characteristic
450	C₄×C₂²⋊C₄	C₂³	1	1	yes	characteristic
451	#376	—	2	1	no	—
452	C₄³	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	C₂⁵	—	2	1	no	—
488	C₂²×Q₈	—	2	1	no	—
489	C₂²×Q₈	C₂×D₄	1	1	yes	characteristic
490	C₂²×Q₈	C₂⁴	1	1	yes	characteristic
491	C₂²×Q₈	C₂⁴	1	1	yes	characteristic
492	C₂²×D₄	—	2	2	no	—
493	C₂²×D₄	—	2	1	no	—
494	C₂²×D₄	—	2	1	no	—
495	C₂²×D₄	—	2	1	no	—
496	C₂²×D₄	—	4	1	no	—
497	C₂²×D₄	—	4	1	no	—
498	C₂²×D₄	—	4	1	no	—
499	C₂²×D₄	—	4	1	no	—
500	C₂²×D₄	—	4	1	no	—
501	C₂²×D₄	C₂×D₄	1	1	yes	characteristic
502	C₂²×D₄	C₂⁴	1	1	yes	characteristic
503	C₂²×D₄	C₂⁴	1	1	yes	characteristic
504	C₂³×C₄	—	2	1	no	—
505	C₂³×C₄	—	2	1	no	—
506	C₂³×C₄	C₂⁴	1	1	yes	characteristic
507	C₂³×C₄	C₂⁴	1	1	yes	characteristic
508	C₂×Q₁₆	—	4	1	no	—
509	C₂×Q₁₆	—	4	1	no	—
510	C₂×Q₁₆	—	4	1	no	—
511	C₂×SD₁₆	—	2	2	no	—
512	C₂×SD₁₆	—	2	2	no	—
513	C₂×SD₁₆	—	4	1	no	—
514	C₂×SD₁₆	—	4	1	no	—
515	C₂×SD₁₆	—	4	1	no	—
516	C₂×SD₁₆	—	4	1	no	—
517	C₂×M₁₆	—	2	2	no	—
518	C₂×M₁₆	—	4	1	no	—
519	C₂×M₁₆	—	4	1	no	—
520	C₂²×C₈	—	2	2	no	—
521	C₂²×C₈	—	4	1	no	—
522	C₂²×C₈	—	4	1	no	—
523	C₂²×C₈	C₂⁴	1	1	yes	characteristic
524	C₂²×C₈	C₂⁴	1	1	yes	characteristic
525	C₂²×C₈	C₂⁴	1	1	yes	characteristic
526	C₂²×C₈	C₂⁴	1	1	yes	characteristic
527	C₂²×C₈	C₂⁴	1	1	yes	characteristic
528	C₂²×C₈	C₂⁴	1	1	yes	characteristic
529	C₂²×C₈	C₂⁴	1	1	yes	characteristic
530	C₂²×C₈	C₂⁴	1	1	yes	characteristic
531	C₄⋊Q₈	—	2	2	no	—
532	C₄⋊Q₈	—	4	1	no	—
533	#126	—	8	2	no	—
534	#125	—	4	1	no	—
535	#125	—	4	1	no	—
536	#124	—	2	2	no	—
537	#124	—	4	2	no	—
538	#124	—	4	1	no	—
539	#124	—	4	1	no	—
540	#124	—	4	1	no	—
541	C₂²⋊Q₈	—	2	2	no	—
542	C₂²⋊Q₈	—	4	1	no	—
543	C₂²⋊Q₈	—	4	1	no	—
544	C₂²⋊Q₈	—	4	1	no	—
545	C₂²⋊Q₈	—	4	1	no	—
546	C₂²⋊Q₈	—	4	1	no	—
547	C₂²⋊Q₈	—	4	1	no	—
548	C₂²⋊Q₈	—	4	1	no	—
549	C₂²⋊Q₈	—	8	2	no	—
550	#121	—	2	2	no	—
551	#121	—	4	1	no	—
552	#121	—	4	1	no	—
553	#121	—	4	1	no	—
554	#120	—	8	2	no	—
555	C₄×Q₈	—	4	1	no	—
556	C₄×Q₈	—	4	1	no	—
557	C₄×Q₈	—	4	4	no	—
558	C₄×Q₈	—	4	1	no	—
559	C₄×Q₈	—	4	1	no	—
560	C₄×Q₈	—	4	1	no	—
561	C₄×Q₈	—	4	1	no	—
562	C₄×D₄	—	4	1	no	—
563	C₄×D₄	—	4	1	no	—
564	C₄×D₄	—	4	1	no	—
565	C₄×D₄	—	4	1	no	—
566	C₄×D₄	—	4	1	no	—
567	C₄×D₄	—	4	1	no	—
568	#117	—	2	2	no	—
569	#117	—	4	1	no	—
570	#117	—	4	1	no	—
571	#117	—	4	1	no	—
572	#117	—	4	1	no	—
573	#117	—	4	1	no	—
574	C₂×C₄⋊C₄	—	2	1	no	—
575	C₂×C₄⋊C₄	—	2	1	no	—
576	C₂×C₄⋊C₄	—	2	1	no	—
577	C₂×C₄⋊C₄	—	2	1	no	—
578	C₂×C₄⋊C₄	—	2	1	no	—
579	C₂×C₄⋊C₄	—	2	1	no	—
580	C₂×C₄⋊C₄	—	2	1	no	—
581	C₂×C₄⋊C₄	—	2	1	no	—
582	C₂×C₄⋊C₄	—	2	1	no	—
583	C₂×C₄⋊C₄	—	2	1	no	—
584	C₂×C₄⋊C₄	—	2	1	no	—
