Subgroups — #6940651

Order 512.

1477 conjugacy classes of subgroups.

The subgroup lattice has 1248 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#36293	C₂	1	1	yes	maximal, characteristic
2	#36280	C₂	1	1	yes	maximal, characteristic, complemented
3	#32861	C₂	1	1	yes	maximal, characteristic, complemented
4	#32825	C₂	1	1	yes	maximal, characteristic, complemented
5	#32532	C₂	1	1	yes	maximal, characteristic, complemented
6	#32485	C₂	1	1	yes	maximal, characteristic, complemented
7	#31976	C₂	1	1	yes	maximal, characteristic, complemented
8	#31974	C₂	1	1	yes	maximal, characteristic, complemented
9	#31906	C₂	1	1	yes	maximal, characteristic, complemented
10	#31878	C₂	1	1	yes	maximal, characteristic, complemented
11	#31235	C₂	1	1	yes	maximal, characteristic, complemented
12	#31163	C₂	1	1	yes	maximal, characteristic, complemented
13	#30146	C₂	1	1	yes	maximal, characteristic, complemented
14	#30135	C₂	1	1	yes	maximal, characteristic, complemented
15	#29995	C₂	1	1	yes	maximal, characteristic, complemented
16	#29833	C₂	1	1	yes	maximal, characteristic, complemented
17	#29771	C₂	1	1	yes	maximal, characteristic, complemented
18	#29537	C₂	1	1	yes	maximal, characteristic, complemented
19	#28281	C₂	1	1	yes	maximal, characteristic, complemented
20	#26346	C₂	1	1	yes	maximal, characteristic, complemented
21	#26340	C₂	1	1	yes	maximal, characteristic, complemented
22	#26002	C₂	1	1	yes	maximal, characteristic, complemented
23	#25950	C₂	1	1	yes	maximal, characteristic
24	#25206	C₂	1	1	yes	maximal, characteristic, complemented
25	#25084	C₂	1	1	yes	maximal, characteristic
26	#24602	C₂	1	1	yes	maximal, characteristic, complemented
27	#24530	C₂	1	1	yes	maximal, characteristic
28	#24501	C₂	1	1	yes	maximal, characteristic
29	#24479	C₂	1	1	yes	maximal, characteristic
30	C₂×#2065	C₂	1	1	yes	maximal, characteristic
31	#21972	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×#484	C₂²	1	1	yes	characteristic
33	C₂×#479	C₂²	1	1	yes	characteristic, complemented
34	C₂×#475	C₂²	1	1	yes	characteristic, complemented
35	C₂×#474	C₂²	1	1	yes	characteristic
36	C₂×#467	C₂²	1	1	yes	characteristic
37	C₂×#464	C₂²	1	1	yes	characteristic
38	C₂×#450	C₂²	1	1	yes	characteristic
39	C₂×#431	C₂²	1	1	yes	characteristic
40	C₂²×#106	C₂²	1	1	yes	characteristic
41	C₂²×C₄⋊C₈	C₂²	1	1	yes	characteristic
42	C₂²×#102	C₂²	1	1	yes	characteristic
43	C₂²×#102	C₂²	1	1	yes	characteristic
44	#2863	C₂²	1	1	yes	characteristic, complemented
45	#2861	C₂²	1	1	yes	characteristic
46	#2860	C₂²	1	1	yes	characteristic
47	#2859	C₂²	1	1	yes	characteristic, complemented
48	#2855	C₂²	1	1	yes	characteristic
49	#2855	C₂²	1	1	yes	characteristic
50	#2612	—	2	1	no	—
51	#2606	—	2	1	no	—
52	#2597	—	2	1	no	—
53	#2585	—	2	1	no	—
54	#2531	—	2	1	no	—
55	#2526	—	2	1	no	—
56	#2513	C₂²	1	1	yes	characteristic
57	#2511	C₂²	1	1	yes	characteristic, complemented
58	#2507	C₂²	1	1	yes	characteristic, complemented
59	#2507	C₂²	1	1	yes	characteristic, complemented
60	#2502	C₂²	1	1	yes	characteristic
61	#2482	—	2	1	no	—
62	#2480	—	2	1	no	—
63	#2479	—	2	1	no	—
64	#2473	—	2	1	no	—
65	#2462	—	2	1	no	—
66	#2454	C₂²	1	1	yes	characteristic
67	#2451	C₂²	1	1	yes	characteristic, complemented
68	#2448	C₂²	1	1	yes	characteristic
69	#2447	C₂²	1	1	yes	characteristic
70	#2442	C₂²	1	1	yes	characteristic
71	#2440	C₂²	1	1	yes	characteristic
72	#2438	—	2	1	no	—
73	#2435	C₂²	1	1	yes	characteristic
74	#2360	—	2	1	no	—
75	#2360	C₂²	1	1	yes	characteristic
76	#2360	C₂²	1	1	yes	characteristic
77	#2345	C₂²	1	1	yes	characteristic
78	#2343	—	2	1	no	—
79	#2342	—	2	1	no	—
80	#2342	—	2	1	no	—
81	D₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
82	C₄×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
