Subgroups — #6378166

Order 512.

1800 conjugacy classes of subgroups.

The subgroup lattice has 1245 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#3258	C₂	1	1	yes	maximal, characteristic
2	#34281	C₂	1	1	yes	maximal, characteristic, complemented
3	#34279	C₂	1	1	yes	maximal, characteristic
4	#22203	C₂	1	1	yes	maximal, characteristic, complemented
5	#22201	C₂	1	1	yes	maximal, characteristic
6	#22197	C₂	1	1	yes	maximal, characteristic, complemented
7	#22195	C₂	1	1	yes	maximal, characteristic
8	#22156	C₂	1	1	yes	maximal, characteristic, complemented
9	#22156	C₂	1	1	yes	maximal, characteristic, complemented
10	#22154	C₂	1	1	yes	maximal, characteristic, complemented
11	#22152	C₂	1	1	yes	maximal, characteristic, complemented
12	#22121	C₂	1	1	yes	maximal, characteristic, complemented
13	#22120	C₂	1	1	yes	maximal, characteristic, complemented
14	#22119	C₂	1	1	yes	maximal, characteristic, complemented
15	#22118	C₂	1	1	yes	maximal, characteristic, complemented
16	#21966	C₂	1	1	yes	maximal, characteristic, complemented
17	#21898	C₂	1	1	yes	maximal, characteristic, complemented
18	#21896	C₂	1	1	yes	maximal, characteristic
19	#21626	C₂	1	1	yes	maximal, characteristic, complemented
20	#21625	C₂	1	1	yes	maximal, characteristic, complemented
21	#21621	C₂	1	1	yes	maximal, characteristic, complemented
22	#21619	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄×#470	C₂	1	1	yes	maximal, characteristic, complemented
24	C₄×#468	C₂	1	1	yes	maximal, characteristic
25	#21528	C₂	1	1	yes	maximal, characteristic
26	#21527	C₂	1	1	yes	maximal, characteristic, complemented
27	#21516	C₂	1	1	yes	maximal, characteristic, complemented
28	#21514	C₂	1	1	yes	maximal, characteristic, complemented
29	#21512	C₂	1	1	yes	maximal, characteristic, complemented
30	#21511	C₂	1	1	yes	maximal, characteristic, complemented
31	#20427	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×#542	C₂²	1	1	yes	characteristic
33	C₂×#541	C₂²	1	1	yes	characteristic
34	#3258	C₄	1	16	yes	complemented
35	C₂×#479	C₂²	1	1	yes	characteristic
36	C₂×#477	C₂²	1	1	yes	characteristic
37	C₂×#475	C₂²	1	1	yes	characteristic
38	C₂×#478	C₂²	1	1	yes	characteristic
39	C₂×#470	C₂²	1	1	yes	characteristic
40	C₂×#468	C₂²	1	1	yes	characteristic
41	C₂×#467	C₂²	1	1	yes	characteristic
42	C₂×#465	C₂²	1	1	yes	characteristic
43	C₂×#464	C₂²	1	1	yes	characteristic
44	C₂×#464	C₂²	1	1	yes	characteristic
45	C₂×#462	C₂²	1	1	yes	characteristic
46	C₂×#461	C₂²	1	1	yes	characteristic
47	C₂×#441	C₂²	1	1	yes	characteristic
48	C₂×#440	C₂²	1	1	yes	characteristic
49	C₂×C₄×Q₁₆	C₂²	1	1	yes	characteristic
50	C₂×C₄×SD₁₆	C₂²	1	1	yes	characteristic
51	C₂×#424	C₂²	1	1	yes	characteristic
52	C₂×#424	C₂²	1	1	yes	characteristic
53	C₂×C₄×M₁₆	C₂²	1	1	yes	characteristic
54	C₂²×#97	C₂²	1	1	yes	characteristic
55	#2374	—	2	1	no	—
56	#2373	—	2	1	no	—
57	#2373	—	2	1	no	—
58	#2373	—	2	1	no	—
59	#2373	—	2	1	no	—
60	#2373	—	2	1	no	—
61	#2373	—	2	1	no	—
62	#2372	—	2	1	no	—
63	#2371	—	2	1	no	—
64	#2371	—	2	1	no	—
65	#2370	—	2	1	no	—
66	#2370	—	2	1	no	—
67	#2368	—	2	1	no	—
68	#2367	—	2	1	no	—
69	#2362	—	2	1	no	—
70	#2359	—	2	1	no	—
71	#2331	C₂²	1	1	yes	characteristic
72	#2330	C₂²	1	1	yes	characteristic
73	#2327	C₂²	1	1	yes	characteristic
74	#2326	C₂²	1	1	yes	characteristic
75	#2324	C₂²	1	1	yes	characteristic
76	#2323	C₂²	1	1	yes	characteristic
77	#2323	C₂²	1	1	yes	characteristic
78	#2323	C₂²	1	1	yes	characteristic
79	#2314	C₂²	1	1	yes	characteristic
80	#2314	C₂²	1	1	yes	characteristic
81	C₄×C₄⋊Q₈	C₂²	1	1	yes	characteristic
82	C₄×C₄⋊Q₈	C₂²	1	1	yes	characteristic
83	C₄×#125	C₂²	1	1	yes	characteristic
84	C₄×#124	C₂²	1	1	yes	characteristic
85	C₄×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