585	C₂×C₄⋊C₄	—	2	1	no	—
586	C₂×C₄⋊C₄	—	2	1	no	—
587	C₂×C₄⋊C₄	—	2	1	no	—
588	C₂×C₄⋊C₄	—	2	1	no	—
589	C₂×C₄⋊C₄	—	2	1	no	—
590	C₂×C₄⋊C₄	—	2	1	no	—
591	C₂×C₄⋊C₄	—	2	1	no	—
592	C₂×C₄⋊C₄	—	2	1	no	—
593	C₂×C₄⋊C₄	—	2	1	no	—
594	C₂×C₄⋊C₄	—	2	1	no	—
595	C₂×C₄⋊C₄	—	2	1	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	C₂×D₄	1	1	yes	characteristic
600	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
601	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
602	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
603	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
604	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
605	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
606	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
607	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
608	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
609	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
610	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
611	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
612	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
613	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
614	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
615	C₂×C₂²⋊C₄	—	2	1	no	—
616	C₂×C₂²⋊C₄	—	2	1	no	—
617	C₂×C₂²⋊C₄	—	2	1	no	—
618	C₂×C₂²⋊C₄	—	2	1	no	—
619	C₂×C₂²⋊C₄	—	2	1	no	—
620	C₂×C₂²⋊C₄	—	2	1	no	—
621	C₂×C₂²⋊C₄	—	2	1	no	—
622	C₂×C₂²⋊C₄	—	2	1	no	—
623	C₂×C₂²⋊C₄	—	2	1	no	—
624	C₂×C₂²⋊C₄	—	2	1	no	—
625	C₂×C₂²⋊C₄	—	2	1	no	—
626	C₂×C₂²⋊C₄	—	2	1	no	—
627	C₂×C₂²⋊C₄	—	2	1	no	—
628	C₂×C₂²⋊C₄	—	2	1	no	—
629	C₂×C₂²⋊C₄	—	2	1	no	—
630	C₂×C₂²⋊C₄	—	2	1	no	—
631	C₂×C₂²⋊C₄	—	2	1	no	—
632	C₂×C₂²⋊C₄	—	2	1	no	—
633	C₂×C₂²⋊C₄	—	2	1	no	—
634	C₂×C₂²⋊C₄	—	2	1	no	—
635	C₂×C₂²⋊C₄	—	2	1	no	—
636	C₂×C₂²⋊C₄	—	2	1	no	—
637	C₂×C₂²⋊C₄	—	2	1	no	—
638	C₂×C₂²⋊C₄	—	2	1	no	—
639	C₂×C₂²⋊C₄	—	2	1	no	—
640	C₂×C₂²⋊C₄	—	2	1	no	—
641	C₂×C₂²⋊C₄	—	2	1	no	—
642	C₂×C₂²⋊C₄	—	2	1	no	—
643	C₂×C₂²⋊C₄	—	2	1	no	—
644	C₂×C₂²⋊C₄	—	2	1	no	—
645	C₂×C₂²⋊C₄	—	2	1	no	—
646	C₂×C₂²⋊C₄	—	2	1	no	—
647	C₂×C₂²⋊C₄	—	2	1	no	—
648	C₂×C₂²⋊C₄	—	4	4	no	—
649	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
650	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
651	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
652	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
653	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
654	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
655	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
656	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