83	C₄×#124	C₂²	1	1	yes	characteristic
84	#2295	C₂²	1	1	yes	characteristic, complemented
85	#2293	C₂²	1	1	yes	characteristic
86	C₂×#390	C₂²	1	1	yes	characteristic
87	C₂×#389	C₂²	1	1	yes	characteristic
88	C₄×#117	C₂²	1	1	yes	characteristic
89	#2101	C₂²	1	1	yes	characteristic, complemented
90	#2097	C₂²	1	1	yes	characteristic, complemented
91	#2096	C₂²	1	1	yes	characteristic, complemented
92	#2093	C₂²	1	1	yes	characteristic
93	#2088	C₂²	1	1	yes	characteristic, complemented
94	#2088	C₂²	1	1	yes	characteristic, complemented
95	#2088	C₂²	1	1	yes	characteristic, complemented
96	#2087	C₂²	1	1	yes	characteristic, complemented
97	#2087	C₂²	1	1	yes	characteristic, complemented
98	#2087	C₂²	1	1	yes	characteristic, complemented
99	#2087	C₂²	1	1	yes	characteristic, complemented
100	#2086	C₂²	1	1	yes	characteristic, complemented
101	#2083	C₂²	1	1	yes	characteristic, complemented
102	#2072	C₂²	1	1	yes	characteristic, complemented
103	#2071	C₂²	1	1	yes	characteristic
104	#2071	C₂²	1	1	yes	characteristic
105	#2068	C₂²	1	1	yes	characteristic, complemented
106	#2068	C₂²	1	1	yes	characteristic, complemented
107	#2068	C₂²	1	1	yes	characteristic, complemented
108	#2068	C₂²	1	1	yes	characteristic, complemented
109	#2068	C₂²	1	1	yes	characteristic, complemented
110	#2068	C₂²	1	1	yes	characteristic, complemented
111	#2068	C₂²	1	1	yes	characteristic, complemented
112	#2067	C₂²	1	1	yes	characteristic
113	#2067	C₂²	1	1	yes	characteristic
114	#2067	C₂²	1	1	yes	characteristic
115	#2067	C₂²	1	1	yes	characteristic
116	#2067	C₂²	1	1	yes	characteristic
117	#2066	C₂²	1	1	yes	characteristic, complemented
118	#2066	C₂²	1	1	yes	characteristic, complemented
119	#2065	C₂²	1	1	yes	characteristic
120	#2065	C₂²	1	1	yes	characteristic
121	#2065	C₂²	1	1	yes	characteristic
122	#2065	C₂²	1	1	yes	characteristic
123	#2065	C₂²	1	1	yes	characteristic
124	#2065	C₂²	1	1	yes	characteristic
125	#2065	C₂²	1	1	yes	characteristic
126	#2065	C₂²	1	1	yes	characteristic
127	#2065	C₂²	1	1	yes	characteristic
128	#2065	C₂²	1	1	yes	characteristic
129	#2059	C₂²	1	1	yes	characteristic, complemented
130	#2059	C₂²	1	1	yes	characteristic, complemented
131	#2058	C₂²	1	1	yes	characteristic, complemented
132	#2056	C₂²	1	1	yes	characteristic, complemented
133	#2056	C₂²	1	1	yes	characteristic, complemented
134	#2056	C₂²	1	1	yes	characteristic, complemented
135	#2055	C₂²	1	1	yes	characteristic
136	#2055	C₂²	1	1	yes	characteristic
137	#2055	C₂²	1	1	yes	characteristic
138	#2055	C₂²	1	1	yes	characteristic
139	#2055	C₂²	1	1	yes	characteristic
140	#2042	C₂²	1	1	yes	characteristic
141	#2042	C₂²	1	1	yes	characteristic
142	#2042	C₂²	1	1	yes	characteristic
143	#2023	C₂²	1	1	yes	characteristic
144	#2015	C₂²	1	1	yes	characteristic
145	#1989	C₂²	1	1	yes	characteristic, complemented
146	#1983	C₂²	1	1	yes	characteristic
147	#1983	C₂²	1	1	yes	characteristic
148	#1983	C₂²	1	1	yes	characteristic
149	#1968	C₂²	1	1	yes	characteristic
150	#1968	C₂²	1	1	yes	characteristic
151	#1949	C₂²	1	1	yes	characteristic, complemented
152	#1949	C₂²	1	1	yes	characteristic, complemented
153	#1948	C₂²	1	1	yes	characteristic, complemented
154	#1947	C₂²	1	1	yes	characteristic, complemented
155	#1942	C₂²	1	1	yes	characteristic, complemented
156	#1942	C₂²	1	1	yes	characteristic, complemented
157	#1939	C₂²	1	1	yes	characteristic, complemented
158	#1939	C₂²	1	1	yes	characteristic, complemented
159	#1939	C₂²	1	1	yes	characteristic, complemented
160	#1939	C₂²	1	1	yes	characteristic, complemented
161	#1934	C₂²	1	1	yes	characteristic
162	#1934	C₂²	1	1	yes	characteristic
163	#1933	C₂²	1	1	yes	characteristic, complemented
164	#1933	C₂²	1	1	yes	characteristic, complemented
