Subgroups — #6768215

Order 512.

1644 conjugacy classes of subgroups.

The subgroup lattice has 1294 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#36416	C₂	1	1	yes	maximal, characteristic, complemented
2	#34700	C₂	1	1	yes	maximal, characteristic
3	#32959	C₂	1	1	yes	maximal, characteristic, complemented
4	#31581	C₂	1	1	yes	maximal, characteristic, complemented
5	#31463	C₂	1	1	yes	maximal, characteristic, complemented
6	#31379	C₂	1	1	yes	maximal, characteristic, complemented
7	#31135	C₂	1	1	yes	maximal, characteristic, complemented
8	#31106	C₂	1	1	yes	maximal, characteristic, complemented
9	#30951	C₂	1	1	yes	maximal, characteristic, complemented
10	#30811	C₂	1	1	yes	maximal, characteristic, complemented
11	#30654	C₂	1	1	yes	maximal, characteristic, complemented
12	#30171	C₂	1	1	yes	maximal, characteristic, complemented
13	#30082	C₂	1	1	yes	maximal, characteristic, complemented
14	#29580	C₂	1	1	yes	maximal, characteristic, complemented
15	#29393	C₂	1	1	yes	maximal, characteristic, complemented
16	#29242	C₂	1	1	yes	maximal, characteristic, complemented
17	#29164	C₂	1	1	yes	maximal, characteristic, complemented
18	#28787	C₂	1	1	yes	maximal, characteristic, complemented
19	#27281	C₂	1	1	yes	maximal, characteristic, complemented
20	#27271	C₂	1	1	yes	maximal, characteristic, complemented
21	#26223	C₂	1	1	yes	maximal, characteristic, complemented
22	#26151	C₂	1	1	yes	maximal, characteristic, complemented
23	#26075	C₂	1	1	yes	maximal, characteristic, complemented
24	#25675	C₂	1	1	yes	maximal, characteristic, complemented
25	#24886	C₂	1	1	yes	maximal, characteristic
26	#24886	C₂	1	1	yes	maximal, characteristic
27	#24068	C₂	1	1	yes	maximal, characteristic, complemented
28	#22788	C₂	1	1	yes	maximal, characteristic, complemented
29	#22224	C₂	1	1	yes	maximal, characteristic, complemented
30	#22080	C₂	1	1	yes	maximal, characteristic, complemented
31	#20873	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×#529	C₂²	1	1	yes	characteristic
33	C₂²×C₄×D₄	C₂²	1	1	yes	characteristic
34	C₂×#499	C₂²	1	1	yes	characteristic, complemented
35	C₂×#489	C₂²	1	1	yes	characteristic
36	C₂×#488	C₂²	1	1	yes	characteristic
37	C₂×#485	C₂²	1	1	yes	characteristic, complemented
38	C₂×#482	C₂²	1	1	yes	characteristic
39	C₂×#482	C₂²	1	1	yes	characteristic
40	C₂×#478	C₂²	1	1	yes	characteristic
41	C₂×#478	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	#2859	C₂²	1	1	yes	characteristic, complemented
46	#2851	C₂²	1	1	yes	characteristic
47	#2851	C₂²	1	1	yes	characteristic, complemented
48	#2589	—	2	1	no	—
49	#2589	—	2	1	no	—
50	#2587	—	2	1	no	—
51	#2587	—	2	1	no	—
52	#2580	—	2	1	no	—
53	#2571	C₂²	1	1	yes	characteristic, complemented
54	#2566	—	2	1	no	—
55	#2552	C₂²	1	1	yes	characteristic, complemented
56	#2480	—	2	1	no	—
57	#2468	—	2	1	no	—
58	#2457	—	2	1	no	—
59	#2454	C₂²	1	1	yes	characteristic
60	#2447	C₂²	1	1	yes	characteristic
61	#2442	C₂²	1	1	yes	characteristic
62	#2441	C₂²	1	1	yes	characteristic
63	#2441	C₂²	1	1	yes	characteristic, complemented
64	#2439	C₂²	1	1	yes	characteristic
65	#2439	C₂²	1	1	yes	characteristic, complemented
66	#2435	C₂²	1	1	yes	characteristic
67	#2427	C₂²	1	1	yes	characteristic
68	#2420	C₂²	1	1	yes	characteristic
69	#2418	—	2	1	no	—
70	#2417	C₂²	1	1	yes	characteristic
71	#2408	C₂²	1	1	yes	characteristic
72	#2395	—	2	1	no	—
73	#2392	—	2	1	no	—
74	#2370	—	2	1	no	—
75	#2355	—	2	1	no	—
76	#2354	C₂²	1	1	yes	characteristic
77	#2354	C₂²	1	1	yes	characteristic
78	C₄×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
79	C₄×#124	C₂²	1	1	yes	characteristic
80	C₄×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
81	C₄×#121	C₂²	1	1	yes	characteristic
82	C₄×#120	—	2	1	no	—
83	#2296	C₂²	1	1	yes	characteristic
84	#2296	C₂²	1	1	yes	characteristic, complemented
85	#2293	C₂²	1	1	yes	characteristic
86	#2280	—	2	1	no	—
87	C₄²×D₄	C₂²	1	1	yes	characteristic
88	#2101	C₂²	1	1	yes	characteristic, complemented
89	#2100	C₂²	1	1	yes	characteristic, complemented
90	#2097	C₂²	1	1	yes	characteristic, complemented
91	#2095	C₂²	1	1	yes	characteristic, complemented