657	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
658	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
659	C₂×C₄²	—	2	1	no	—
660	C₂×C₄²	—	2	1	no	—
661	C₂×C₄²	—	2	1	no	—
662	C₂×C₄²	—	2	1	no	—
663	C₂×C₄²	—	2	1	no	—
664	C₂×C₄²	—	2	1	no	—
665	C₂×C₄²	—	2	1	no	—
666	C₂×C₄²	—	2	1	no	—
667	C₂×C₄²	—	2	1	no	—
668	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
669	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
670	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
671	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
672	C₂×C₄²	C₂⁴	1	1	yes	characteristic
673	C₂×C₄²	C₂⁴	1	1	yes	characteristic
674	C₂×C₄²	C₂⁴	1	1	yes	characteristic
675	C₂×C₄²	C₂⁴	1	1	yes	characteristic
676	C₂×C₄²	C₂⁴	1	1	yes	characteristic
677	#107	—	4	1	no	—
678	#107	—	4	1	no	—
679	#107	—	4	1	no	—
680	#107	—	4	1	no	—
681	#107	—	4	1	no	—
682	#106	—	2	2	no	—
683	#106	—	2	2	no	—
684	#106	—	4	1	no	—
685	#106	—	4	1	no	—
686	C₄⋊C₈	—	2	2	no	—
687	C₄⋊C₈	—	2	2	no	—
688	C₄⋊C₈	—	4	1	no	—
689	C₄⋊C₈	—	4	1	no	—
690	#103	—	2	2	no	—
691	#103	—	2	2	no	—
692	#103	—	2	2	no	—
693	#103	—	2	2	no	—
694	#103	—	4	1	no	—
695	#103	—	4	1	no	—
696	#103	—	4	1	no	—
697	#103	—	4	1	no	—
698	#103	—	4	1	no	—
699	#103	—	4	1	no	—
700	#103	—	4	1	no	—
701	#103	—	4	1	no	—
702	#102	—	2	2	no	—
703	#102	—	2	2	no	—
704	#102	—	2	2	no	—
705	#102	—	2	2	no	—
706	#102	—	2	2	no	—
707	#102	—	4	1	no	—
708	#102	—	4	1	no	—
709	#102	—	4	1	no	—
710	#102	—	4	1	no	—
711	#102	—	4	1	no	—
712	#102	—	4	1	no	—
713	#102	—	4	1	no	—
714	#102	—	4	1	no	—
715	#102	#41	1	4	yes	—
716	C₂²⋊C₈	—	2	2	no	—
717	C₂²⋊C₈	—	2	2	no	—
718	C₂²⋊C₈	—	4	1	no	—
719	C₂²⋊C₈	—	4	1	no	—
720	C₂²⋊C₈	—	4	1	no	—
721	C₂²⋊C₈	—	4	1	no	—
722	#97	—	2	2	no	—
723	#97	—	2	2	no	—
724	#97	—	4	1	no	—
725	#97	—	4	1	no	—
726	#97	—	4	1	no	—
727	C₄×C₈	—	4	1	no	—
728	C₄×C₈	—	4	1	no	—
729	C₄×C₈	—	4	1	no	—
730	#95	—	2	1	no	—
731	#95	—	2	1	no	—
732	#95	—	2	1	no	—
733	#95	—	2	1	no	—
734	#95	—	2	1	no	—
735	#95	—	2	1	no	—
736	#95	—	2	1	no	—
737	#95	—	2	1	no	—
738	#95	—	2	1	no	—
739	#95	—	2	1	no	—
740	#95	—	2	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	C₂×D₄	1	1	yes	characteristic
769	#95	C₂×D₄	1	1	yes	characteristic
770	#95	C₂×D₄	1	1	yes	characteristic
771	#95	C₂×D₄	1	1	yes	characteristic
772	#95	C₂×D₄	1	1	yes	characteristic
773	#95	C₂×D₄	1	1	yes	characteristic
774	#95	C₂×D₄	1	1	yes	characteristic
775	#95	C₂×D₄	1	1	yes	characteristic
776	C₂⁴	—	2	1	no	—
777	C₂⁴	—	2	1	no	—
778	C₂⁴	—	4	2	no	—
779	C₂⁴	—	4	2	no	—
780	C₂⁴	—	8	1	no	—
781	C₂⁴	—	8	1	no	—
782	C₂⁴	—	8	1	no	—
783	C₂⁴	—	8	1	no	—
784	C₂⁴	—	8	1	no	—