165	#1928	C₂²	1	1	yes	characteristic, complemented
166	#1925	C₂²	1	1	yes	characteristic
167	#1925	C₂²	1	1	yes	characteristic
168	#1925	C₂²	1	1	yes	characteristic
169	#1920	C₂²	1	1	yes	characteristic, complemented
170	#1920	C₂²	1	1	yes	characteristic, complemented
171	#1919	C₂²	1	1	yes	characteristic, complemented
172	#1918	C₂²	1	1	yes	characteristic, complemented
173	#1892	C₂²	1	1	yes	characteristic
174	#1892	C₂²	1	1	yes	characteristic
175	#1880	C₂²	1	1	yes	characteristic
176	#1878	C₂²	1	1	yes	characteristic, complemented
177	#1877	C₂²	1	1	yes	characteristic
178	#1877	C₂²	1	1	yes	characteristic
179	#1872	C₂²	1	1	yes	characteristic
180	#1872	C₂²	1	1	yes	characteristic
181	#1865	C₂²	1	1	yes	characteristic, complemented
182	#1865	C₂²	1	1	yes	characteristic, complemented
183	#1862	C₂²	1	1	yes	characteristic
184	#1862	C₂²	1	1	yes	characteristic
185	#1853	C₂²	1	1	yes	characteristic
186	#1852	C₂²	1	1	yes	characteristic
187	#1850	C₂²	1	1	yes	characteristic
188	#1850	C₂²	1	1	yes	characteristic
189	#1850	C₂²	1	1	yes	characteristic
190	#1850	C₂²	1	1	yes	characteristic
191	#1842	C₂²	1	1	yes	characteristic, complemented
192	#1842	C₂²	1	1	yes	characteristic, complemented
193	#1831	C₂²	1	1	yes	characteristic, complemented
194	#1831	C₂²	1	1	yes	characteristic, complemented
195	#1824	C₂²	1	1	yes	characteristic
196	#1808	C₂²	1	1	yes	characteristic
197	#1803	C₂²	1	1	yes	characteristic, complemented
198	#1802	C₂²	1	1	yes	characteristic
199	#1802	C₂²	1	1	yes	characteristic
200	#1802	C₂²	1	1	yes	characteristic
201	#1786	C₂²	1	1	yes	characteristic
202	C₂×#340	C₂²	1	1	yes	characteristic
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	C₂³×C₈	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	—	2	1	no	—
212	C₂×#125	C₂³	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×C₄×Q₈	—	2	1	no	—
219	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
220	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
221	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
222	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
223	C₂×#117	—	2	1	no	—
224	C₂×#117	D₄	1	1	yes	characteristic
225	C₂×#117	D₄	1	1	yes	characteristic
226	C₂²×C₄⋊C₄	—	2	1	no	—
227	C₂²×C₄⋊C₄	C₂³	1	1	yes	characteristic
228	C₂²×C₄⋊C₄	C₂³	1	1	yes	characteristic
229	C₂²×C₄⋊C₄	C₂³	1	1	yes	characteristic
230	C₂²×C₂²⋊C₄	—	2	1	no	—
231	C₂²×C₂²⋊C₄	—	2	1	no	—
232	C₂²×C₂²⋊C₄	—	2	1	no	—
233	C₂²×C₄²	C₂³	1	1	yes	characteristic
234	#484	—	4	2	no	—
235	#479	—	4	2	no	—
236	#475	—	4	2	no	—
237	#474	—	4	2	no	—
238	#467	—	4	2	no	—
239	#464	—	4	2	no	—
240	#450	—	4	2	no	—
241	#431	—	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×#107	C₂³	1	1	yes	characteristic
248	C₂×#107	C₂³	1	1	yes	characteristic
249	C₂×#106	—	4	2	no	—
250	C₂×#106	C₂³	1	1	yes	characteristic
251	C₂×#106	C₂³	1	1	yes	characteristic
252	C₂×#106	C₂³	1	1	yes	characteristic
253	C₂×#106	C₂³	1	1	yes	characteristic
254	C₂×#106	C₂³	1	1	yes	characteristic
255	C₂×#106	C₂³	1	1	yes	characteristic
256	C₂×C₄⋊C₈	—	4	2	no	—
257	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
258	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
259	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
260	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
261	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
262	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
263	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
264	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
265	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
266	C₂×C₄⋊C₈	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×#103	C₂³	1	1	yes	characteristic
272	C₂×#103	C₂³	1	1	yes	characteristic