92	#2094	C₂²	1	1	yes	characteristic
93	#2094	C₂²	1	1	yes	characteristic
94	#2088	C₂²	1	1	yes	characteristic, complemented
95	#2086	C₂²	1	1	yes	characteristic, complemented
96	#2085	C₂²	1	1	yes	characteristic, complemented
97	#2085	C₂²	1	1	yes	characteristic, complemented
98	#2085	C₂²	1	1	yes	characteristic, complemented
99	#2084	C₂²	1	1	yes	characteristic, complemented
100	#2083	C₂²	1	1	yes	characteristic, complemented
101	#2077	C₂²	1	1	yes	characteristic, complemented
102	#2075	C₂²	1	1	yes	characteristic, complemented
103	#2073	C₂²	1	1	yes	characteristic
104	#2072	C₂²	1	1	yes	characteristic, complemented
105	#2071	C₂²	1	1	yes	characteristic
106	#2071	C₂²	1	1	yes	characteristic
107	#2071	C₂²	1	1	yes	characteristic
108	#2068	C₂²	1	1	yes	characteristic, complemented
109	#2066	C₂²	1	1	yes	characteristic, complemented
110	#2059	C₂²	1	1	yes	characteristic, complemented
111	#2059	C₂²	1	1	yes	characteristic, complemented
112	#2059	C₂²	1	1	yes	characteristic, complemented
113	#2059	C₂²	1	1	yes	characteristic, complemented
114	#2057	C₂²	1	1	yes	characteristic, complemented
115	#2042	C₂²	1	1	yes	characteristic
116	#2042	C₂²	1	1	yes	characteristic
117	#2042	C₂²	1	1	yes	characteristic
118	#2042	C₂²	1	1	yes	characteristic
119	#2036	C₂²	1	1	yes	characteristic, complemented
120	#2035	C₂²	1	1	yes	characteristic, complemented
121	#2034	C₂²	1	1	yes	characteristic
122	#2034	C₂²	1	1	yes	characteristic
123	#2033	C₂²	1	1	yes	characteristic
124	#2033	C₂²	1	1	yes	characteristic
125	#2026	C₂²	1	1	yes	characteristic, complemented
126	#2025	C₂²	1	1	yes	characteristic
127	#2023	C₂²	1	1	yes	characteristic
128	#1993	C₂²	1	1	yes	characteristic, complemented
129	#1991	C₂²	1	1	yes	characteristic, complemented
130	#1959	C₂²	1	1	yes	characteristic
131	#1958	C₂²	1	1	yes	characteristic
132	#1943	C₂²	1	1	yes	characteristic, complemented
133	#1943	C₂²	1	1	yes	characteristic, complemented
134	#1942	C₂²	1	1	yes	characteristic, complemented
135	#1941	C₂²	1	1	yes	characteristic, complemented
136	#1936	C₂²	1	1	yes	characteristic
137	#1936	C₂²	1	1	yes	characteristic
138	#1934	C₂²	1	1	yes	characteristic
139	#1934	C₂²	1	1	yes	characteristic
140	#1927	C₂²	1	1	yes	characteristic, complemented
141	#1927	C₂²	1	1	yes	characteristic, complemented
142	#1925	C₂²	1	1	yes	characteristic
143	#1925	C₂²	1	1	yes	characteristic
144	#1925	C₂²	1	1	yes	characteristic
145	#1925	C₂²	1	1	yes	characteristic
146	#1924	C₂²	1	1	yes	characteristic, complemented
147	#1924	C₂²	1	1	yes	characteristic, complemented
148	#1921	C₂²	1	1	yes	characteristic, complemented
149	#1921	C₂²	1	1	yes	characteristic, complemented
150	#1920	C₂²	1	1	yes	characteristic, complemented
151	#1920	C₂²	1	1	yes	characteristic, complemented
152	#1919	C₂²	1	1	yes	characteristic, complemented
153	#1919	C₂²	1	1	yes	characteristic, complemented
154	#1916	C₂²	1	1	yes	characteristic, complemented
155	#1916	C₂²	1	1	yes	characteristic, complemented
156	#1894	C₂²	1	1	yes	characteristic
157	#1894	C₂²	1	1	yes	characteristic
158	#1875	C₂²	1	1	yes	characteristic
159	#1875	C₂²	1	1	yes	characteristic
160	#1873	C₂²	1	1	yes	characteristic
161	#1873	C₂²	1	1	yes	characteristic
162	#1873	C₂²	1	1	yes	characteristic, complemented
163	#1870	C₂²	1	1	yes	characteristic
164	#1870	C₂²	1	1	yes	characteristic
165	#1865	C₂²	1	1	yes	characteristic, complemented
166	#1865	C₂²	1	1	yes	characteristic, complemented
167	#1864	C₂²	1	1	yes	characteristic
168	#1864	C₂²	1	1	yes	characteristic
169	#1864	C₂²	1	1	yes	characteristic
170	#1864	C₂²	1	1	yes	characteristic
171	#1864	C₂²	1	1	yes	characteristic
172	#1864	C₂²	1	1	yes	characteristic
173	#1863	C₂²	1	1	yes	characteristic, complemented
174	#1863	C₂²	1	1	yes	characteristic, complemented
175	#1862	C₂²	1	1	yes	characteristic
176	#1862	C₂²	1	1	yes	characteristic
177	#1862	C₂²	1	1	yes	characteristic
178	#1862	C₂²	1	1	yes	characteristic
179	#1862	C₂²	1	1	yes	characteristic
180	#1862	C₂²	1	1	yes	characteristic
181	#1854	C₂²	1	1	yes	characteristic
182	#1854	C₂²	1	1	yes	characteristic
183	#1854	C₂²	1	1	yes	characteristic, complemented