785	C₂⁴	C₂²×D₄	1	1	yes	characteristic
786	C₂⁴	C₂²×D₄	1	1	yes	characteristic
787	C₂×Q₈	—	2	1	no	—
788	C₂×Q₈	—	2	1	no	—
789	C₂×Q₈	—	2	1	no	—
790	C₂×Q₈	—	2	1	no	—
791	C₂×Q₈	—	2	1	no	—
792	C₂×Q₈	—	2	1	no	—
793	C₂×Q₈	—	2	1	no	—
794	C₂×Q₈	—	2	1	no	—
795	C₂×Q₈	—	2	1	no	—
796	C₂×Q₈	—	2	1	no	—
797	C₂×Q₈	—	2	1	no	—
798	C₂×Q₈	—	2	1	no	—
799	C₂×Q₈	—	4	1	no	—
800	C₂×Q₈	—	4	1	no	—
801	C₂×Q₈	—	4	1	no	—
802	C₂×Q₈	—	4	2	no	—
803	C₂×Q₈	—	4	2	no	—
804	C₂×Q₈	—	8	1	no	—
805	C₂×D₄	—	2	1	no	—
806	C₂×D₄	—	2	1	no	—
807	C₂×D₄	—	2	1	no	—
808	C₂×D₄	—	2	1	no	—
809	C₂×D₄	—	2	1	no	—
810	C₂×D₄	—	2	1	no	—
811	C₂×D₄	—	2	1	no	—
812	C₂×D₄	—	2	1	no	—
813	C₂×D₄	—	2	1	no	—
814	C₂×D₄	—	2	1	no	—
815	C₂×D₄	—	2	1	no	—
816	C₂×D₄	—	4	1	no	—
817	C₂×D₄	—	4	1	no	—
818	C₂×D₄	—	4	1	no	—
819	C₂×D₄	—	4	2	no	—
820	C₂×D₄	—	4	4	no	—
821	C₂×D₄	—	4	2	no	—
822	C₂×D₄	—	8	1	no	—
823	C₂×D₄	—	8	1	no	—
824	C₂×D₄	—	8	2	no	—
825	C₂×D₄	—	8	2	no	—
826	C₂×D₄	—	8	2	no	—
827	C₂×D₄	—	8	1	no	—
828	C₂×D₄	—	8	1	no	—
829	C₂×D₄	—	8	1	no	—
830	C₂×D₄	—	8	1	no	—
831	C₂×D₄	—	8	1	no	—
832	C₂×D₄	C₂×#41	1	2	yes	—
833	C₂²×C₄	—	2	1	no	—
834	C₂²×C₄	—	2	1	no	—
835	C₂²×C₄	—	2	1	no	—
836	C₂²×C₄	—	2	1	no	—
837	C₂²×C₄	—	2	1	no	—
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	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	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	—	2	1	no	—
859	C₂²×C₄	—	4	2	no	—
860	C₂²×C₄	—	4	2	no	—
861	C₂²×C₄	—	8	1	no	—
862	C₂²×C₄	—	8	1	no	—
863	C₂²×C₄	—	8	1	no	—
864	C₂²×C₄	—	8	1	no	—
865	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
866	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
867	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
868	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
869	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
870	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
871	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
872	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
873	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
874	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
875	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
876	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
877	C₂²×C₄	C₂⁵	1	1	yes	characteristic
878	Q₁₆	—	8	2	no	—
879	SD₁₆	—	8	2	no	—
880	SD₁₆	—	8	2	no	—
881	M₁₆	—	8	2	no	—
882	C₂×C₈	—	2	1	no	—
883	C₂×C₈	—	2	1	no	—
884	C₂×C₈	—	2	1	no	—
885	C₂×C₈	—	2	1	no	—
886	C₂×C₈	—	2	1	no	—
887	C₂×C₈	—	2	1	no	—
888	C₂×C₈	—	2	1	no	—
889	C₂×C₈	—	2	1	no	—
890	C₂×C₈	—	2	1	no	—
891	C₂×C₈	—	2	1	no	—
892	C₂×C₈	—	2	1	no	—