273	C₂×#103	C₂³	1	1	yes	characteristic
274	C₂×#103	C₂³	1	1	yes	characteristic
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×#102	—	4	2	no	—
284	C₂×#102	—	4	2	no	—
285	C₂×#102	C₂³	1	1	yes	characteristic
286	C₂×#102	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×C₄×C₈	C₂³	1	1	yes	characteristic
302	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
303	#400	—	2	1	no	—
304	#400	—	2	1	no	—
305	#400	—	2	1	no	—
306	#399	—	2	1	no	—
307	#399	—	2	1	no	—
308	#398	—	2	1	no	—
309	#398	—	2	1	no	—
310	#398	—	2	1	no	—
311	#398	—	2	1	no	—
312	#398	—	2	1	no	—
313	#398	—	2	1	no	—
314	#398	—	2	1	no	—
315	#398	—	2	1	no	—
316	#398	—	2	1	no	—
317	#397	—	2	1	no	—
318	#397	—	2	1	no	—
319	#397	—	2	1	no	—
320	#397	—	2	1	no	—
321	#397	—	2	1	no	—
322	#396	—	2	1	no	—
323	#395	—	2	1	no	—
324	#395	—	2	1	no	—
325	#394	—	2	1	no	—
326	#394	—	2	1	no	—
327	#391	—	2	1	no	—
328	#391	—	2	1	no	—
329	#391	C₂³	1	1	yes	characteristic
330	#391	C₂³	1	1	yes	characteristic
331	#391	C₂³	1	1	yes	characteristic
332	#391	C₂³	1	1	yes	characteristic
333	#391	C₂³	1	1	yes	characteristic
334	#391	C₂³	1	1	yes	characteristic
335	#391	C₂³	1	1	yes	characteristic
336	#391	C₂³	1	1	yes	characteristic
337	#390	—	2	1	no	—
338	#390	—	2	1	no	—
339	#390	C₂³	1	1	yes	characteristic
340	#390	C₂³	1	1	yes	characteristic
341	#390	C₂³	1	1	yes	characteristic
342	#390	C₂³	1	1	yes	characteristic
343	#390	C₂³	1	1	yes	characteristic
344	#390	C₂³	1	1	yes	characteristic
345	#390	C₂³	1	1	yes	characteristic
346	#390	C₂³	1	1	yes	characteristic
347	#389	—	2	1	no	—
348	#389	—	2	1	no	—
349	#389	—	2	1	no	—
350	#389	—	2	1	no	—
351	#389	—	2	1	no	—
352	#389	—	2	1	no	—
353	#389	—	2	1	no	—
354	#389	—	2	1	no	—
355	#389	—	2	1	no	—
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	#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	#388	—	2	1	no	—
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	#387	—	2	1	no	—
388	#387	—	2	1	no	—
389	#387	—	2	1	no	—
390	#387	—	2	1	no	—
391	#387	—	2	1	no	—
392	#387	—	2	1	no	—
393	#387	—	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	—	2	1	no	—
401	#387	—	2	1	no	—
402	#387	—	2	1	no	—
403	#387	—	2	1	no	—
404	#387	—	2	1	no	—
405	#386	—	2	1	no	—
406	#386	—	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	—	2	1	no	—
416	#385	—	2	1	no	—
417	#384	C₂³	1	1	yes	characteristic
418	#384	C₂³	1	1	yes	characteristic
419	#384	C₂³	1	1	yes	characteristic
420	#383	—	2	1	no	—
421	#382	—	2	1	no	—
422	#382	C₂³	1	1	yes	characteristic
423	#381	—	2	1	no	—
424	#381	—	2	1	no	—
425	#381	—	2	1	no	—
426	#380	—	2	1	no	—
427	#380	—	2	1	no	—
428	#380	—	2	1	no	—
429	#380	C₂³	1	1	yes	characteristic
430	#380	C₂³	1	1	yes	characteristic
431	#379	—	2	1	no	—
432	#379	—	2	1	no	—
433	#379	—	2	1	no	—
434	C₄×C₄⋊C₄	—	2	1	no	—
435	C₄×C₄⋊C₄	—	2	1	no	—
436	C₄×C₄⋊C₄	D₄	1	1	yes	characteristic
437	C₄×C₄⋊C₄	D₄	1	1	yes	characteristic
438	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
439	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
448	C₄×C₂²⋊C₄	—	2	1	no	—
449	C₄×C₂²⋊C₄	—	2	1	no	—
450	C₄×C₂²⋊C₄	D₄	1	1	yes	characteristic
451	C₄×C₂²⋊C₄	D₄	1	1	yes	characteristic
452	C₄×C₂²⋊C₄	C₂³	1	1	yes	characteristic
453	C₄×C₂²⋊C₄	C₂³	1	1	yes	characteristic
454	#376	—	2	1	no	—
455	#376	D₄	1	1	yes	characteristic
456	#376	D₄	1	1	yes	characteristic
457	C₂×#95	—	2	1	no	—
458	C₄³	C₂³	1	1	yes	characteristic
459	C₄³	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	#340	C₂³	1	1	yes	characteristic
481	#340	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	C₂⁵	—	2	1	no	—
491	C₂²×Q₈	—	2	1	no	—
492	C₂²×Q₈	C₂⁴	1	1	yes	characteristic
493	C₂²×Q₈	C₂⁴	1	1	yes	characteristic
494	C₂²×D₄	—	2	2	no	—
495	C₂²×D₄	—	2	1	no	—
496	C₂²×D₄	—	2	2	no	—