184	#1853	C₂²	1	1	yes	characteristic
185	#1852	C₂²	1	1	yes	characteristic
186	#1847	C₂²	1	1	yes	characteristic, complemented
187	#1839	C₂²	1	1	yes	characteristic, complemented
188	#1825	C₂²	1	1	yes	characteristic, complemented
189	#1817	C₂²	1	1	yes	characteristic, complemented
190	#1809	C₂²	1	1	yes	characteristic
191	#1809	C₂²	1	1	yes	characteristic
192	#1804	C₂²	1	1	yes	characteristic
193	#1804	C₂²	1	1	yes	characteristic
194	#1797	C₂²	1	1	yes	characteristic
195	#1786	C₂²	1	1	yes	characteristic
196	#1786	C₂²	1	1	yes	characteristic
197	#1753	C₂²	1	1	yes	characteristic
198	#1753	C₂²	1	1	yes	characteristic
199	C₄×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
200	#1745	C₂²	1	1	yes	characteristic, complemented
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×M₁₆	C₂³	1	1	yes	characteristic
206	C₂²×M₁₆	C₂³	1	1	yes	characteristic
207	C₂×C₄⋊Q₈	C₂³	1	1	yes	characteristic
208	#529	—	4	2	no	—
209	#529	—	4	2	no	—
210	C₂×#126	—	2	1	no	—
211	C₂×#125	—	2	1	no	—
212	C₂×#125	C₂³	1	1	yes	characteristic
213	C₂×#125	C₂³	1	1	yes	characteristic
214	C₂×#125	C₂³	1	1	yes	characteristic
215	C₂×#124	C₂³	1	1	yes	characteristic
216	C₂×#124	C₂³	1	1	yes	characteristic
217	C₂×#123	—	2	1	no	—
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×D₄	—	2	1	no	—
226	C₂×C₄×D₄	—	2	1	no	—
227	C₂×C₄×D₄	—	2	1	no	—
228	C₂×C₄×D₄	—	2	1	no	—
229	C₂×C₄×D₄	—	4	2	no	—
230	C₂×C₄×D₄	—	4	2	no	—
231	C₂×C₄×D₄	D₄	1	1	yes	characteristic
232	C₂×C₄×D₄	D₄	1	1	yes	characteristic
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×#117	—	2	1	no	—
239	C₂×#117	—	2	1	no	—
240	C₂×#117	C₂³	1	1	yes	characteristic
241	C₂×#117	C₂³	1	1	yes	characteristic
242	C₂×#117	C₂³	1	1	yes	characteristic
243	C₂×#117	C₂³	1	1	yes	characteristic
244	C₂²×C₄⋊C₄	C₂³	1	1	yes	characteristic
245	C₂²×C₂²⋊C₄	—	2	1	no	—
246	C₂²×C₄²	C₂³	1	1	yes	characteristic
247	C₂²×C₄²	C₂³	1	1	yes	characteristic
248	#499	—	4	2	no	—
249	#489	—	2	4	no	—
250	#488	—	4	2	no	—
251	#485	—	4	2	no	—
252	#482	—	2	4	no	—
253	#482	—	4	2	no	—
254	#478	—	4	2	no	—
255	#478	—	4	2	no	—
256	#428	—	4	2	no	—
257	C₂×#107	C₂³	1	1	yes	characteristic
258	C₂×#107	C₂³	1	1	yes	characteristic
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×#107	C₂³	1	1	yes	characteristic
264	C₂×#107	C₂³	1	1	yes	characteristic
265	C₂×#106	C₂³	1	1	yes	characteristic
266	C₂×#106	C₂³	1	1	yes	characteristic
267	C₂×#106	C₂³	1	1	yes	characteristic
268	C₂×#106	C₂³	1	1	yes	characteristic
269	C₂×#106	C₂³	1	1	yes	characteristic
270	C₂×#106	C₂³	1	1	yes	characteristic
271	C₂×#106	C₂³	1	1	yes	characteristic
272	C₂×#106	C₂³	1	1	yes	characteristic
273	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
274	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
275	#418	—	2	4	no	—
276	#418	—	4	2	no	—
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×#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×#102	C₂³	1	1	yes	characteristic
300	C₂×#102	C₂³	1	1	yes	characteristic
301	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
302	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
303	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
304	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
305	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
306	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
307	C₂×#97	C₂³	1	1	yes	characteristic
308	C₂×#97	C₂³	1	1	yes	characteristic
309	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
310	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
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	#399	—	2	1	no	—
317	#398	—	2	1	no	—
318	#398	—	2	1	no	—
319	#398	—	2	1	no	—
320	#398	—	2	1	no	—
321	#397	—	2	1	no	—
322	#397	—	2	1	no	—
323	#397	—	2	1	no	—
324	#397	—	2	1	no	—
325	#396	—	2	1	no	—
326	#396	—	2	1	no	—
327	#396	—	2	1	no	—
328	#396	—	2	1	no	—
329	#396	—	2	1	no	—
330	#396	—	2	1	no	—
331	#394	—	2	1	no	—
332	#394	—	2	1	no	—
333	#394	—	2	1	no	—
334	#394	—	2	1	no	—
335	#394	—	2	1	no	—
336	#393	—	2	1	no	—
337	#393	—	2	1	no	—
338	#392	—	2	1	no	—
339	#391	—	2	1	no	—
340	#391	—	2	1	no	—
341	#391	—	2	1	no	—