893	C₂×C₈	—	2	1	no	—
894	C₂×C₈	—	2	1	no	—
895	C₂×C₈	—	2	1	no	—
896	C₂×C₈	—	2	1	no	—
897	C₂×C₈	—	2	1	no	—
898	C₂×C₈	—	2	1	no	—
899	C₂×C₈	—	2	1	no	—
900	C₂×C₈	—	2	1	no	—
901	C₂×C₈	—	2	1	no	—
902	C₂×C₈	—	2	1	no	—
903	C₂×C₈	—	2	1	no	—
904	C₂×C₈	—	8	2	no	—
905	C₂×C₈	C₂×#41	1	2	yes	—
906	C₂×C₈	H(5,𝔽₂)	1	2	yes	—
907	C₄⋊C₄	—	2	1	no	—
908	C₄⋊C₄	—	2	1	no	—
909	C₄⋊C₄	—	2	1	no	—
910	C₄⋊C₄	—	2	1	no	—
911	C₄⋊C₄	—	2	1	no	—
912	C₄⋊C₄	—	2	1	no	—
913	C₄⋊C₄	—	2	1	no	—
914	C₄⋊C₄	—	2	1	no	—
915	C₄⋊C₄	—	2	1	no	—
916	C₄⋊C₄	—	2	1	no	—
917	C₄⋊C₄	—	2	1	no	—
918	C₄⋊C₄	—	2	1	no	—
919	C₄⋊C₄	—	2	1	no	—
920	C₄⋊C₄	—	2	1	no	—
921	C₄⋊C₄	—	2	1	no	—
922	C₄⋊C₄	—	2	1	no	—
923	C₄⋊C₄	—	2	1	no	—
924	C₄⋊C₄	—	2	1	no	—
925	C₄⋊C₄	—	2	1	no	—
926	C₄⋊C₄	—	2	1	no	—
927	C₄⋊C₄	—	2	1	no	—
928	C₄⋊C₄	—	2	1	no	—
929	C₄⋊C₄	—	2	1	no	—
930	C₄⋊C₄	—	4	1	no	—
931	C₄⋊C₄	—	4	1	no	—
932	C₄⋊C₄	—	4	1	no	—
933	C₄⋊C₄	—	4	1	no	—
934	C₄⋊C₄	—	4	2	no	—
935	C₄⋊C₄	—	4	2	no	—
936	C₄⋊C₄	—	4	2	no	—
937	C₄⋊C₄	—	4	2	no	—
938	C₄⋊C₄	—	4	2	no	—
939	C₄⋊C₄	—	4	2	no	—
940	C₄⋊C₄	—	4	2	no	—
941	C₄⋊C₄	—	8	1	no	—
942	C₄⋊C₄	—	8	1	no	—
943	C₄⋊C₄	—	8	1	no	—
944	C₄⋊C₄	—	8	1	no	—
945	C₄⋊C₄	—	8	1	no	—
946	C₄⋊C₄	—	8	1	no	—
947	C₄⋊C₄	—	8	1	no	—
948	C₄⋊C₄	—	8	1	no	—
949	C₄⋊C₄	—	8	1	no	—
950	C₄⋊C₄	—	8	1	no	—
951	C₄⋊C₄	—	8	1	no	—
952	C₄⋊C₄	—	8	1	no	—
953	C₄⋊C₄	—	8	1	no	—
954	C₄⋊C₄	—	8	1	no	—
955	C₄⋊C₄	—	8	1	no	—
956	C₄⋊C₄	—	8	1	no	—
957	C₄⋊C₄	—	8	1	no	—
958	C₄⋊C₄	—	8	1	no	—
959	C₄⋊C₄	C₂×#41	1	2	yes	—
960	C₂²⋊C₄	—	2	2	no	—
961	C₂²⋊C₄	—	2	2	no	—
962	C₂²⋊C₄	—	4	1	no	—
963	C₂²⋊C₄	—	4	1	no	—
964	C₂²⋊C₄	—	4	1	no	—
965	C₂²⋊C₄	—	4	1	no	—
966	C₂²⋊C₄	—	4	1	no	—
967	C₂²⋊C₄	—	4	1	no	—
968	C₂²⋊C₄	—	4	1	no	—
969	C₂²⋊C₄	—	4	1	no	—
970	C₂²⋊C₄	—	4	2	no	—
971	C₂²⋊C₄	—	4	2	no	—
972	C₂²⋊C₄	—	4	2	no	—
973	C₂²⋊C₄	—	4	2	no	—
974	C₂²⋊C₄	—	4	2	no	—
975	C₂²⋊C₄	—	4	2	no	—
976	C₂²⋊C₄	—	4	2	no	—
977	C₂²⋊C₄	—	4	2	no	—
978	C₂²⋊C₄	—	4	2	no	—
979	C₂²⋊C₄	—	4	2	no	—
980	C₂²⋊C₄	—	8	1	no	—
981	C₂²⋊C₄	—	8	1	no	—
982	C₂²⋊C₄	—	8	1	no	—
983	C₂²⋊C₄	—	8	1	no	—
984	C₂²⋊C₄	—	8	1	no	—
985	C₂²⋊C₄	—	8	1	no	—
986	C₂²⋊C₄	—	8	1	no	—
987	C₂²⋊C₄	—	8	1	no	—
988	C₂²⋊C₄	—	8	1	no	—
989	C₂²⋊C₄	—	8	1	no	—
990	C₂²⋊C₄	—	8	1	no	—
991	C₂²⋊C₄	—	8	1	no	—
992	C₂²⋊C₄	—	8	1	no	—
993	C₂²⋊C₄	—	8	1	no	—
994	C₂²⋊C₄	—	8	1	no	—
995	C₂²⋊C₄	—	8	1	no	—
996	C₂²⋊C₄	—	8	1	no	—
997	C₂²⋊C₄	—	8	1	no	—
998	C₂²⋊C₄	—	8	1	no	—
999	C₂²⋊C₄	—	8	1	no	—
1000	C₂²⋊C₄	—	8	1	no	—
1001	C₂²⋊C₄	—	8	1	no	—
1002	C₂²⋊C₄	—	8	1	no	—
1003	C₄²	—	2	2	no	—
1004	C₄²	—	2	1	no	—
1005	C₄²	—	2	1	no	—
1006	C₄²	—	2	1	no	—
1007	C₄²	—	2	1	no	—
1008	C₄²	—	2	1	no	—
1009	C₄²	—	2	1	no	—
1010	C₄²	—	2	1	no	—