497	C₂²×D₄	—	2	2	no	—
498	C₂²×D₄	—	4	1	no	—
499	C₂²×D₄	—	4	1	no	—
500	C₂²×D₄	—	4	1	no	—
501	C₂²×D₄	C₂⁴	1	1	yes	characteristic
502	C₂²×D₄	C₂⁴	1	1	yes	characteristic
503	C₂³×C₄	—	2	1	no	—
504	C₂³×C₄	—	2	1	no	—
505	C₂³×C₄	—	2	1	no	—
506	C₂³×C₄	—	2	1	no	—
507	C₂³×C₄	—	2	1	no	—
508	C₂³×C₄	C₂×D₄	1	1	yes	characteristic
509	C₂³×C₄	C₂×D₄	1	1	yes	characteristic
510	C₂³×C₄	C₂⁴	1	1	yes	characteristic
511	C₂×Q₁₆	—	4	1	no	—
512	C₂×Q₁₆	—	4	1	no	—
513	C₂×Q₁₆	—	4	1	no	—
514	C₂×SD₁₆	—	2	2	no	—
515	C₂×SD₁₆	—	4	1	no	—
516	C₂×SD₁₆	—	4	1	no	—
517	C₂×SD₁₆	—	4	1	no	—
518	C₂×SD₁₆	—	4	1	no	—
519	C₂×SD₁₆	—	4	1	no	—
520	C₂²×C₈	—	2	2	no	—
521	C₂²×C₈	—	2	2	no	—
522	C₂²×C₈	—	4	1	no	—
523	C₂²×C₈	—	4	1	no	—
524	C₂²×C₈	—	4	1	no	—
525	C₂²×C₈	—	4	1	no	—
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	C₂²×C₈	C₂⁴	1	1	yes	characteristic
532	C₂²×C₈	C₂⁴	1	1	yes	characteristic
533	C₂²×C₈	C₂⁴	1	1	yes	characteristic
534	C₄⋊Q₈	—	2	2	no	—
535	C₄⋊Q₈	—	4	1	no	—
536	#126	—	8	2	no	—
537	#125	—	4	1	no	—
538	#125	—	4	1	no	—
539	#125	—	8	2	no	—
540	#124	—	2	2	no	—
541	#124	—	4	1	no	—
542	#124	—	4	1	no	—
543	#124	—	4	1	no	—
544	C₂²⋊Q₈	—	2	2	no	—
545	C₂²⋊Q₈	—	2	2	no	—
546	C₂²⋊Q₈	—	2	2	no	—
547	C₂²⋊Q₈	—	2	2	no	—
548	C₂²⋊Q₈	—	4	4	no	—
549	C₄×Q₈	—	2	2	no	—
550	C₄×Q₈	—	4	1	no	—
551	C₄×Q₈	—	4	1	no	—
552	C₄×Q₈	—	4	1	no	—
553	C₄×Q₈	—	8	2	no	—
554	C₄×D₄	—	2	2	no	—
555	C₄×D₄	—	4	1	no	—
556	C₄×D₄	—	4	1	no	—
557	C₄×D₄	—	4	1	no	—
558	#117	—	2	4	no	—
559	#117	—	2	4	no	—
560	#117	—	8	2	no	—
561	C₂×C₄⋊C₄	—	2	2	no	—
562	C₂×C₄⋊C₄	—	2	2	no	—
563	C₂×C₄⋊C₄	—	2	2	no	—
564	C₂×C₄⋊C₄	—	2	1	no	—
565	C₂×C₄⋊C₄	—	2	1	no	—
566	C₂×C₄⋊C₄	—	2	1	no	—
567	C₂×C₄⋊C₄	—	2	1	no	—
568	C₂×C₄⋊C₄	—	2	1	no	—
569	C₂×C₄⋊C₄	—	2	1	no	—
570	C₂×C₄⋊C₄	—	2	1	no	—
571	C₂×C₄⋊C₄	—	2	1	no	—
572	C₂×C₄⋊C₄	—	2	1	no	—
573	C₂×C₄⋊C₄	—	2	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	—	4	1	no	—
597	C₂×C₄⋊C₄	—	4	1	no	—
598	C₂×C₄⋊C₄	—	4	1	no	—
599	C₂×C₄⋊C₄	—	8	2	no	—
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	C₂×D₄	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×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
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	—	4	4	no	—
643	C₂×C₂²⋊C₄	—	4	4	no	—
644	C₂×C₂²⋊C₄	—	8	2	no	—
645	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
646	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
647	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
648	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
649	C₂×C₄²	—	2	2	no	—
650	C₂×C₄²	—	2	2	no	—
651	C₂×C₄²	—	2	1	no	—
652	C₂×C₄²	—	2	1	no	—
653	C₂×C₄²	—	2	1	no	—
654	C₂×C₄²	—	2	1	no	—
655	C₂×C₄²	—	2	1	no	—
656	C₂×C₄²	—	2	1	no	—
657	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
658	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
659	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
660	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
661	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
662	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
663	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
664	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
665	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
666	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
667	C₂×C₄²	C₂⁴	1	1	yes	characteristic
668	C₂×C₄²	C₂⁴	1	1	yes	characteristic
669	C₂×C₄²	C₂⁴	1	1	yes	characteristic
670	C₂×C₄²	C₂⁴	1	1	yes	characteristic
671	C₂×C₄²	C₂⁴	1	1	yes	characteristic
672	C₂×C₄²	C₂⁴	1	1	yes	characteristic
673	#107	—	2	2	no	—
674	#107	—	4	1	no	—
675	#107	—	4	1	no	—
676	#107	—	4	1	no	—
677	#107	—	4	1	no	—
678	#107	—	4	1	no	—
679	#107	—	4	1	no	—
680	#106	—	2	2	no	—
681	#106	—	2	2	no	—
682	#106	—	4	1	no	—
683	#106	—	4	1	no	—