342	#391	C₂³	1	1	yes	characteristic
343	#391	C₂³	1	1	yes	characteristic
344	#390	—	2	1	no	—
345	#390	—	2	1	no	—
346	#390	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	#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	—	2	1	no	—
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	#388	—	2	1	no	—
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	#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	#386	—	2	1	no	—
390	#386	—	2	1	no	—
391	#386	—	2	1	no	—
392	#386	—	2	1	no	—
393	#385	—	2	1	no	—
394	#385	—	2	1	no	—
395	#385	—	2	1	no	—
396	#385	—	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	#384	—	2	1	no	—
406	#384	C₂³	1	1	yes	characteristic
407	#384	C₂³	1	1	yes	characteristic
408	#384	C₂³	1	1	yes	characteristic
409	#382	—	2	1	no	—
410	#382	—	2	1	no	—
411	#382	C₂³	1	1	yes	characteristic
412	#382	C₂³	1	1	yes	characteristic
413	#382	C₂³	1	1	yes	characteristic
414	#381	—	2	1	no	—
415	#381	—	2	1	no	—
416	#380	—	2	1	no	—
417	#380	—	2	1	no	—
418	#380	—	2	1	no	—
419	#380	—	2	1	no	—
420	#380	C₂³	1	1	yes	characteristic
421	#380	C₂³	1	1	yes	characteristic
422	#380	C₂³	1	1	yes	characteristic
423	#380	C₂³	1	1	yes	characteristic
424	#380	C₂³	1	1	yes	characteristic
425	#380	C₂³	1	1	yes	characteristic
426	#379	—	2	1	no	—
427	#379	—	2	1	no	—
428	#379	—	2	1	no	—
429	C₄×C₄⋊C₄	—	2	1	no	—
430	C₄×C₄⋊C₄	—	2	1	no	—
431	C₄×C₄⋊C₄	—	2	1	no	—
432	C₄×C₄⋊C₄	—	2	1	no	—
433	C₄×C₄⋊C₄	—	2	1	no	—
434	C₄×C₄⋊C₄	—	2	1	no	—
435	C₄×C₄⋊C₄	—	2	1	no	—
436	C₄×C₄⋊C₄	—	2	1	no	—
437	C₄×C₄⋊C₄	D₄	1	1	yes	characteristic
438	C₄×C₄⋊C₄	D₄	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×C₂²⋊C₄	—	2	1	no	—
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	D₄	1	1	yes	characteristic
449	C₄×C₂²⋊C₄	D₄	1	1	yes	characteristic
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	C₄³	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	C₂⁴	1	1	yes	characteristic
496	C₂²×D₄	—	2	2	no	—
497	C₂²×D₄	—	2	2	no	—
498	C₂²×D₄	—	2	1	no	—
499	C₂²×D₄	—	2	1	no	—
500	C₂²×D₄	—	2	1	no	—
501	C₂²×D₄	—	2	2	no	—
502	C₂²×D₄	—	2	2	no	—
503	C₂²×D₄	—	4	1	no	—
504	C₂²×D₄	—	4	1	no	—
505	C₂²×D₄	C₂×D₄	1	1	yes	characteristic
506	C₂²×D₄	C₂⁴	1	1	yes	characteristic
507	C₂²×D₄	C₂⁴	1	1	yes	characteristic
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	—	4	4	no	—
514	C₂³×C₄	—	4	4	no	—
515	C₂³×C₄	—	8	2	no	—
516	C₂³×C₄	C₂×D₄	1	1	yes	characteristic
517	C₂³×C₄	C₂×D₄	1	1	yes	characteristic
518	C₂³×C₄	C₂×D₄	1	1	yes	characteristic
519	C₂³×C₄	C₂×D₄	1	1	yes	characteristic
520	C₂³×C₄	C₂⁴	1	1	yes	characteristic
521	C₂³×C₄	C₂⁴	1	1	yes	characteristic
522	C₂×M₁₆	—	2	2	no	—
523	C₂×M₁₆	—	2	2	no	—
524	C₂×M₁₆	—	2	2	no	—
525	C₂×M₁₆	—	4	1	no	—
526	C₂×M₁₆	—	4	1	no	—
527	C₂×M₁₆	—	4	1	no	—
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	C₂²×C₈	C₂⁴	1	1	yes	characteristic
535	C₂²×C₈	C₂⁴	1	1	yes	characteristic
536	C₄⋊Q₈	—	2	2	no	—
537	C₄⋊Q₈	—	4	1	no	—
538	#126	—	4	4	no	—
539	#125	—	2	2	no	—
540	#125	—	4	1	no	—
541	#125	—	4	1	no	—
542	#125	—	4	1	no	—
543	#125	—	4	1	no	—
544	#125	—	4	1	no	—
545	#125	—	4	4	no	—
546	#124	—	2	2	no	—
547	#124	—	2	2	no	—
548	#124	—	4	1	no	—
549	#124	—	4	1	no	—
550	#123	—	4	4	no	—
551	C₂²⋊Q₈	—	2	2	no	—
552	C₂²⋊Q₈	—	2	2	no	—
553	C₂²⋊Q₈	—	2	2	no	—
554	C₂²⋊Q₈	—	4	1	no	—
555	#121	—	2	2	no	—
556	#121	—	2	2	no	—
557	#121	—	4	1	no	—
558	#121	—	4	1	no	—
559	#120	—	4	4	no	—
560	C₄×Q₈	—	4	1	no	—
561	C₄×Q₈	—	4	1	no	—
562	C₄×Q₈	—	4	4	no	—
563	C₄×D₄	—	2	2	no	—
564	C₄×D₄	—	2	2	no	—
565	C₄×D₄	—	2	2	no	—
566	C₄×D₄	—	2	2	no	—
567	C₄×D₄	—	2	2	no	—
568	C₄×D₄	—	2	2	no	—
569	C₄×D₄	—	4	1	no	—
570	C₄×D₄	—	4	1	no	—
571	C₄×D₄	—	4	1	no	—
572	C₄×D₄	—	4	1	no	—
573	C₄×D₄	—	4	2	no	—
574	C₄×D₄	—	4	2	no	—
575	C₄×D₄	—	4	4	no	—
576	C₄×D₄	—	4	4	no	—
577	C₄×D₄	—	4	4	no	—
578	C₄×D₄	—	8	2	no	—
579	#117	—	2	2	no	—
580	#117	—	2	2	no	—
581	#117	—	4	1	no	—
582	#117	—	4	1	no	—
583	#117	—	4	4	no	—
584	#117	—	4	1	no	—
585	#117	—	4	1	no	—
586	#117	—	4	1	no	—
587	#117	—	4	1	no	—
588	#117	—	8	2	no	—
589	C₂×C₄⋊C₄	—	2	2	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	—	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	—	4	1	no	—