1011	C₄²	—	2	1	no	—
1012	C₄²	—	2	1	no	—
1013	C₄²	—	2	1	no	—
1014	C₄²	—	4	1	no	—
1015	C₄²	—	4	1	no	—
1016	C₄²	—	4	1	no	—
1017	C₄²	—	4	2	no	—
1018	C₄²	—	4	2	no	—
1019	C₄²	—	4	2	no	—
1020	C₄²	—	8	1	no	—
1021	C₄²	—	8	1	no	—
1022	C₄²	—	8	1	no	—
1023	C₄²	—	8	1	no	—
1024	C₄²	—	8	1	no	—
1025	C₄²	—	8	1	no	—
1026	C₂³	—	2	1	no	—
1027	C₂³	—	2	1	no	—
1028	C₂³	—	2	1	no	—
1029	C₂³	—	2	1	no	—
1030	C₂³	—	2	1	no	—
1031	C₂³	—	2	1	no	—
1032	C₂³	—	2	2	no	—
1033	C₂³	—	2	1	no	—
1034	C₂³	—	2	1	no	—
1035	C₂³	—	2	1	no	—
1036	C₂³	—	2	1	no	—
1037	C₂³	—	2	1	no	—
1038	C₂³	—	2	1	no	—
1039	C₂³	—	2	1	no	—
1040	C₂³	—	2	1	no	—
1041	C₂³	—	4	1	no	—
1042	C₂³	—	4	1	no	—
1043	C₂³	—	4	1	no	—
1044	C₂³	—	4	1	no	—
1045	C₂³	—	4	1	no	—
1046	C₂³	—	4	1	no	—
1047	C₂³	—	4	1	no	—
1048	C₂³	—	4	1	no	—
1049	C₂³	—	4	1	no	—
1050	C₂³	—	4	1	no	—
1051	C₂³	—	4	1	no	—
1052	C₂³	—	4	1	no	—
1053	C₂³	—	4	1	no	—
1054	C₂³	—	8	4	no	—
1055	C₂³	—	8	4	no	—
1056	C₂³	—	16	2	no	—
1057	C₂³	—	16	2	no	—
1058	C₂³	—	16	2	no	—
1059	C₂³	—	16	2	no	—
1060	C₂³	—	16	2	no	—
1061	C₂³	C₂³×D₄	1	1	yes	characteristic
1062	Q₈	—	4	1	no	—
1063	Q₈	—	4	1	no	—
1064	Q₈	—	4	1	no	—
1065	Q₈	—	4	1	no	—
1066	Q₈	—	4	1	no	—
1067	Q₈	—	4	1	no	—
1068	Q₈	—	4	1	no	—
1069	Q₈	—	4	1	no	—
1070	Q₈	—	8	2	no	—
1071	Q₈	—	8	4	no	—
1072	D₄	—	2	2	no	—
1073	D₄	—	2	2	no	—
1074	D₄	—	4	1	no	—
1075	D₄	—	4	1	no	—
1076	D₄	—	4	1	no	—
1077	D₄	—	4	1	no	—
1078	D₄	—	4	1	no	—
1079	D₄	—	4	1	no	—
1080	D₄	—	8	2	no	—
1081	D₄	—	8	4	no	—
1082	D₄	—	16	2	no	—
1083	D₄	—	16	2	no	—
1084	C₂×C₄	—	2	1	no	—
1085	C₂×C₄	—	2	1	no	—
1086	C₂×C₄	—	2	1	no	—
1087	C₂×C₄	—	2	1	no	—
1088	C₂×C₄	—	2	1	no	—
1089	C₂×C₄	—	2	1	no	—
1090	C₂×C₄	—	2	1	no	—
1091	C₂×C₄	—	2	1	no	—
1092	C₂×C₄	—	2	1	no	—
1093	C₂×C₄	—	2	1	no	—
1094	C₂×C₄	—	2	1	no	—
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	1	no	—
1102	C₂×C₄	—	2	1	no	—
1103	C₂×C₄	—	2	2	no	—
1104	C₂×C₄	—	2	1	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	—	4	1	no	—
1121	C₂×C₄	—	4	1	no	—
1122	C₂×C₄	—	4	1	no	—
1123	C₂×C₄	—	4	1	no	—
1124	C₂×C₄	—	4	1	no	—
1125	C₂×C₄	—	4	1	no	—
1126	C₂×C₄	—	4	1	no	—
1127	C₂×C₄	—	4	1	no	—
1128	C₂×C₄	—	4	1	no	—
1129	C₂×C₄	—	4	1	no	—
1130	C₂×C₄	—	4	1	no	—
1131	C₂×C₄	—	4	1	no	—
1132	C₂×C₄	—	4	1	no	—
1133	C₂×C₄	—	4	1	no	—
1134	C₂×C₄	—	4	1	no	—
1135	C₂×C₄	—	4	1	no	—
1136	C₂×C₄	—	4	1	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	—	16	2	no	—
1170	C₂×C₄	—	16	2	no	—
1171	C₂×C₄	#575	1	2	yes	—
1172	C₂×C₄	C₂²×#41	1	1	yes	characteristic
1173	C₂×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
1174	C₂×C₄	#585	1	1	yes	characteristic
1175	C₂×C₄	#585	1	1	yes	characteristic