86	C₄×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
87	C₄×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
88	C₄×#121	C₂²	1	1	yes	characteristic
89	#2295	C₂²	1	1	yes	characteristic
90	#2295	C₂²	1	1	yes	characteristic
91	#2295	C₂²	1	1	yes	characteristic
92	#2293	C₂²	1	1	yes	characteristic
93	#2276	C₂²	1	1	yes	characteristic
94	#2276	C₂²	1	1	yes	characteristic
95	#2276	C₂²	1	1	yes	characteristic
96	#2275	C₂²	1	1	yes	characteristic
97	C₄×#117	C₂²	1	1	yes	characteristic
98	#1989	C₂²	1	1	yes	characteristic
99	#1989	C₂²	1	1	yes	characteristic
100	#1988	C₂²	1	1	yes	characteristic
101	#1987	C₂²	1	1	yes	characteristic
102	#1983	C₂²	1	1	yes	characteristic
103	#1983	C₂²	1	1	yes	characteristic
104	#1981	C₂²	1	1	yes	characteristic
105	#1981	C₂²	1	1	yes	characteristic
106	#1973	C₂²	1	1	yes	characteristic
107	#1973	C₂²	1	1	yes	characteristic
108	#1971	C₂²	1	1	yes	characteristic
109	#1971	C₂²	1	1	yes	characteristic
110	#1949	C₂²	1	1	yes	characteristic
111	#1949	C₂²	1	1	yes	characteristic
112	#1949	C₂²	1	1	yes	characteristic
113	#1949	C₂²	1	1	yes	characteristic
114	#1948	C₂²	1	1	yes	characteristic
115	#1948	C₂²	1	1	yes	characteristic
116	#1947	C₂²	1	1	yes	characteristic
117	#1947	C₂²	1	1	yes	characteristic
118	#1944	C₂²	1	1	yes	characteristic
119	#1944	C₂²	1	1	yes	characteristic
120	#1943	C₂²	1	1	yes	characteristic
121	#1943	C₂²	1	1	yes	characteristic
122	#1936	C₂²	1	1	yes	characteristic
123	#1936	C₂²	1	1	yes	characteristic
124	#1935	C₂²	1	1	yes	characteristic
125	#1935	C₂²	1	1	yes	characteristic
126	#1935	C₂²	1	1	yes	characteristic
127	#1935	C₂²	1	1	yes	characteristic
128	#1935	C₂²	1	1	yes	characteristic
129	#1935	C₂²	1	1	yes	characteristic
130	#1928	C₂²	1	1	yes	characteristic
131	#1928	C₂²	1	1	yes	characteristic
132	#1928	C₂²	1	1	yes	characteristic
133	#1927	C₂²	1	1	yes	characteristic
134	#1927	C₂²	1	1	yes	characteristic
135	#1927	C₂²	1	1	yes	characteristic
136	#1926	C₂²	1	1	yes	characteristic
137	#1925	C₂²	1	1	yes	characteristic
138	#1921	C₂²	1	1	yes	characteristic
139	#1920	C₂²	1	1	yes	characteristic
140	#1919	C₂²	1	1	yes	characteristic
141	#1919	C₂²	1	1	yes	characteristic
142	#1919	C₂²	1	1	yes	characteristic
143	#1918	C₂²	1	1	yes	characteristic
144	#1918	C₂²	1	1	yes	characteristic
145	#1918	C₂²	1	1	yes	characteristic
146	#1895	C₂²	1	1	yes	characteristic
147	#1894	C₂²	1	1	yes	characteristic
148	#1894	C₂²	1	1	yes	characteristic
149	#1894	C₂²	1	1	yes	characteristic
150	#1893	C₂²	1	1	yes	characteristic
151	#1892	C₂²	1	1	yes	characteristic
152	#1892	C₂²	1	1	yes	characteristic
153	#1892	C₂²	1	1	yes	characteristic
154	#1880	C₂²	1	1	yes	characteristic
155	#1880	C₂²	1	1	yes	characteristic
156	#1878	C₂²	1	1	yes	characteristic
157	#1878	C₂²	1	1	yes	characteristic
158	#1878	C₂²	1	1	yes	characteristic
159	#1878	C₂²	1	1	yes	characteristic
160	#1877	C₂²	1	1	yes	characteristic
161	#1877	C₂²	1	1	yes	characteristic
162	#1865	C₂²	1	1	yes	characteristic
163	#1865	C₂²	1	1	yes	characteristic
164	#1864	C₂²	1	1	yes	characteristic
165	#1864	C₂²	1	1	yes	characteristic
166	#1863	C₂²	1	1	yes	characteristic
167	#1863	C₂²	1	1	yes	characteristic
168	#1863	C₂²	1	1	yes	characteristic
169	#1863	C₂²	1	1	yes	characteristic
170	#1809	C₂²	1	1	yes	characteristic
171	#1809	C₂²	1	1	yes	characteristic
172	#1808	C₂²	1	1	yes	characteristic
173	#1807	C₂²	1	1	yes	characteristic
174	#1805	C₂²	1	1	yes	characteristic
175	#1805	C₂²	1	1	yes	characteristic
176	#1805	C₂²	1	1	yes	characteristic
177	#1804	C₂²	1	1	yes	characteristic
178	#1803	C₂²	1	1	yes	characteristic
179	#1803	C₂²	1	1	yes	characteristic
180	#1803	C₂²	1	1	yes	characteristic
181	#1802	C₂²	1	1	yes	characteristic