684	#106	—	4	1	no	—
685	#106	—	4	1	no	—
686	C₄⋊C₈	—	4	1	no	—
687	C₄⋊C₈	—	4	1	no	—
688	C₄⋊C₈	—	4	1	no	—
689	C₄⋊C₈	—	4	1	no	—
690	C₄⋊C₈	—	4	1	no	—
691	C₄⋊C₈	—	4	1	no	—
692	C₄⋊C₈	—	4	1	no	—
693	C₄⋊C₈	—	4	1	no	—
694	C₄⋊C₈	—	4	1	no	—
695	C₄⋊C₈	—	4	1	no	—
696	C₄⋊C₈	—	4	1	no	—
697	C₄⋊C₈	—	4	1	no	—
698	C₄⋊C₈	—	4	1	no	—
699	C₄⋊C₈	—	4	1	no	—
700	#103	—	2	2	no	—
701	#103	—	4	1	no	—
702	#103	—	4	1	no	—
703	#103	—	4	1	no	—
704	#103	—	4	1	no	—
705	#103	—	4	1	no	—
706	#103	—	4	1	no	—
707	#103	—	4	1	no	—
708	#103	—	4	1	no	—
709	#103	—	4	1	no	—
710	#103	—	4	1	no	—
711	#103	—	4	1	no	—
712	#102	—	2	2	no	—
713	#102	—	2	2	no	—
714	#102	—	2	2	no	—
715	#102	—	4	1	no	—
716	#102	—	4	1	no	—
717	#102	—	4	1	no	—
718	#102	—	4	1	no	—
719	#102	—	4	1	no	—
720	#102	—	4	1	no	—
721	#102	—	4	1	no	—
722	#102	—	4	1	no	—
723	#102	—	4	1	no	—
724	#102	—	4	1	no	—
725	#102	—	4	1	no	—
726	C₂²⋊C₈	—	2	2	no	—
727	C₂²⋊C₈	—	2	2	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	—	2	1	no	—
769	#95	—	2	1	no	—
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	#95	C₂×D₄	1	1	yes	characteristic
777	#95	C₂×D₄	1	1	yes	characteristic
778	C₂⁴	—	2	1	no	—
779	C₂⁴	—	2	1	no	—
780	C₂⁴	—	4	2	no	—
781	C₂⁴	—	4	2	no	—
782	C₂⁴	—	4	2	no	—
783	C₂⁴	—	4	2	no	—
784	C₂⁴	—	8	1	no	—
785	C₂⁴	—	8	1	no	—
786	C₂⁴	—	8	1	no	—
787	C₂⁴	C₂²×D₄	1	1	yes	characteristic
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	—	2	1	no	—
800	C₂×Q₈	—	4	2	no	—
801	C₂×Q₈	—	4	2	no	—
802	C₂×Q₈	—	8	1	no	—
803	C₂×D₄	—	2	1	no	—
804	C₂×D₄	—	2	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	—	4	4	no	—
815	C₂×D₄	—	4	4	no	—
816	C₂×D₄	—	4	2	no	—
817	C₂×D₄	—	4	2	no	—
818	C₂×D₄	—	8	2	no	—
819	C₂×D₄	—	8	2	no	—
820	C₂×D₄	—	8	1	no	—
821	C₂×D₄	2₋¹⁺⁴	1	2	yes	—
822	C₂²×C₄	—	2	2	no	—
823	C₂²×C₄	—	2	2	no	—
824	C₂²×C₄	—	2	1	no	—
825	C₂²×C₄	—	2	1	no	—
826	C₂²×C₄	—	2	1	no	—
827	C₂²×C₄	—	2	1	no	—
828	C₂²×C₄	—	2	1	no	—
829	C₂²×C₄	—	2	2	no	—
830	C₂²×C₄	—	2	1	no	—
831	C₂²×C₄	—	2	1	no	—
832	C₂²×C₄	—	2	1	no	—
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	—	4	1	no	—
844	C₂²×C₄	—	4	1	no	—
845	C₂²×C₄	—	4	2	no	—
846	C₂²×C₄	—	4	2	no	—
847	C₂²×C₄	—	4	2	no	—
848	C₂²×C₄	—	4	2	no	—
849	C₂²×C₄	—	4	2	no	—
850	C₂²×C₄	—	4	2	no	—
851	C₂²×C₄	—	4	2	no	—
852	C₂²×C₄	—	8	1	no	—
853	C₂²×C₄	—	8	1	no	—
854	C₂²×C₄	—	8	1	no	—
855	C₂²×C₄	—	8	1	no	—
856	C₂²×C₄	—	8	1	no	—
857	C₂²×C₄	—	8	1	no	—
858	C₂²×C₄	—	8	1	no	—
859	C₂²×C₄	—	8	1	no	—
860	C₂²×C₄	#137	1	4	yes	—
861	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
862	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
863	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
864	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
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	H(5,𝔽₂)	1	2	yes	—
875	C₂²×C₄	2₋¹⁺⁴	1	2	yes	—
876	C₂²×C₄	C₂⁵	1	1	yes	characteristic
877	Q₁₆	—	8	2	no	—
878	SD₁₆	—	8	2	no	—
879	SD₁₆	—	8	2	no	—
880	C₂×C₈	—	2	1	no	—
881	C₂×C₈	—	2	1	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	—	4	4	no	—
905	C₂×C₈	—	8	2	no	—
906	C₄⋊C₄	—	2	2	no	—
907	C₄⋊C₄	—	2	2	no	—
908	C₄⋊C₄	—	2	2	no	—
909	C₄⋊C₄	—	2	2	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	—	2	1	no	—
931	C₄⋊C₄	—	2	1	no	—
932	C₄⋊C₄	—	2	1	no	—
933	C₄⋊C₄	—	4	2	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	—	4	2	no	—
942	C₄⋊C₄	—	4	2	no	—
943	C₄⋊C₄	—	4	2	no	—
944	C₄⋊C₄	—	4	2	no	—
945	C₄⋊C₄	—	4	2	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	—	8	1	no	—
960	C₄⋊C₄	—	8	1	no	—
961	C₄⋊C₄	—	8	1	no	—
962	C₄⋊C₄	—	8	1	no	—
963	C₄⋊C₄	—	8	1	no	—
964	C₄⋊C₄	—	8	1	no	—
965	C₄⋊C₄	H(5,𝔽₂)	1	2	yes	—
966	C₂²⋊C₄	—	2	2	no	—
967	C₂²⋊C₄	—	2	2	no	—
968	C₂²⋊C₄	—	2	2	no	—
969	C₂²⋊C₄	—	4	2	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	—	4	2	no	—
981	C₂²⋊C₄	—	4	2	no	—