1176	C₂×C₄	#585	1	1	yes	characteristic
1177	C₂×C₄	#585	1	1	yes	characteristic
1178	C₈	—	2	2	no	—
1179	C₈	—	2	2	no	—
1180	C₈	—	4	1	no	—
1181	C₈	—	4	1	no	—
1182	C₈	—	4	1	no	—
1183	C₈	—	4	1	no	—
1184	C₈	—	4	1	no	—
1185	C₈	—	4	1	no	—
1186	C₂²	—	4	1	no	—
1187	C₂²	—	4	1	no	—
1188	C₂²	—	4	2	no	—
1189	C₂²	—	4	1	no	—
1190	C₂²	—	4	2	no	—
1191	C₂²	—	4	1	no	—
1192	C₂²	—	4	1	no	—
1193	C₂²	—	4	1	no	—
1194	C₂²	—	4	1	no	—
1195	C₂²	—	4	1	no	—
1196	C₂²	—	4	1	no	—
1197	C₂²	—	4	1	no	—
1198	C₂²	—	4	1	no	—
1199	C₂²	—	4	1	no	—
1200	C₂²	—	4	1	no	—
1201	C₂²	—	4	1	no	—
1202	C₂²	—	4	2	no	—
1203	C₂²	—	8	1	no	—
1204	C₂²	—	8	1	no	—
1205	C₂²	—	8	1	no	—
1206	C₂²	—	8	1	no	—
1207	C₂²	—	8	1	no	—
1208	C₂²	—	8	1	no	—
1209	C₂²	—	8	1	no	—
1210	C₂²	—	8	1	no	—
1211	C₂²	—	8	1	no	—
1212	C₂²	—	8	1	no	—
1213	C₂²	—	8	1	no	—
1214	C₂²	—	16	8	no	—
1215	C₂²	D₄×#41	1	1	yes	characteristic
1216	C₂²	#3496	1	1	yes	characteristic
1217	C₂²	#3500	1	1	yes	characteristic
1218	C₂²	C₂×#575	1	1	yes	characteristic
1219	C₂²	#3584	1	1	yes	characteristic
1220	C₂²	#3585	1	1	yes	characteristic
1221	C₂²	#3586	1	1	yes	characteristic
1222	C₄	—	2	2	no	—
1223	C₄	—	4	1	no	—
1224	C₄	—	4	2	no	—
1225	C₄	—	4	1	no	—
1226	C₄	—	4	1	no	—
1227	C₄	—	4	1	no	—
1228	C₄	—	4	1	no	—
1229	C₄	—	4	1	no	—
1230	C₄	—	4	1	no	—
1231	C₄	—	4	1	no	—
1232	C₄	—	4	1	no	—
1233	C₄	—	4	1	no	—
1234	C₄	—	4	1	no	—
1235	C₄	—	8	1	no	—
1236	C₄	—	8	1	no	—
1237	C₄	—	8	1	no	—
1238	C₄	—	8	1	no	—
1239	C₄	—	8	1	no	—
1240	C₄	—	8	1	no	—
1241	C₄	—	8	1	no	—
1242	C₄	—	8	1	no	—
1243	C₄	—	8	1	no	—
1244	C₄	—	8	1	no	—
1245	C₄	—	8	1	no	—
1246	C₄	—	8	1	no	—
1247	C₄	—	8	1	no	—
1248	C₄	#3455	1	1	yes	characteristic
1249	C₄	#3514	1	1	yes	characteristic
1250	C₄	#3560	1	1	yes	characteristic
1251	C₄	#3566	1	1	yes	characteristic
1252	C₂	—	8	1	no	—
1253	C₂	—	8	1	no	—
1254	C₂	—	8	2	no	—
1255	C₂	—	16	1	no	—
1256	C₂	#39390	1	1	yes	characteristic
1257	C₂	#61442	1	1	yes	characteristic
1258	C₂	#61513	1	1	yes	characteristic
1259	C₂	#62304	1	1	yes	characteristic
1260	C₂	#62348	1	1	yes	characteristic
1261	C₂	#62585	1	1	yes	characteristic
1262	C₂	#62607	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³	C₂³×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁵
prime radical	#2408	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³ ◁ C₄×#124 ◁ G
LECS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #39527	C₂	semidirect
3. #33268	C₂	semidirect
4. #32643	C₂	semidirect
5. #32556	C₂	semidirect
6. #32063	C₂	semidirect
7. #31733	C₂	semidirect
9. #31451	C₂	semidirect
10. #31133	C₂	semidirect