622	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
623	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
624	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
625	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
626	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
627	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
628	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
629	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
630	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
631	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
632	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
633	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
634	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
635	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
636	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
637	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
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	—	2	1	no	—
649	C₂×C₂²⋊C₄	—	2	1	no	—
650	C₂×C₂²⋊C₄	—	2	1	no	—
651	C₂×C₂²⋊C₄	—	2	1	no	—
652	C₂×C₂²⋊C₄	—	2	1	no	—
653	C₂×C₂²⋊C₄	—	2	1	no	—
654	C₂×C₂²⋊C₄	—	2	1	no	—
655	C₂×C₂²⋊C₄	—	2	1	no	—
656	C₂×C₂²⋊C₄	—	2	1	no	—
657	C₂×C₂²⋊C₄	—	2	1	no	—
658	C₂×C₂²⋊C₄	—	2	1	no	—
659	C₂×C₂²⋊C₄	—	2	1	no	—
660	C₂×C₂²⋊C₄	—	2	1	no	—
661	C₂×C₂²⋊C₄	—	2	1	no	—
662	C₂×C₂²⋊C₄	—	2	1	no	—
663	C₂×C₂²⋊C₄	—	2	1	no	—
664	C₂×C₂²⋊C₄	—	2	1	no	—
665	C₂×C₂²⋊C₄	—	2	1	no	—
666	C₂×C₂²⋊C₄	—	2	1	no	—
667	C₂×C₂²⋊C₄	—	2	1	no	—
668	C₂×C₂²⋊C₄	—	4	4	no	—
669	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
670	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
671	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
672	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
673	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
674	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
675	C₂×C₄²	—	2	1	no	—
676	C₂×C₄²	—	2	1	no	—
677	C₂×C₄²	—	2	1	no	—
678	C₂×C₄²	—	2	1	no	—
679	C₂×C₄²	—	2	1	no	—
680	C₂×C₄²	—	2	1	no	—
681	C₂×C₄²	—	2	1	no	—
682	C₂×C₄²	—	2	1	no	—
683	C₂×C₄²	—	4	1	no	—
684	C₂×C₄²	—	4	1	no	—
685	C₂×C₄²	—	4	1	no	—
686	C₂×C₄²	—	4	1	no	—
687	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
688	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
689	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
690	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
691	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
692	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
693	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
694	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
695	C₂×C₄²	C₂⁴	1	1	yes	characteristic
696	C₂×C₄²	C₂⁴	1	1	yes	characteristic
697	C₂×C₄²	C₂⁴	1	1	yes	characteristic
698	C₂×C₄²	C₂⁴	1	1	yes	characteristic
699	C₂×C₄²	C₂⁴	1	1	yes	characteristic
700	#107	—	2	2	no	—
701	#107	—	2	2	no	—
702	#107	—	2	2	no	—
703	#107	—	4	1	no	—
704	#107	—	4	1	no	—
705	#107	—	4	1	no	—
706	#107	—	4	1	no	—
707	#107	—	4	1	no	—
708	#106	—	2	2	no	—
709	#106	—	2	2	no	—
710	#106	—	2	2	no	—
711	#106	—	4	1	no	—
712	#106	—	4	1	no	—
713	#106	—	4	1	no	—
714	#106	—	4	1	no	—
715	#106	—	4	1	no	—
716	C₄⋊C₈	—	4	1	no	—
717	C₄⋊C₈	—	4	1	no	—
718	#103	—	2	2	no	—
719	#103	—	2	2	no	—
720	#103	—	4	1	no	—
721	#103	—	4	1	no	—
722	#103	—	4	1	no	—
723	#103	—	4	1	no	—
724	#103	—	4	1	no	—
725	#103	—	4	1	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	—	2	2	no	—
734	#102	—	2	2	no	—
735	#102	—	4	1	no	—
736	#102	—	4	1	no	—
737	#102	—	4	1	no	—
738	#102	—	4	1	no	—
739	#102	—	4	1	no	—
740	#102	—	4	1	no	—
741	#102	#41	1	4	yes	—
742	C₂²⋊C₈	—	2	2	no	—
743	C₂²⋊C₈	—	2	2	no	—
744	C₂²⋊C₈	—	2	2	no	—
745	C₂²⋊C₈	—	4	1	no	—
746	C₂²⋊C₈	—	4	1	no	—
747	C₂²⋊C₈	—	4	1	no	—
748	#97	—	2	2	no	—
749	#97	—	4	1	no	—
750	C₄×C₈	—	4	1	no	—
751	C₄×C₈	—	4	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	—	2	1	no	—
782	#95	—	2	1	no	—
783	#95	—	2	1	no	—
784	#95	—	2	1	no	—
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	—	4	2	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	C₂⁴	C₂²×D₄	1	1	yes	characteristic