182	#1776	C₂²	1	1	yes	characteristic
183	#1776	C₂²	1	1	yes	characteristic
184	C₄×#107	C₂²	1	1	yes	characteristic
185	C₄×#106	C₂²	1	1	yes	characteristic
186	#1768	C₂²	1	1	yes	characteristic
187	#1768	C₂²	1	1	yes	characteristic
188	#1768	C₂²	1	1	yes	characteristic
189	#1768	C₂²	1	1	yes	characteristic
190	#1767	C₂²	1	1	yes	characteristic
191	#1767	C₂²	1	1	yes	characteristic
192	#1767	C₂²	1	1	yes	characteristic
193	#1767	C₂²	1	1	yes	characteristic
194	#1763	C₂²	1	1	yes	characteristic
195	#1763	C₂²	1	1	yes	characteristic
196	#1763	C₂²	1	1	yes	characteristic
197	#1762	C₂²	1	1	yes	characteristic
198	C₄×#103	C₂²	1	1	yes	characteristic
199	C₄×#103	C₂²	1	1	yes	characteristic
200	C₄×#103	C₂²	1	1	yes	characteristic
201	C₄×#102	C₂²	1	1	yes	characteristic
202	#1729	C₂²	1	1	yes	characteristic
203	#1729	C₂²	1	1	yes	characteristic
204	C₂²×Q₁₆	C₂³	1	1	yes	characteristic
205	C₂²×Q₁₆	C₂³	1	1	yes	characteristic
206	C₂²×SD₁₆	C₂³	1	1	yes	characteristic
207	C₂²×SD₁₆	C₂³	1	1	yes	characteristic
208	C₂²×M₁₆	C₂³	1	1	yes	characteristic
209	C₂²×M₁₆	C₂³	1	1	yes	characteristic
210	C₂³×C₈	C₂³	1	1	yes	characteristic
211	C₂³×C₈	C₂³	1	1	yes	characteristic
212	#542	—	2	4	no	—
213	#542	C₂×C₄	1	8	yes	—
214	#541	—	2	4	no	—
215	#541	C₂×C₄	1	8	yes	complemented
216	C₂×C₄⋊Q₈	C₂³	1	1	yes	characteristic
217	C₂×C₄⋊Q₈	C₂³	1	1	yes	characteristic
218	C₂×#126	—	2	1	no	—
219	C₂×#126	—	2	1	no	—
220	C₂×#126	—	2	1	no	—
221	C₂×#125	—	2	1	no	—
222	C₂×#125	—	2	1	no	—
223	C₂×#125	C₂³	1	1	yes	characteristic
224	C₂×#124	—	2	1	no	—
225	C₂×#124	C₂³	1	1	yes	characteristic
226	C₂×#123	—	2	1	no	—
227	C₂×C₂²⋊Q₈	—	2	1	no	—
228	C₂×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
229	C₂×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
230	C₂×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
231	C₂×#121	C₂³	1	1	yes	characteristic
232	C₂×C₄×Q₈	—	2	1	no	—
233	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
234	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
235	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
236	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
237	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
238	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
239	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
240	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
241	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
242	C₂×C₄×D₄	—	2	1	no	—
243	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
244	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
245	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
246	C₂×#117	—	2	1	no	—
247	C₂×#117	C₂³	1	1	yes	characteristic
248	C₂×#117	C₂³	1	1	yes	characteristic
249	C₂²×C₄²	C₂³	1	1	yes	characteristic
250	#479	C₂×C₄	1	8	yes	complemented
251	#478	C₂×C₄	1	8	yes	complemented
252	#477	C₂×C₄	1	8	yes	complemented
253	#475	C₂×C₄	1	8	yes	complemented
254	#470	C₂×C₄	1	8	yes	complemented
255	#468	C₂×C₄	1	8	yes	—
256	#467	C₂×C₄	1	8	yes	complemented
257	#465	C₂×C₄	1	8	yes	—
258	#464	C₂×C₄	1	8	yes	complemented
259	#464	C₂×C₄	1	8	yes	complemented
260	#462	C₂×C₄	1	8	yes	complemented
261	#461	C₂×C₄	1	8	yes	complemented
262	#441	—	4	2	no	—
263	#440	—	4	2	no	—
264	C₄×Q₁₆	—	4	2	no	—
265	C₄×SD₁₆	—	4	2	no	—
266	C₂×#107	C₂³	1	1	yes	characteristic
267	C₂×#107	C₂³	1	1	yes	characteristic
268	C₂×#107	C₂³	1	1	yes	characteristic
269	C₂×#107	C₂³	1	1	yes	characteristic
270	C₂×#107	C₂³	1	1	yes	characteristic
271	C₂×#107	C₂³	1	1	yes	characteristic
272	C₂×#106	C₂³	1	1	yes	characteristic
273	C₂×#106	C₂³	1	1	yes	characteristic
274	C₂×#106	C₂³	1	1	yes	characteristic
275	C₂×#106	C₂³	1	1	yes	characteristic
276	C₂×#106	C₂³	1	1	yes	characteristic
277	C₂×#106	C₂³	1	1	yes	characteristic