982	C₂²⋊C₄	—	4	2	no	—
983	C₂²⋊C₄	—	4	2	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	#135	1	4	yes	—
996	C₄²	—	2	2	no	—
997	C₄²	—	2	2	no	—
998	C₄²	—	2	2	no	—
999	C₄²	—	2	2	no	—
1000	C₄²	—	2	2	no	—
1001	C₄²	—	2	2	no	—
1002	C₄²	—	2	1	no	—
1003	C₄²	—	2	1	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	1	no	—
1018	C₄²	—	4	2	no	—
1019	C₄²	—	8	1	no	—
1020	C₄²	—	8	1	no	—
1021	C₄²	—	8	1	no	—
1022	C₄²	—	8	1	no	—
1023	C₄²	—	8	1	no	—
1024	C₂³	—	2	1	no	—
1025	C₂³	—	2	1	no	—
1026	C₂³	—	2	1	no	—
1027	C₂³	—	2	1	no	—
1028	C₂³	—	2	2	no	—
1029	C₂³	—	4	1	no	—
1030	C₂³	—	4	1	no	—
1031	C₂³	—	4	1	no	—
1032	C₂³	—	4	1	no	—
1033	C₂³	—	4	1	no	—
1034	C₂³	—	4	1	no	—
1035	C₂³	—	4	1	no	—
1036	C₂³	—	4	1	no	—
1037	C₂³	—	4	1	no	—
1038	C₂³	—	4	1	no	—
1039	C₂³	—	4	1	no	—
1040	C₂³	—	4	1	no	—
1041	C₂³	—	4	1	no	—
1042	C₂³	—	8	4	no	—
1043	C₂³	—	8	4	no	—
1044	C₂³	—	8	4	no	—
1045	C₂³	—	8	4	no	—
1046	C₂³	—	16	2	no	—
1047	C₂³	—	16	2	no	—
1048	C₂³	—	16	2	no	—
1049	C₂³	#537	1	2	yes	—
1050	C₂³	C₂×#135	1	2	yes	—
1051	C₂³	C₂×#137	1	2	yes	—
1052	C₂³	C₂³×D₄	1	1	yes	characteristic
1053	Q₈	—	4	1	no	—
1054	Q₈	—	4	1	no	—
1055	Q₈	—	4	1	no	—
1056	Q₈	—	4	1	no	—
1057	Q₈	—	4	1	no	—
1058	Q₈	—	4	1	no	—
1059	Q₈	—	4	1	no	—
1060	Q₈	—	4	1	no	—
1061	Q₈	—	8	4	no	—
1062	D₄	—	2	2	no	—
1063	D₄	—	2	2	no	—
1064	D₄	—	4	1	no	—
1065	D₄	—	4	1	no	—
1066	D₄	—	4	1	no	—
1067	D₄	—	4	1	no	—
1068	D₄	—	4	1	no	—
1069	D₄	—	4	1	no	—
1070	D₄	—	8	4	no	—
1071	C₂×C₄	—	2	1	no	—
1072	C₂×C₄	—	2	1	no	—
1073	C₂×C₄	—	2	1	no	—
1074	C₂×C₄	—	2	1	no	—
1075	C₂×C₄	—	2	1	no	—
1076	C₂×C₄	—	2	1	no	—
1077	C₂×C₄	—	2	1	no	—
1078	C₂×C₄	—	2	1	no	—
1079	C₂×C₄	—	2	8	no	—
1080	C₂×C₄	—	2	1	no	—
1081	C₂×C₄	—	2	1	no	—
1082	C₂×C₄	—	2	2	no	—
1083	C₂×C₄	—	2	2	no	—
1084	C₂×C₄	—	2	2	no	—
1085	C₂×C₄	—	2	2	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	2	no	—
1102	C₂×C₄	—	2	1	no	—
1103	C₂×C₄	—	2	1	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	—	4	1	no	—
1112	C₂×C₄	—	4	1	no	—
1113	C₂×C₄	—	4	1	no	—
1114	C₂×C₄	—	4	1	no	—
1115	C₂×C₄	—	4	1	no	—
1116	C₂×C₄	—	4	1	no	—
1117	C₂×C₄	—	4	1	no	—
1118	C₂×C₄	—	4	1	no	—
1119	C₂×C₄	—	4	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	—	8	4	no	—
1153	C₂×C₄	—	8	2	no	—
1154	C₂×C₄	—	8	4	no	—
1155	C₂×C₄	—	16	2	no	—
1156	C₂×C₄	—	16	2	no	—
1157	C₂×C₄	—	16	2	no	—
1158	C₂×C₄	#537	1	2	yes	—
1159	C₂×C₄	C₂×#135	1	2	yes	—
1160	C₂×C₄	C₂×#135	1	2	yes	—
1161	C₂×C₄	C₂×#137	1	2	yes	—
1162	C₂×C₄	C₂×#137	1	2	yes	—
1163	C₂×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
1164	C₂×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
1165	C₂×C₄	C₂×2₋¹⁺⁴	1	1	yes	characteristic
1166	C₂×C₄	C₂×2₋¹⁺⁴	1	1	yes	characteristic
1167	C₂×C₄	#585	1	1	yes	characteristic
1168	C₂×C₄	#585	1	1	yes	characteristic
1169	C₈	—	4	1	no	—
1170	C₈	—	4	1	no	—
1171	C₈	—	4	1	no	—
1172	C₈	—	4	1	no	—
1173	C₈	—	4	1	no	—
1174	C₈	—	4	1	no	—
1175	C₈	—	4	1	no	—
1176	C₈	—	4	1	no	—
1177	C₂²	—	2	2	no	—
1178	C₂²	—	2	2	no	—
1179	C₂²	—	2	2	no	—
1180	C₂²	—	2	2	no	—
1181	C₂²	—	2	2	no	—
1182	C₂²	—	2	2	no	—
1183	C₂²	—	4	2	no	—
1184	C₂²	—	4	2	no	—
1185	C₂²	—	4	2	no	—
1186	C₂²	—	8	1	no	—
1187	C₂²	—	8	1	no	—
1188	C₂²	—	8	1	no	—
1189	C₂²	—	8	1	no	—
1190	C₂²	—	8	1	no	—
1191	C₂²	—	8	1	no	—
1192	C₂²	—	8	1	no	—
1193	C₂²	—	8	1	no	—
1194	C₂²	—	8	1	no	—
1195	C₂²	—	8	1	no	—
1196	C₂²	—	8	1	no	—
1197	C₂²	—	16	8	no	—
1198	C₂²	#3248	1	4	yes	—
1199	C₂²	C₂×#537	1	1	yes	characteristic
1200	C₂²	#3488	1	1	yes	characteristic
1201	C₂²	#3489	1	1	yes	characteristic
1202	C₂²	C₂²×#135	1	1	yes	characteristic
1203	C₂²	C₂²×#137	1	1	yes	characteristic
1204	C₂²	#3585	1	1	yes	characteristic
1205	C₂²	#3585	1	1	yes	characteristic
1206	C₄	—	2	2	no	—
1207	C₄	—	2	2	no	—
1208	C₄	—	2	2	no	—
1209	C₄	—	2	2	no	—