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	—	4	2	no	—
809	C₂×Q₈	—	4	2	no	—
810	C₂×Q₈	—	8	1	no	—
811	C₂×D₄	—	2	8	no	—
812	C₂×D₄	—	2	2	no	—
813	C₂×D₄	—	2	2	no	—
814	C₂×D₄	—	2	1	no	—
815	C₂×D₄	—	2	1	no	—
816	C₂×D₄	—	2	1	no	—
817	C₂×D₄	—	2	1	no	—
818	C₂×D₄	—	2	1	no	—
819	C₂×D₄	—	2	1	no	—
820	C₂×D₄	—	2	1	no	—
821	C₂×D₄	—	2	1	no	—
822	C₂×D₄	—	2	1	no	—
823	C₂×D₄	—	2	1	no	—
824	C₂×D₄	—	4	4	no	—
825	C₂×D₄	—	4	4	no	—
826	C₂×D₄	—	4	1	no	—
827	C₂×D₄	—	4	2	no	—
828	C₂×D₄	—	4	2	no	—
829	C₂×D₄	—	4	4	no	—
830	C₂×D₄	—	4	2	no	—
831	C₂×D₄	—	4	2	no	—
832	C₂×D₄	—	4	2	no	—
833	C₂×D₄	—	4	2	no	—
834	C₂×D₄	—	4	2	no	—
835	C₂×D₄	—	8	1	no	—
836	C₂×D₄	—	8	1	no	—
837	C₂×D₄	C₂×#41	1	2	yes	—
838	C₂×D₄	H(5,𝔽₂)	1	2	yes	—
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	1	no	—
845	C₂²×C₄	—	2	1	no	—
846	C₂²×C₄	—	2	2	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	2	no	—
854	C₂²×C₄	—	2	1	no	—
855	C₂²×C₄	—	2	1	no	—
856	C₂²×C₄	—	2	1	no	—
857	C₂²×C₄	—	2	1	no	—
858	C₂²×C₄	—	2	1	no	—
859	C₂²×C₄	—	2	1	no	—
860	C₂²×C₄	—	2	1	no	—
861	C₂²×C₄	—	2	1	no	—
862	C₂²×C₄	—	2	1	no	—
863	C₂²×C₄	—	2	1	no	—
864	C₂²×C₄	—	2	1	no	—
865	C₂²×C₄	—	2	1	no	—
866	C₂²×C₄	—	4	1	no	—
867	C₂²×C₄	—	4	1	no	—
868	C₂²×C₄	—	4	1	no	—
869	C₂²×C₄	—	4	1	no	—
870	C₂²×C₄	—	4	1	no	—
871	C₂²×C₄	—	4	1	no	—
872	C₂²×C₄	—	4	1	no	—
873	C₂²×C₄	—	4	1	no	—
874	C₂²×C₄	—	4	1	no	—
875	C₂²×C₄	—	4	1	no	—
876	C₂²×C₄	—	4	2	no	—
877	C₂²×C₄	—	4	2	no	—
878	C₂²×C₄	—	4	2	no	—
879	C₂²×C₄	—	4	2	no	—
880	C₂²×C₄	—	4	2	no	—
881	C₂²×C₄	—	4	2	no	—
882	C₂²×C₄	—	4	2	no	—
883	C₂²×C₄	—	4	2	no	—
884	C₂²×C₄	—	4	2	no	—
885	C₂²×C₄	—	4	2	no	—
886	C₂²×C₄	—	4	2	no	—
887	C₂²×C₄	—	8	1	no	—
888	C₂²×C₄	—	8	1	no	—
889	C₂²×C₄	—	8	1	no	—
890	C₂²×C₄	—	8	16	no	—
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	2₋¹⁺⁴	1	2	yes	—
904	C₂²×C₄	2₋¹⁺⁴	1	2	yes	—
905	C₂²×C₄	C₂⁵	1	1	yes	characteristic
906	M₁₆	—	4	4	no	—
907	M₁₆	—	8	2	no	—
908	C₂×C₈	—	2	1	no	—
909	C₂×C₈	—	2	1	no	—
910	C₂×C₈	—	2	1	no	—
911	C₂×C₈	—	2	1	no	—
912	C₂×C₈	—	2	1	no	—
913	C₂×C₈	—	2	1	no	—
914	C₂×C₈	—	2	1	no	—
915	C₂×C₈	—	2	1	no	—
916	C₂×C₈	—	2	1	no	—
917	C₂×C₈	—	2	1	no	—
918	C₂×C₈	—	2	1	no	—
919	C₂×C₈	—	2	1	no	—
920	C₂×C₈	—	2	1	no	—
921	C₂×C₈	—	2	1	no	—
922	C₂×C₈	—	2	1	no	—
923	C₂×C₈	—	2	1	no	—
924	C₂×C₈	—	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	C₂×#41	1	2	yes	—
932	C₄⋊C₄	—	2	2	no	—
933	C₄⋊C₄	—	2	2	no	—
934	C₄⋊C₄	—	2	1	no	—
935	C₄⋊C₄	—	2	1	no	—
936	C₄⋊C₄	—	2	1	no	—
937	C₄⋊C₄	—	2	1	no	—
938	C₄⋊C₄	—	2	1	no	—
939	C₄⋊C₄	—	2	1	no	—
940	C₄⋊C₄	—	2	1	no	—
941	C₄⋊C₄	—	2	1	no	—
942	C₄⋊C₄	—	2	1	no	—
943	C₄⋊C₄	—	2	1	no	—
944	C₄⋊C₄	—	2	1	no	—
945	C₄⋊C₄	—	2	1	no	—
946	C₄⋊C₄	—	2	1	no	—
947	C₄⋊C₄	—	2	1	no	—
948	C₄⋊C₄	—	2	1	no	—
949	C₄⋊C₄	—	2	1	no	—
950	C₄⋊C₄	—	2	1	no	—
951	C₄⋊C₄	—	2	1	no	—
952	C₄⋊C₄	—	2	1	no	—
953	C₄⋊C₄	—	2	1	no	—
954	C₄⋊C₄	—	2	1	no	—
955	C₄⋊C₄	—	2	1	no	—
956	C₄⋊C₄	—	2	1	no	—
957	C₄⋊C₄	—	2	1	no	—
958	C₄⋊C₄	—	4	1	no	—
959	C₄⋊C₄	—	4	2	no	—
960	C₄⋊C₄	—	4	2	no	—
961	C₄⋊C₄	—	4	2	no	—
962	C₄⋊C₄	—	4	2	no	—
963	C₄⋊C₄	—	4	2	no	—
964	C₄⋊C₄	—	4	2	no	—
965	C₄⋊C₄	—	4	2	no	—
966	C₄⋊C₄	—	4	2	no	—
967	C₄⋊C₄	—	4	2	no	—
968	C₄⋊C₄	—	4	2	no	—
969	C₄⋊C₄	—	4	2	no	—
970	C₄⋊C₄	—	4	2	no	—
971	C₄⋊C₄	—	4	2	no	—
972	C₄⋊C₄	—	4	2	no	—
973	C₄⋊C₄	—	4	2	no	—
974	C₄⋊C₄	—	4	2	no	—
975	C₄⋊C₄	—	8	1	no	—
976	C₄⋊C₄	—	8	1	no	—
977	C₄⋊C₄	—	8	1	no	—
978	C₄⋊C₄	—	8	1	no	—
979	C₄⋊C₄	—	8	1	no	—
980	C₄⋊C₄	—	8	1	no	—
981	C₄⋊C₄	—	8	1	no	—
982	C₄⋊C₄	—	8	1	no	—
983	C₄⋊C₄	—	8	1	no	—
984	C₄⋊C₄	—	8	1	no	—
985	C₄⋊C₄	—	8	1	no	—
986	C₄⋊C₄	—	8	1	no	—
987	C₄⋊C₄	—	8	1	no	—
988	C₄⋊C₄	—	8	1	no	—
989	C₄⋊C₄	—	8	1	no	—
990	C₄⋊C₄	C₂×#41	1	2	yes	—
991	C₄⋊C₄	H(5,𝔽₂)	1	2	yes	—
992	C₂²⋊C₄	—	2	4	no	—
993	C₂²⋊C₄	—	2	2	no	—
994	C₂²⋊C₄	—	2	2	no	—
995	C₂²⋊C₄	—	4	1	no	—
996	C₂²⋊C₄	—	4	1	no	—
997	C₂²⋊C₄	—	4	1	no	—
998	C₂²⋊C₄	—	4	1	no	—
999	C₂²⋊C₄	—	4	2	no	—
1000	C₂²⋊C₄	—	4	2	no	—
1001	C₂²⋊C₄	—	4	2	no	—
1002	C₂²⋊C₄	—	4	2	no	—
1003	C₂²⋊C₄	—	4	2	no	—
1004	C₂²⋊C₄	—	4	2	no	—
1005	C₂²⋊C₄	—	4	2	no	—
1006	C₂²⋊C₄	—	4	2	no	—
1007	C₂²⋊C₄	—	4	2	no	—
1008	C₂²⋊C₄	—	4	2	no	—
1009	C₂²⋊C₄	—	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	—	8	1	no	—