278	#424	—	2	4	no	—
279	#424	C₂×C₄	1	8	yes	complemented
280	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
281	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
282	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
283	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
284	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
285	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
286	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
287	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
288	C₂×#103	C₂³	1	1	yes	characteristic
289	C₂×#103	C₂³	1	1	yes	characteristic
290	C₂×#103	C₂³	1	1	yes	characteristic
291	C₂×#103	C₂³	1	1	yes	characteristic
292	C₂×#103	C₂³	1	1	yes	characteristic
293	C₂×#103	C₂³	1	1	yes	characteristic
294	C₂×#103	C₂³	1	1	yes	characteristic
295	C₂×#103	C₂³	1	1	yes	characteristic
296	C₂×#103	C₂³	1	1	yes	characteristic
297	C₂×#103	C₂³	1	1	yes	characteristic
298	C₂×#103	C₂³	1	1	yes	characteristic
299	C₂×#103	C₂³	1	1	yes	characteristic
300	C₂×#103	C₂³	1	1	yes	characteristic
301	C₂×#103	C₂³	1	1	yes	characteristic
302	C₂×#103	C₂³	1	1	yes	characteristic
303	C₂×#103	C₂³	1	1	yes	characteristic
304	C₂×#103	C₂³	1	1	yes	characteristic
305	C₂×#103	C₂³	1	1	yes	characteristic
306	C₂×#102	C₂³	1	1	yes	characteristic
307	C₂×#102	C₂³	1	1	yes	characteristic
308	C₂×#102	C₂³	1	1	yes	characteristic
309	C₂×#102	C₂³	1	1	yes	characteristic
310	C₂×#102	C₂³	1	1	yes	characteristic
311	C₂×#102	C₂³	1	1	yes	characteristic
312	C₄×M₁₆	—	4	2	no	—
313	C₂×#97	—	4	2	no	—
314	C₂×#97	C₂³	1	1	yes	characteristic
315	C₂×#97	C₂³	1	1	yes	characteristic
316	C₂×#97	C₂³	1	1	yes	characteristic
317	C₂×#97	C₂³	1	1	yes	characteristic
318	C₂×#97	C₂³	1	1	yes	characteristic
319	C₂×#97	C₂³	1	1	yes	characteristic
320	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
321	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
322	#391	—	2	1	no	—
323	#391	—	2	1	no	—
324	#391	—	2	1	no	—
325	#391	C₂³	1	1	yes	characteristic
326	#391	C₂³	1	1	yes	characteristic
327	#391	C₂³	1	1	yes	characteristic
328	#391	C₂³	1	1	yes	characteristic
329	#391	C₂³	1	1	yes	characteristic
330	#391	C₂³	1	1	yes	characteristic
331	#390	—	2	1	no	—
332	#390	C₂³	1	1	yes	characteristic
333	#390	C₂³	1	1	yes	characteristic
334	#389	—	2	1	no	—
335	#389	—	2	1	no	—
336	#389	—	2	1	no	—
337	#389	—	2	1	no	—
338	#389	—	2	1	no	—
339	#389	—	2	1	no	—
340	#389	—	2	1	no	—
341	#389	—	2	1	no	—
342	#389	C₂³	1	1	yes	characteristic
343	#389	C₂³	1	1	yes	characteristic
344	#389	C₂³	1	1	yes	characteristic
345	#389	C₂³	1	1	yes	characteristic
346	#389	C₂³	1	1	yes	characteristic
347	#389	C₂³	1	1	yes	characteristic
348	#389	C₂³	1	1	yes	characteristic
349	#389	C₂³	1	1	yes	characteristic
350	#388	—	2	1	no	—
351	#388	—	2	1	no	—
352	#388	—	2	1	no	—
353	#388	—	2	1	no	—
354	#388	—	2	1	no	—
355	#388	—	2	1	no	—
356	#388	—	2	1	no	—
357	#388	—	2	1	no	—
358	#388	—	2	1	no	—
359	#388	—	2	1	no	—
360	#388	—	2	1	no	—
361	#388	—	2	1	no	—
362	#388	—	2	1	no	—
363	#388	—	2	1	no	—
364	#388	—	2	1	no	—
365	#388	—	2	1	no	—
366	#388	—	2	1	no	—
367	#388	—	2	1	no	—
368	#387	—	2	1	no	—
369	#387	—	2	1	no	—
370	#387	—	2	1	no	—
371	#387	—	2	1	no	—
372	#387	—	2	1	no	—
373	#387	—	2	1	no	—
374	#387	—	2	1	no	—
375	#387	—	2	1	no	—
376	#387	—	2	1	no	—
377	#387	—	2	1	no	—
378	#387	—	2	1	no	—
379	#387	—	2	1	no	—
380	#387	—	2	1	no	—
381	#387	—	2	1	no	—
382	#387	—	2	1	no	—
383	#387	—	2	1	no	—
384	#387	—	2	1	no	—
385	#387	—	2	1	no	—
386	#387	—	2	1	no	—
387	#387	—	2	1	no	—
388	#387	—	2	1	no	—
389	#387	—	2	1	no	—
390	#387	—	2	1	no	—
391	#387	—	2	1	no	—
392	#387	—	2	1	no	—
393	#387	—	2	1	no	—
394	#386	—	2	1	no	—