1210	C₄	—	2	2	no	—
1211	C₄	—	4	1	no	—
1212	C₄	—	4	2	no	—
1213	C₄	—	4	1	no	—
1214	C₄	—	4	1	no	—
1215	C₄	—	4	1	no	—
1216	C₄	—	4	1	no	—
1217	C₄	—	4	1	no	—
1218	C₄	—	4	1	no	—
1219	C₄	—	4	1	no	—
1220	C₄	—	8	1	no	—
1221	C₄	—	8	1	no	—
1222	C₄	—	8	1	no	—
1223	C₄	—	8	1	no	—
1224	C₄	—	8	1	no	—
1225	C₄	—	8	1	no	—
1226	C₄	—	8	1	no	—
1227	C₄	—	8	1	no	—
1228	C₄	—	8	1	no	—
1229	C₄	—	8	1	no	—
1230	C₄	—	8	1	no	—
1231	C₄	—	8	1	no	—
1232	C₄	—	8	1	no	—
1233	C₄	#3535	1	1	yes	characteristic
1234	C₄	#3538	1	1	yes	characteristic
1235	C₄	#3542	1	1	yes	characteristic
1236	C₄	#3564	1	1	yes	characteristic
1237	C₂	—	2	4	no	—
1238	C₂	—	8	2	no	—
1239	C₂	—	16	1	no	—
1240	C₂	#41984	1	1	yes	characteristic
1241	C₂	C₂×#3248	1	1	yes	characteristic
1242	C₂	#60937	1	1	yes	characteristic
1243	C₂	#61955	1	1	yes	characteristic
1244	C₂	#61965	1	1	yes	characteristic
1245	C₂	#62103	1	1	yes	characteristic
1246	C₂	#62108	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×#117 ◁ G
LECS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
2. #36280	C₂	semidirect
3. #32861	C₂	semidirect
4. #32825	C₂	semidirect
5. #32532	C₂	semidirect
6. #32485	C₂	semidirect
7. #31976	C₂	semidirect
8. #31974	C₂	semidirect
9. #31906	C₂	semidirect
10. #31878	C₂	semidirect
11. #31235	C₂	semidirect
12. #31163	C₂	semidirect
13. #30146	C₂	semidirect
14. #30135	C₂	semidirect
15. #29995	C₂	semidirect
16. #29833	C₂	semidirect
17. #29771	C₂	semidirect
18. #29537	C₂	semidirect
19. #28281	C₂	semidirect
20. #26346	C₂	semidirect
21. #26340	C₂	semidirect
22. #26002	C₂	semidirect
24. #25206	C₂	semidirect
26. #24602	C₂	semidirect
31. #21972	C₂	semidirect
33. C₂×#479	C₂²	semidirect
34. C₂×#475	C₂²	semidirect
44. #2863	C₂²	semidirect
47. #2859	C₂²	semidirect
57. #2511	C₂²	semidirect
58. #2507	C₂²	semidirect
59. #2507	C₂²	semidirect
67. #2451	C₂²	semidirect
82. C₄×C₄⋊Q₈	C₂²	semidirect
84. #2295	C₂²	semidirect
89. #2101	C₂²	semidirect
90. #2097	C₂²	semidirect
91. #2096	C₂²	semidirect
93. #2088	C₂²	semidirect
94. #2088	C₂²	semidirect
95. #2088	C₂²	semidirect
96. #2087	C₂²	semidirect
97. #2087	C₂²	semidirect
98. #2087	C₂²	semidirect
99. #2087	C₂²	semidirect
100. #2086	C₂²	semidirect
101. #2083	C₂²	semidirect
102. #2072	C₂²	semidirect
105. #2068	C₂²	semidirect
106. #2068	C₂²	semidirect
107. #2068	C₂²	semidirect
108. #2068	C₂²	semidirect
109. #2068	C₂²	semidirect
110. #2068	C₂²	semidirect
111. #2068	C₂²	semidirect
117. #2066	C₂²	semidirect
118. #2066	C₂²	semidirect
129. #2059	C₂²	semidirect
130. #2059	C₂²	semidirect
131. #2058	C₂²	semidirect
132. #2056	C₂²	semidirect
133. #2056	C₂²	semidirect
134. #2056	C₂²	semidirect
145. #1989	C₂²	semidirect
151. #1949	C₂²	semidirect
152. #1949	C₂²	semidirect
153. #1948	C₂²	semidirect
154. #1947	C₂²	semidirect
155. #1942	C₂²	semidirect
156. #1942	C₂²	semidirect
157. #1939	C₂²	semidirect
158. #1939	C₂²	semidirect
159. #1939	C₂²	semidirect
160. #1939	C₂²	semidirect
163. #1933	C₂²	semidirect
164. #1933	C₂²	semidirect
165. #1928	C₂²	semidirect
169. #1920	C₂²	semidirect
170. #1920	C₂²	semidirect
171. #1919	C₂²	semidirect
172. #1918	C₂²	semidirect
176. #1878	C₂²	semidirect
181. #1865	C₂²	semidirect
182. #1865	C₂²	semidirect
191. #1842	C₂²	semidirect
192. #1842	C₂²	semidirect
193. #1831	C₂²	semidirect
194. #1831	C₂²	semidirect
197. #1803	C₂²	semidirect

Maximal subgroups

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

subgroup	index
#36293	2
#36280	2
#32861	2
#32825	2
#32532	2
#32485	2
#31976	2
#31974	2
#31906	2
#31878	2
#31235	2
#31163	2
#30146	2
#30135	2
#29995	2
#29833	2
#29771	2
#29537	2
#28281	2
#26346	2
#26340	2
#26002	2
#25950	2
#25206	2
#25084	2
#24602	2
#24530	2
#24501	2
#24479	2
C₂×#2065	2
#21972	2