11. #31012	C₂	semidirect
12. #30146	C₂	semidirect
13. #30136	C₂	semidirect
14. #29042	C₂	semidirect
15. #28993	C₂	semidirect
16. #28929	C₂	semidirect
17. #28859	C₂	semidirect
18. #27718	C₂	semidirect
19. #27281	C₂	semidirect
20. #27227	C₂	semidirect
21. #27173	C₂	semidirect
22. #27038	C₂	semidirect
23. #26936	C₂	semidirect
24. #25482	C₂	semidirect
25. #25299	C₂	semidirect
26. #25251	C₂	semidirect
28. #23131	C₂	semidirect
29. #22584	C₂	semidirect
30. C₄×#489	C₂	semidirect
31. #21632	C₂	semidirect
33. C₂×#485	C₂²	semidirect
38. C₂×#446	C₂²	semidirect
41. #2863	C₂²	semidirect
54. #2584	C₂²	semidirect
55. #2581	C₂²	semidirect
62. #2495	C₂²	semidirect
63. #2492	C₂²	semidirect
67. #2441	C₂²	semidirect
78. #2362	C₂²	semidirect
83. C₄×C₄⋊Q₈	C₂²	semidirect
86. #2101	C₂²	semidirect
87. #2101	C₂²	semidirect
88. #2099	C₂²	semidirect
89. #2097	C₂²	semidirect
90. #2088	C₂²	semidirect
91. #2087	C₂²	semidirect
92. #2087	C₂²	semidirect
93. #2083	C₂²	semidirect
98. #2072	C₂²	semidirect
100. #2068	C₂²	semidirect
103. #2066	C₂²	semidirect
106. #2058	C₂²	semidirect
107. #2056	C₂²	semidirect
115. #2036	C₂²	semidirect
119. #2026	C₂²	semidirect
124. #2001	C₂²	semidirect
126. #1993	C₂²	semidirect
127. #1992	C₂²	semidirect
128. #1985	C₂²	semidirect
131. #1971	C₂²	semidirect
136. #1949	C₂²	semidirect
137. #1947	C₂²	semidirect
138. #1944	C₂²	semidirect
139. #1943	C₂²	semidirect
140. #1942	C₂²	semidirect
141. #1942	C₂²	semidirect
147. #1935	C₂²	semidirect
148. #1935	C₂²	semidirect
149. #1935	C₂²	semidirect
150. #1935	C₂²	semidirect
153. #1933	C₂²	semidirect
154. #1927	C₂²	semidirect
159. #1924	C₂²	semidirect
161. #1923	C₂²	semidirect
162. #1920	C₂²	semidirect
163. #1920	C₂²	semidirect
164. #1920	C₂²	semidirect
165. #1919	C₂²	semidirect
169. #1892	C₂²	semidirect
171. #1878	C₂²	semidirect
177. #1873	C₂²	semidirect
179. #1863	C₂²	semidirect
180. #1863	C₂²	semidirect
183. #1854	C₂²	semidirect
184. #1836	C₂²	semidirect
185. #1831	C₂²	semidirect
187. #1825	C₂²	semidirect
192. C₄×#103	C₂²	semidirect
193. C₄×#103	C₂²	semidirect
194. C₄×#103	C₂²	semidirect
199. #1752	C₂²	semidirect
200. C₈×C₂²⋊C₄	C₂²	semidirect
201. #1735	C₂²	semidirect
202. C₄×#97	C₂²	semidirect

Maximal subgroups

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

subgroup	index
#39527	2
#39024	2
#33268	2
#32643	2
#32556	2
#32063	2
#31733	2
#31676	2
#31451	2
#31133	2
#31012	2
#30146	2
#30136	2
#29042	2
#28993	2
#28929	2
#28859	2
#27718	2
#27281	2
#27227	2
#27173	2
#27038	2
#26936	2
#25482	2
#25299	2
#25251	2
#25120	2
#23131	2
#22584	2
C₄×#489	2
#21632	2