395	#386	—	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	#384	C₂³	1	1	yes	characteristic
403	#384	C₂³	1	1	yes	characteristic
404	#382	C₂³	1	1	yes	characteristic
405	#382	C₂³	1	1	yes	characteristic
406	#380	C₂³	1	1	yes	characteristic
407	#380	C₂³	1	1	yes	characteristic
408	#380	C₂³	1	1	yes	characteristic
409	#380	C₂³	1	1	yes	characteristic
410	C₄×C₄⋊C₄	—	2	1	no	—
411	C₄×C₄⋊C₄	—	2	1	no	—
412	C₄×C₄⋊C₄	—	2	1	no	—
413	C₄×C₄⋊C₄	—	2	1	no	—
414	C₄×C₄⋊C₄	—	2	1	no	—
415	C₄×C₄⋊C₄	—	2	1	no	—
416	C₄×C₄⋊C₄	—	2	1	no	—
417	C₄×C₄⋊C₄	—	2	1	no	—
418	C₄×C₄⋊C₄	—	2	1	no	—
419	C₄×C₄⋊C₄	—	2	1	no	—
420	C₄×C₄⋊C₄	—	2	1	no	—
421	C₄×C₄⋊C₄	—	2	1	no	—
422	C₄×C₄⋊C₄	—	2	1	no	—
423	C₄×C₄⋊C₄	—	2	1	no	—
424	C₄×C₄⋊C₄	—	2	1	no	—
425	C₄×C₄⋊C₄	—	2	1	no	—
426	C₄×C₄⋊C₄	—	2	1	no	—
427	C₄×C₄⋊C₄	—	2	1	no	—
428	C₄×C₄⋊C₄	—	2	1	no	—
429	C₄×C₄⋊C₄	—	2	1	no	—
430	C₄×C₄⋊C₄	D₄	1	1	yes	characteristic
431	C₄×C₄⋊C₄	D₄	1	1	yes	characteristic
432	C₄×C₄⋊C₄	D₄	1	1	yes	characteristic
433	C₄×C₄⋊C₄	D₄	1	1	yes	characteristic
434	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
435	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
436	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
437	C₄×C₄⋊C₄	C₂³	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×C₄⋊C₄	C₂³	1	1	yes	characteristic
445	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
451	C₄×C₂²⋊C₄	—	2	1	no	—
452	C₄×C₂²⋊C₄	—	2	1	no	—
453	C₄×C₂²⋊C₄	—	2	1	no	—
454	C₄×C₂²⋊C₄	—	2	1	no	—
455	C₄×C₂²⋊C₄	—	2	1	no	—
456	C₄×C₂²⋊C₄	D₄	1	1	yes	characteristic
457	C₄×C₂²⋊C₄	D₄	1	1	yes	characteristic
458	C₄×C₂²⋊C₄	D₄	1	1	yes	characteristic
459	C₄×C₂²⋊C₄	D₄	1	1	yes	characteristic
460	#376	—	2	1	no	—
461	#376	—	2	1	no	—
462	#376	—	2	1	no	—
463	#376	—	2	1	no	—
464	#376	—	2	1	no	—
465	#376	—	2	1	no	—
466	#376	C₂³	1	1	yes	characteristic
467	#376	C₂³	1	1	yes	characteristic
468	C₂×#95	—	2	1	no	—
469	C₄³	C₂³	1	1	yes	characteristic
470	C₄³	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	#340	C₂³	1	1	yes	characteristic
483	#340	C₂³	1	1	yes	characteristic
484	#340	C₂³	1	1	yes	characteristic
485	#340	C₂³	1	1	yes	characteristic
486	#340	C₂³	1	1	yes	characteristic
487	#340	C₂³	1	1	yes	characteristic
488	#340	C₂³	1	1	yes	characteristic
489	#340	C₂³	1	1	yes	characteristic
490	#340	C₂³	1	1	yes	characteristic
491	#340	C₂³	1	1	yes	characteristic
492	#340	C₂³	1	1	yes	characteristic
493	#340	C₂³	1	1	yes	characteristic
494	#340	C₂³	1	1	yes	characteristic
495	#336	C₂³	1	1	yes	characteristic
496	#336	C₂³	1	1	yes	characteristic
497	#336	C₂³	1	1	yes	characteristic
498	#336	C₂³	1	1	yes	characteristic
499	#336	C₂³	1	1	yes	characteristic
500	#336	C₂³	1	1	yes	characteristic
501	#336	C₂³	1	1	yes	characteristic
502	#336	C₂³	1	1	yes	characteristic
503	C₂²×Q₈	—	2	1	no	—
504	C₂²×Q₈	C₂⁴	1	1	yes	characteristic
505	C₂²×Q₈	C₂⁴	1	1	yes	characteristic
506	C₂²×Q₈	C₂⁴	1	1	yes	characteristic
507	C₂²×D₄	—	2	1	no	—
508	C₂²×D₄	C₂⁴	1	1	yes	characteristic
509	C₂³×C₄	—	2	1	no	—
510	C₂³×C₄	—	2	1	no	—
511	C₂³×C₄	—	2	1	no	—
512	C₂³×C₄	C₂×D₄	1	1	yes	characteristic
513	C₂³×C₄	C₂×D₄	1	1	yes	characteristic
514	C₂³×C₄	C₂⁴	1	1	yes	characteristic
515	C₂×Q₁₆	—	4	1	no	—
516	C₂×Q₁₆	—	4	1	no	—
517	C₂×Q₁₆	—	4	1	no	—
518	C₂×Q₁₆	—	4	1	no	—
519	C₂×Q₁₆	C₂²×C₄	1	4	yes	—
520	C₂×Q₁₆	C₂²×C₄	1	4	yes	—
521	C₂×SD₁₆	—	4	1	no	—
522	C₂×SD₁₆	—	4	1	no	—
523	C₂×SD₁₆	—	4	1	no	—
524	C₂×SD₁₆	—	4	1	no	—
525	C₂×SD₁₆	C₂²×C₄	1	4	yes	—
526	C₂×SD₁₆	C₂²×C₄	1	4	yes	—
527	C₂×M₁₆	—	2	2	no	—
528	C₂×M₁₆	—	4	1	no	—
529	C₂×M₁₆	—	4	1	no	—
530	C₂×M₁₆	—	4	1	no	—
531	C₂×M₁₆	—	4	1	no	—
532	C₂×M₁₆	C₂²×C₄	1	4	yes	—
533	C₂²×C₈	—	2	2	no	—
534	C₂²×C₈	—	4	1	no	—
535	C₂²×C₈	—	4	1	no	—
536	C₂²×C₈	—	4	1	no	—
537	C₂²×C₈	—	4	1	no	—
538	C₂²×C₈	C₂²×C₄	1	4	yes	—
539	C₂²×C₈	C₂⁴	1	1	yes	characteristic