1016	C₂²⋊C₄	—	8	1	no	—
1017	C₂²⋊C₄	—	8	1	no	—
1018	C₂²⋊C₄	—	8	1	no	—
1019	C₂²⋊C₄	—	8	1	no	—
1020	C₂²⋊C₄	—	8	1	no	—
1021	C₂²⋊C₄	—	8	1	no	—
1022	C₂²⋊C₄	—	8	1	no	—
1023	C₂²⋊C₄	—	8	1	no	—
1024	C₂²⋊C₄	—	8	1	no	—
1025	C₂²⋊C₄	—	8	1	no	—
1026	C₂²⋊C₄	—	8	1	no	—
1027	C₂²⋊C₄	—	8	1	no	—
1028	C₄²	—	2	2	no	—
1029	C₄²	—	2	2	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	—	2	1	no	—
1040	C₄²	—	4	1	no	—
1041	C₄²	—	4	1	no	—
1042	C₄²	—	4	1	no	—
1043	C₄²	—	4	1	no	—
1044	C₄²	—	4	1	no	—
1045	C₄²	—	4	1	no	—
1046	C₄²	—	4	2	no	—
1047	C₄²	—	4	2	no	—
1048	C₄²	—	4	2	no	—
1049	C₄²	—	4	2	no	—
1050	C₄²	—	4	2	no	—
1051	C₄²	—	4	2	no	—
1052	C₄²	—	8	1	no	—
1053	C₄²	—	8	1	no	—
1054	C₂³	—	2	1	no	—
1055	C₂³	—	2	1	no	—
1056	C₂³	—	2	1	no	—
1057	C₂³	—	2	1	no	—
1058	C₂³	—	2	1	no	—
1059	C₂³	—	2	1	no	—
1060	C₂³	—	2	1	no	—
1061	C₂³	—	2	1	no	—
1062	C₂³	—	2	1	no	—
1063	C₂³	—	2	2	no	—
1064	C₂³	—	2	1	no	—
1065	C₂³	—	2	2	no	—
1066	C₂³	—	2	1	no	—
1067	C₂³	—	2	1	no	—
1068	C₂³	—	2	1	no	—
1069	C₂³	—	4	8	no	—
1070	C₂³	—	4	1	no	—
1071	C₂³	—	4	1	no	—
1072	C₂³	—	4	1	no	—
1073	C₂³	—	4	1	no	—
1074	C₂³	—	4	1	no	—
1075	C₂³	—	4	1	no	—
1076	C₂³	—	4	1	no	—
1077	C₂³	—	4	1	no	—
1078	C₂³	—	4	1	no	—
1079	C₂³	—	4	1	no	—
1080	C₂³	—	4	1	no	—
1081	C₂³	—	4	1	no	—
1082	C₂³	—	8	4	no	—
1083	C₂³	—	8	4	no	—
1084	C₂³	—	8	4	no	—
1085	C₂³	—	8	4	no	—
1086	C₂³	—	8	4	no	—
1087	C₂³	—	8	4	no	—
1088	C₂³	#536	1	2	yes	—
1089	C₂³	C₂³×D₄	1	1	yes	characteristic
1090	Q₈	—	4	1	no	—
1091	Q₈	—	4	1	no	—
1092	Q₈	—	4	1	no	—
1093	Q₈	—	4	1	no	—
1094	Q₈	—	8	4	no	—
1095	D₄	—	2	2	no	—
1096	D₄	—	2	2	no	—
1097	D₄	—	2	2	no	—
1098	D₄	—	2	2	no	—
1099	D₄	—	4	4	no	—
1100	D₄	—	4	8	no	—
1101	D₄	—	4	1	no	—
1102	D₄	—	4	1	no	—
1103	D₄	—	4	1	no	—
1104	D₄	—	4	1	no	—
1105	D₄	—	8	4	no	—
1106	D₄	—	8	4	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	2	no	—
1114	C₂×C₄	—	2	2	no	—
1115	C₂×C₄	—	2	2	no	—
1116	C₂×C₄	—	2	2	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	1	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	2	no	—
1131	C₂×C₄	—	2	1	no	—
1132	C₂×C₄	—	2	1	no	—
1133	C₂×C₄	—	2	1	no	—
1134	C₂×C₄	—	2	1	no	—
1135	C₂×C₄	—	2	1	no	—
1136	C₂×C₄	—	2	1	no	—
1137	C₂×C₄	—	2	1	no	—
1138	C₂×C₄	—	2	2	no	—
1139	C₂×C₄	—	2	1	no	—
1140	C₂×C₄	—	2	1	no	—
1141	C₂×C₄	—	2	1	no	—
1142	C₂×C₄	—	2	1	no	—
1143	C₂×C₄	—	2	1	no	—
1144	C₂×C₄	—	2	1	no	—
1145	C₂×C₄	—	2	1	no	—
1146	C₂×C₄	—	4	8	no	—
1147	C₂×C₄	—	4	4	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	—	4	1	no	—
1179	C₂×C₄	—	4	1	no	—
1180	C₂×C₄	—	4	1	no	—
1181	C₂×C₄	—	4	1	no	—
1182	C₂×C₄	—	4	1	no	—
1183	C₂×C₄	—	4	1	no	—
1184	C₂×C₄	—	4	1	no	—
1185	C₂×C₄	—	4	1	no	—
1186	C₂×C₄	—	4	1	no	—
1187	C₂×C₄	—	4	1	no	—
1188	C₂×C₄	—	4	1	no	—
1189	C₂×C₄	—	4	1	no	—
1190	C₂×C₄	—	4	1	no	—
1191	C₂×C₄	—	4	1	no	—
1192	C₂×C₄	—	8	2	no	—
1193	C₂×C₄	—	8	4	no	—
1194	C₂×C₄	—	8	2	no	—
1195	C₂×C₄	—	8	2	no	—
1196	C₂×C₄	—	8	4	no	—
1197	C₂×C₄	—	8	4	no	—
1198	C₂×C₄	—	8	4	no	—
1199	C₂×C₄	#536	1	2	yes	—
1200	C₂×C₄	#575	1	2	yes	—
1201	C₂×C₄	#575	1	2	yes	—
1202	C₂×C₄	C₂²×#41	1	1	yes	characteristic
1203	C₂×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
1204	C₂×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
1205	C₂×C₄	C₂×2₋¹⁺⁴	1	1	yes	characteristic
1206	C₂×C₄	C₂×2₋¹⁺⁴	1	1	yes	characteristic
1207	C₂×C₄	#585	1	1	yes	characteristic
1208	C₈	—	2	2	no	—
1209	C₈	—	4	1	no	—
1210	C₈	—	4	1	no	—
1211	C₈	—	4	1	no	—
1212	C₈	—	4	1	no	—
1213	C₈	—	4	1	no	—
1214	C₈	—	4	1	no	—
1215	C₈	—	4	1	no	—
1216	C₂²	—	2	2	no	—
1217	C₂²	—	2	2	no	—
1218	C₂²	—	2	2	no	—
1219	C₂²	—	4	1	no	—
1220	C₂²	—	4	1	no	—
1221	C₂²	—	4	1	no	—
1222	C₂²	—	4	1	no	—
1223	C₂²	—	4	1	no	—
1224	C₂²	—	4	2	no	—
1225	C₂²	—	4	1	no	—
1226	C₂²	—	4	2	no	—
1227	C₂²	—	4	2	no	—
1228	C₂²	—	4	1	no	—
1229	C₂²	—	4	1	no	—
1230	C₂²	—	4	2	no	—
1231	C₂²	—	4	1	no	—
1232	C₂²	—	4	1	no	—
1233	C₂²	—	4	2	no	—
1234	C₂²	—	4	2	no	—
1235	C₂²	—	4	1	no	—
1236	C₂²	—	8	16	no	—
1237	C₂²	—	8	1	no	—
1238	C₂²	—	8	1	no	—
1239	C₂²	—	8	1	no	—
1240	C₂²	—	8	1	no	—
1241	C₂²	—	8	1	no	—
1242	C₂²	—	8	1	no	—
1243	C₂²	—	8	1	no	—
1244	C₂²	—	8	1	no	—
1245	C₂²	C₂×#536	1	1	yes	characteristic
1246	C₂²	D₄×#41	1	1	yes	characteristic