540	C₂²×C₈	C₂⁴	1	1	yes	characteristic
541	C₂²×C₈	C₂⁴	1	1	yes	characteristic
542	C₂²×C₈	C₂⁴	1	1	yes	characteristic
543	C₂²×C₈	C₂⁴	1	1	yes	characteristic
544	C₂²×C₈	C₂⁴	1	1	yes	characteristic
545	C₂²×C₈	C₂⁴	1	1	yes	characteristic
546	C₂²×C₈	C₂⁴	1	1	yes	characteristic
547	C₄⋊Q₈	—	2	2	no	—
548	C₄⋊Q₈	—	2	2	no	—
549	C₄⋊Q₈	C₂²×C₄	1	4	yes	—
550	C₄⋊Q₈	C₂²×C₄	1	4	yes	—
551	#126	—	2	8	no	—
552	#126	—	2	8	no	—
553	#126	—	2	8	no	—
554	#125	—	2	8	no	—
555	#125	—	2	8	no	—
556	#125	—	2	2	no	—
557	#125	C₂²×C₄	1	4	yes	—
558	#124	—	2	8	no	—
559	#124	—	2	2	no	—
560	#124	C₂²×C₄	1	4	yes	—
561	#123	—	2	8	no	—
562	C₂²⋊Q₈	—	2	2	no	—
563	C₂²⋊Q₈	—	2	2	no	—
564	C₂²⋊Q₈	—	2	2	no	—
565	C₂²⋊Q₈	—	2	8	no	—
566	C₂²⋊Q₈	C₂²×C₄	1	4	yes	—
567	C₂²⋊Q₈	C₂²×C₄	1	4	yes	—
568	C₂²⋊Q₈	C₂²×C₄	1	4	yes	—
569	#121	—	2	2	no	—
570	#121	C₂²×C₄	1	4	yes	—
571	C₄×Q₈	—	2	2	no	—
572	C₄×Q₈	—	2	2	no	—
573	C₄×Q₈	—	2	2	no	—
574	C₄×Q₈	—	2	2	no	—
575	C₄×Q₈	—	2	2	no	—
576	C₄×Q₈	—	2	2	no	—
577	C₄×Q₈	—	2	2	no	—
578	C₄×Q₈	—	2	2	no	—
579	C₄×Q₈	—	2	2	no	—
580	C₄×Q₈	—	4	1	no	—
581	C₄×Q₈	—	4	1	no	—
582	C₄×Q₈	—	4	1	no	—
583	C₄×Q₈	—	4	1	no	—
584	C₄×Q₈	—	4	1	no	—
585	C₄×Q₈	—	4	1	no	—
586	C₄×Q₈	—	8	2	no	—
587	C₄×Q₈	C₂²×C₄	1	4	yes	—
588	C₄×Q₈	C₂²×C₄	1	4	yes	—
589	C₄×Q₈	C₂²×C₄	1	4	yes	—
590	C₄×D₄	—	2	2	no	—
591	C₄×D₄	—	2	2	no	—
592	C₄×D₄	—	2	2	no	—
593	C₄×D₄	—	4	1	no	—
594	C₄×D₄	—	4	1	no	—
595	C₄×D₄	—	8	2	no	—
596	C₄×D₄	C₂²×C₄	1	4	yes	—
597	#117	—	4	1	no	—
598	#117	—	4	1	no	—
599	#117	—	8	2	no	—
600	#117	C₂²×C₄	1	4	yes	—
601	#117	#41	1	4	yes	—
602	C₂×C₄⋊C₄	—	2	1	no	—
603	C₂×C₄⋊C₄	—	2	1	no	—
604	C₂×C₄⋊C₄	—	2	1	no	—
605	C₂×C₄⋊C₄	—	2	1	no	—
606	C₂×C₄⋊C₄	—	2	1	no	—
607	C₂×C₄⋊C₄	—	2	1	no	—
608	C₂×C₄⋊C₄	—	2	1	no	—
609	C₂×C₄⋊C₄	—	2	1	no	—
610	C₂×C₄⋊C₄	—	2	1	no	—
611	C₂×C₄⋊C₄	—	2	1	no	—
612	C₂×C₄⋊C₄	—	2	1	no	—
613	C₂×C₄⋊C₄	—	2	1	no	—
614	C₂×C₄⋊C₄	—	2	1	no	—
615	C₂×C₄⋊C₄	—	2	1	no	—
616	C₂×C₄⋊C₄	—	2	1	no	—
617	C₂×C₄⋊C₄	—	2	1	no	—
618	C₂×C₄⋊C₄	—	2	1	no	—
619	C₂×C₄⋊C₄	—	2	1	no	—
620	C₂×C₄⋊C₄	—	2	1	no	—
621	C₂×C₄⋊C₄	—	2	1	no	—
622	C₂×C₄⋊C₄	—	2	1	no	—
623	C₂×C₄⋊C₄	—	2	1	no	—
624	C₂×C₄⋊C₄	—	2	1	no	—
625	C₂×C₄⋊C₄	—	2	1	no	—
626	C₂×C₄⋊C₄	—	2	1	no	—
627	C₂×C₄⋊C₄	—	2	1	no	—
628	C₂×C₄⋊C₄	—	2	1	no	—
629	C₂×C₄⋊C₄	—	2	1	no	—
630	C₂×C₄⋊C₄	—	2	1	no	—
631	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
632	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
633	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
634	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
635	C₂×C₄⋊C₄	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×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
639	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
640	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
641	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
642	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
643	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
644	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
645	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
646	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
647	C₂×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	C₂×D₄	1	1	yes	characteristic
665	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
666	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
667	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
668	C₂×C₄²	—	2	1	no	—
669	C₂×C₄²	—	2	1	no	—
670	C₂×C₄²	—	2	1	no	—
671	C₂×C₄²	—	2	2	no	—
672	C₂×C₄²	—	2	2	no	—
673	C₂×C₄²	—	2	1	no	—
674	C₂×C₄²	—	2	1	no	—
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	—	2	1	no	—
684	C₂×C₄²	—	2	1	no	—
685	C₂×C₄²	—	2	1	no	—
686	C₂×C₄²	—	2	1	no	—
687	C₂×C₄²	—	2	1	no	—
688	C₂×C₄²	—	2	1	no	—
689	C₂×C₄²	—	2	1	no	—
690	C₂×C₄²	—	2	1	no	—
691	C₂×C₄²	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	C₂×D₄	1	1	yes	characteristic
696	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
697	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
698	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
699	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
700	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
701	C₂×C₄²	C₂⁴	1	1	yes	characteristic
702	C₂×C₄²	C₂⁴	1	1	yes	characteristic
703	C₂×C₄²	C₂⁴	1	1	yes	characteristic
704	C₂×C₄²	C₂⁴	1	1	yes	characteristic
705	C₂×C₄²	C₂⁴	1	1	yes	characteristic
706	C₂×C₄²	C₂⁴	1	1	yes	characteristic
707	#107	—	4	1	no	—
708	#107	—	4	1	no	—
709	#107	—	4	1	no	—
710	#107	—	4	1	no	—
711	#107	C₂²×C₄	1	4	yes	—
712	#107	C₂²×C₄	1	4	yes	—
713	#106	—	4	1	no	—
714	#106	—	4	1	no	—
715	#106	—	4	1	no	—
716	#106	—	4	1	no	—
717	#106	C₂²×C₄	1	4	yes	—
718	#106	C₂²×C₄	1	4	yes	—
719	C₄⋊C₈	—	2	2	no	—
720	C₄⋊C₈	—	2	2	no	—
721	C₄⋊C₈	—	2	2	no	—
722	C₄⋊C₈	—	2	2	no	—
723	C₄⋊C₈	C₂²×C₄	1	4	yes	—
724	C₄⋊C₈	C₂²×C₄	1	4	yes	—
725	C₄⋊C₈	C₂²×C₄	1	4	yes	—
726	C₄⋊C₈	C₂²×C₄	1	4	yes	—
727	#103	—	4	1	no	—
728	#103	—	4	1	no	—
729	#103	—	4	1	no	—
730	#103	—	4	1	no	—
731	#103	—	4	1	no	—
732	#103	—	4	1	no	—
733	#103	—	4	1	no	—
734	#103	—	4	1	no	—
735	#103	—	4	1	no	—
736	#103	—	4	1	no	—
737	#103	—	4	1	no	—
738	#103	—	4	1	no	—
739	#103	C₂²×C₄	1	4	yes	—
740	#103	C₂²×C₄	1	4	yes	—
741	#103	C₂²×C₄	1	4	yes	—
742	#103	C₂²×C₄	1	4	yes	—
743	#103	C₂²×C₄	1	4	yes	—
744	#103	C₂²×C₄	1	4	yes	—
745	#102	—	4	1	no	—
746	#102	—	4	1	no	—
747	#102	—	4	1	no	—
748	#102	—	4	1	no	—
749	#102	C₂²×C₄	1	4	yes	—
750	#102	C₂²×C₄	1	4	yes	—
751	#97	—	2	2	no	—
752	#97	—	2	2	no	—
753	#97	—	4	1	no	—
754	#97	—	4	1	no	—
755	#97	—	4	1	no	—
756	#97	—	4	1	no	—
757	C₄×C₈	—	2	2	no	—
758	C₄×C₈	—	2	2	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	—	2	1	no	—
786	#95	—	2	1	no	—
787	#95	—	2	1	no	—
788	#95	—	2	1	no	—
789	#95	—	2	1	no	—
790	#95	—	2	1	no	—
791	#95	—	2	1	no	—
792	#95	—	2	1	no	—
793	#95	—	2	1	no	—
794	#95	—	2	1	no	—
795	#95	—	2	1	no	—
796	#95	—	2	1	no	—
797	#95	—	2	1	no	—
798	#95	—	2	1	no	—
799	#95	C₂×D₄	1	1	yes	characteristic
800	#95	C₂×D₄	1	1	yes	characteristic
801	#95	C₂×D₄	1	1	yes	characteristic
802	#95	C₂×D₄	1	1	yes	characteristic
803	#95	C₂×D₄	1	1	yes	characteristic
804	#95	C₂×D₄	1	1	yes	characteristic
805	#95	C₂×D₄	1	1	yes	characteristic
806	#95	C₂×D₄	1	1	yes	characteristic
807	C₂⁴	—	2	1	no	—
808	C₂⁴	C₂²×D₄	1	1	yes	characteristic
809	C₂×Q₈	—	2	4	no	—
810	C₂×Q₈	—	2	1	no	—
811	C₂×Q₈	—	2	1	no	—
812	C₂×Q₈	—	2	1	no	—
813	C₂×Q₈	—	2	1	no	—
814	C₂×Q₈	—	2	1	no	—
815	C₂×Q₈	—	2	1	no	—
816	C₂×Q₈	—	2	1	no	—
817	C₂×Q₈	—	2	1	no	—
818	C₂×Q₈	—	2	1	no	—
819	C₂×Q₈	—	2	1	no	—
820	C₂×Q₈	—	2	1	no	—
821	C₂×Q₈	—	2	1	no	—
822	C₂×Q₈	—	2	1	no	—
823	C₂×Q₈	—	2	1	no	—
824	C₂×Q₈	—	2	1	no	—
825	C₂×Q₈	—	8	1	no	—
826	C₂×Q₈	—	8	1	no	—
827	C₂×Q₈	C₂³×C₄	1	2	yes	—
828	C₂×Q₈	C₂³×C₄	1	2	yes	—
829	C₂×Q₈	C₂³×C₄	1	2	yes	—
830	C₂×D₄	—	2	4	no	—
831	C₂×D₄	—	2	1	no	—
832	C₂×D₄	—	2	1	no	—
833	C₂×D₄	—	2	1	no	—
834	C₂×D₄	—	2	1	no	—
835	C₂×D₄	—	2	1	no	—
836	C₂×D₄	—	8	1	no	—
837	C₂×D₄	—	8	1	no	—
838	C₂×D₄	C₂³×C₄	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	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	4	no	—
851	C₂²×C₄	—	2	2	no	—
852	C₂²×C₄	—	2	2	no	—
853	C₂²×C₄	—	2	1	no	—
854	C₂²×C₄	—	2	1	no	—
855	C₂²×C₄	—	2	1	no	—
856	C₂²×C₄	—	2	1	no	—
857	C₂²×C₄	—	2	1	no	—
858	C₂²×C₄	—	2	1	no	—
859	C₂²×C₄	—	2	1	no	—
860	C₂²×C₄	—	2	1	no	—
861	C₂²×C₄	—	4	1	no	—
862	C₂²×C₄	—	4	1	no	—
863	C₂²×C₄	—	4	1	no	—
864	C₂²×C₄	—	4	1	no	—
865	C₂²×C₄	—	4	2	no	—
866	C₂²×C₄	—	4	2	no	—
867	C₂²×C₄	—	8	1	no	—
868	C₂²×C₄	—	8	1	no	—
869	C₂²×C₄	—	8	1	no	—
870	C₂²×C₄	—	8	1	no	—