1247	C₂²	#3484	1	1	yes	characteristic
1248	C₂²	C₂×#575	1	1	yes	characteristic
1249	C₂²	C₂×#575	1	1	yes	characteristic
1250	C₂²	#3584	1	1	yes	characteristic
1251	C₂²	#3585	1	1	yes	characteristic
1252	C₄	—	2	2	no	—
1253	C₄	—	2	2	no	—
1254	C₄	—	2	2	no	—
1255	C₄	—	4	1	no	—
1256	C₄	—	4	1	no	—
1257	C₄	—	4	2	no	—
1258	C₄	—	4	1	no	—
1259	C₄	—	4	1	no	—
1260	C₄	—	4	2	no	—
1261	C₄	—	4	1	no	—
1262	C₄	—	4	1	no	—
1263	C₄	—	4	1	no	—
1264	C₄	—	4	1	no	—
1265	C₄	—	4	1	no	—
1266	C₄	—	8	1	no	—
1267	C₄	—	8	1	no	—
1268	C₄	—	8	1	no	—
1269	C₄	—	8	1	no	—
1270	C₄	—	8	1	no	—
1271	C₄	—	8	1	no	—
1272	C₄	—	8	1	no	—
1273	C₄	—	8	1	no	—
1274	C₄	—	8	1	no	—
1275	C₄	—	8	1	no	—
1276	C₄	—	8	1	no	—
1277	C₄	—	8	1	no	—
1278	C₄	#3492	1	1	yes	characteristic
1279	C₄	#3520	1	1	yes	characteristic
1280	C₄	#3535	1	1	yes	characteristic
1281	C₄	#3541	1	1	yes	characteristic
1282	C₂	—	4	2	no	—
1283	C₂	—	8	1	no	—
1284	C₂	—	8	2	no	—
1285	C₂	—	8	2	no	—
1286	C₂	#38359	1	1	yes	characteristic
1287	C₂	#60866	1	1	yes	characteristic
1288	C₂	#60890	1	1	yes	characteristic
1289	C₂	#61441	1	1	yes	characteristic
1290	C₂	#61464	1	1	yes	characteristic
1291	C₂	#61576	1	1	yes	characteristic
1292	C₂	#61599	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 ◁ C₄²×D₄ ◁ G
LECS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #36416	C₂	semidirect
3. #32959	C₂	semidirect
4. #31581	C₂	semidirect
5. #31463	C₂	semidirect
6. #31379	C₂	semidirect
7. #31135	C₂	semidirect
8. #31106	C₂	semidirect
9. #30951	C₂	semidirect
10. #30811	C₂	semidirect
11. #30654	C₂	semidirect
12. #30171	C₂	semidirect
13. #30082	C₂	semidirect
14. #29580	C₂	semidirect
15. #29393	C₂	semidirect
16. #29242	C₂	semidirect
17. #29164	C₂	semidirect
18. #28787	C₂	semidirect
19. #27281	C₂	semidirect
20. #27271	C₂	semidirect
21. #26223	C₂	semidirect
22. #26151	C₂	semidirect
23. #26075	C₂	semidirect
24. #25675	C₂	semidirect
27. #24068	C₂	semidirect
28. #22788	C₂	semidirect
29. #22224	C₂	semidirect
30. #22080	C₂	semidirect
31. #20873	C₂	semidirect
34. C₂×#499	C₂²	semidirect
37. C₂×#485	C₂²	semidirect
45. #2859	C₂²	semidirect
47. #2851	C₂²	semidirect
53. #2571	C₂²	semidirect
55. #2552	C₂²	semidirect
63. #2441	C₂²	semidirect
65. #2439	C₂²	semidirect
78. C₄×C₄⋊Q₈	C₂²	semidirect
84. #2296	C₂²	semidirect
88. #2101	C₂²	semidirect
89. #2100	C₂²	semidirect
90. #2097	C₂²	semidirect
91. #2095	C₂²	semidirect
94. #2088	C₂²	semidirect
95. #2086	C₂²	semidirect
96. #2085	C₂²	semidirect
97. #2085	C₂²	semidirect
98. #2085	C₂²	semidirect
99. #2084	C₂²	semidirect
100. #2083	C₂²	semidirect
101. #2077	C₂²	semidirect
102. #2075	C₂²	semidirect
104. #2072	C₂²	semidirect
108. #2068	C₂²	semidirect
109. #2066	C₂²	semidirect
110. #2059	C₂²	semidirect
111. #2059	C₂²	semidirect
112. #2059	C₂²	semidirect
113. #2059	C₂²	semidirect
114. #2057	C₂²	semidirect
119. #2036	C₂²	semidirect
120. #2035	C₂²	semidirect
125. #2026	C₂²	semidirect
128. #1993	C₂²	semidirect
129. #1991	C₂²	semidirect
132. #1943	C₂²	semidirect
133. #1943	C₂²	semidirect
134. #1942	C₂²	semidirect
135. #1941	C₂²	semidirect
140. #1927	C₂²	semidirect
141. #1927	C₂²	semidirect
146. #1924	C₂²	semidirect
147. #1924	C₂²	semidirect
148. #1921	C₂²	semidirect
149. #1921	C₂²	semidirect
150. #1920	C₂²	semidirect
151. #1920	C₂²	semidirect
152. #1919	C₂²	semidirect
153. #1919	C₂²	semidirect
154. #1916	C₂²	semidirect
155. #1916	C₂²	semidirect
162. #1873	C₂²	semidirect
165. #1865	C₂²	semidirect
166. #1865	C₂²	semidirect
173. #1863	C₂²	semidirect
174. #1863	C₂²	semidirect
183. #1854	C₂²	semidirect
186. #1847	C₂²	semidirect
187. #1839	C₂²	semidirect
188. #1825	C₂²	semidirect
189. #1817	C₂²	semidirect
199. C₄×C₂²⋊C₈	C₂²	semidirect
200. #1745	C₂²	semidirect

Maximal subgroups

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

subgroup	index
#36416	2
#34700	2
#32959	2
#31581	2
#31463	2
#31379	2
#31135	2
#31106	2
#30951	2
#30811	2
#30654	2
#30171	2
#30082	2
#29580	2
#29393	2
#29242	2
#29164	2
#28787	2
#27281	2
#27271	2
#26223	2
#26151	2
#26075	2
#25675	2
#24886	2
#24068	2
#22788	2
#22224	2
#22080	2
#20873	2