871	C₂²×C₄	—	8	1	no	—
872	C₂²×C₄	—	8	1	no	—
873	C₂²×C₄	C₂³×C₄	1	2	yes	—
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	C₂²×D₄	1	1	yes	characteristic
878	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
879	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
880	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
881	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
882	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
883	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
884	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
885	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
886	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
887	C₂²×C₄	C₂×#41	1	2	yes	—
888	C₂²×C₄	C₂⁵	1	1	yes	characteristic
889	Q₁₆	—	4	4	no	—
890	Q₁₆	—	4	4	no	—
891	SD₁₆	—	4	4	no	—
892	SD₁₆	—	4	4	no	—
893	M₁₆	—	4	4	no	—
894	M₁₆	—	4	4	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	—	2	1	no	—
905	C₂×C₈	—	2	1	no	—
906	C₂×C₈	—	2	1	no	—
907	C₂×C₈	—	2	1	no	—
908	C₂×C₈	—	2	1	no	—
909	C₂×C₈	—	2	1	no	—
910	C₂×C₈	—	2	1	no	—
911	C₂×C₈	—	2	1	no	—
912	C₂×C₈	—	2	1	no	—
913	C₂×C₈	—	2	1	no	—
914	C₂×C₈	—	2	1	no	—
915	C₂×C₈	—	4	4	no	—
916	C₂×C₈	—	4	4	no	—
917	C₂×C₈	C₂³×C₄	1	2	yes	—
918	C₂×C₈	C₂³×C₄	1	2	yes	—
919	C₂×C₈	C₂³×C₄	1	2	yes	—
920	C₂×C₈	C₂³×C₄	1	2	yes	—
921	C₄⋊C₄	—	2	4	no	—
922	C₄⋊C₄	—	2	4	no	—
923	C₄⋊C₄	—	2	4	no	—
924	C₄⋊C₄	—	2	4	no	—
925	C₄⋊C₄	—	2	4	no	—
926	C₄⋊C₄	—	2	4	no	—
927	C₄⋊C₄	—	2	4	no	—
928	C₄⋊C₄	—	2	4	no	—
929	C₄⋊C₄	—	2	4	no	—
930	C₄⋊C₄	—	2	4	no	—
931	C₄⋊C₄	—	2	4	no	—
932	C₄⋊C₄	—	2	1	no	—
933	C₄⋊C₄	—	2	1	no	—
934	C₄⋊C₄	—	2	1	no	—
935	C₄⋊C₄	—	2	1	no	—
936	C₄⋊C₄	—	2	1	no	—
937	C₄⋊C₄	—	2	1	no	—
938	C₄⋊C₄	—	2	1	no	—
939	C₄⋊C₄	—	2	1	no	—
940	C₄⋊C₄	—	2	1	no	—
941	C₄⋊C₄	—	2	1	no	—
942	C₄⋊C₄	—	2	1	no	—
943	C₄⋊C₄	—	2	1	no	—
944	C₄⋊C₄	—	2	1	no	—
945	C₄⋊C₄	—	2	1	no	—
946	C₄⋊C₄	—	2	1	no	—
947	C₄⋊C₄	—	2	1	no	—
948	C₄⋊C₄	—	2	1	no	—
949	C₄⋊C₄	—	2	1	no	—
950	C₄⋊C₄	—	2	1	no	—
951	C₄⋊C₄	—	2	1	no	—
952	C₄⋊C₄	—	4	1	no	—
953	C₄⋊C₄	—	4	1	no	—
954	C₄⋊C₄	—	4	2	no	—
955	C₄⋊C₄	—	4	2	no	—
956	C₄⋊C₄	—	4	2	no	—
957	C₄⋊C₄	—	4	2	no	—
958	C₄⋊C₄	—	4	2	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	—	8	1	no	—
965	C₄⋊C₄	—	8	1	no	—
966	C₄⋊C₄	—	8	1	no	—
967	C₄⋊C₄	—	8	1	no	—
968	C₄⋊C₄	—	8	1	no	—
969	C₄⋊C₄	—	8	1	no	—
970	C₄⋊C₄	—	8	1	no	—
971	C₄⋊C₄	—	8	1	no	—
972	C₄⋊C₄	C₄×D₄	1	4	yes	—
973	C₄⋊C₄	C₄×D₄	1	4	yes	—
974	C₄⋊C₄	C₂³×C₄	1	2	yes	—
975	C₄⋊C₄	C₂³×C₄	1	2	yes	—
976	C₄⋊C₄	C₂³×C₄	1	2	yes	—
977	C₄⋊C₄	C₂³×C₄	1	2	yes	—
978	C₂²⋊C₄	—	2	4	no	—
979	C₂²⋊C₄	—	2	4	no	—
980	C₂²⋊C₄	—	2	4	no	—
981	C₂²⋊C₄	—	2	4	no	—
982	C₂²⋊C₄	—	2	4	no	—
983	C₂²⋊C₄	—	2	4	no	—
984	C₂²⋊C₄	—	2	4	no	—
985	C₂²⋊C₄	—	4	1	no	—
986	C₂²⋊C₄	—	4	1	no	—
987	C₂²⋊C₄	—	4	2	no	—
988	C₂²⋊C₄	—	4	2	no	—
989	C₂²⋊C₄	—	4	2	no	—
990	C₂²⋊C₄	—	4	2	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	C₄×D₄	1	4	yes	—
998	C₂²⋊C₄	C₄×D₄	1	4	yes	—
999	C₄²	—	2	4	no	—
1000	C₄²	—	2	4	no	—
1001	C₄²	—	2	4	no	—
1002	C₄²	—	2	2	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	—	4	1	no	—
1011	C₄²	—	4	1	no	—
1012	C₄²	—	4	1	no	—
1013	C₄²	—	4	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	—	4	2	no	—
1020	C₄²	—	4	2	no	—
1021	C₄²	—	4	2	no	—
1022	C₄²	—	4	2	no	—
1023	C₄²	—	4	2	no	—
1024	C₄²	—	8	1	no	—
1025	C₄²	—	8	1	no	—
1026	C₄²	—	8	1	no	—
1027	C₄²	—	8	1	no	—
1028	C₄²	—	8	1	no	—
1029	C₄²	—	8	1	no	—
1030	C₄²	—	8	1	no	—
1031	C₄²	—	8	1	no	—
1032	C₄²	—	8	1	no	—
1033	C₄²	—	8	1	no	—
1034	C₄²	—	8	1	no	—
1035	C₄²	—	8	1	no	—
1036	C₄²	C₂³×C₄	1	2	yes	—
1037	C₄²	C₂³×C₄	1	2	yes	—
1038	C₄²	C₂×#41	1	2	yes	—
1039	C₄²	C₂×#41	1	2	yes	—
1040	C₄²	H(5,𝔽₂)	1	2	yes	—
1041	C₄²	2₋¹⁺⁴	1	2	yes	—
1042	C₂³	—	2	1	no	—
1043	C₂³	—	2	1	no	—
1044	C₂³	—	2	1	no	—
1045	C₂³	—	2	1	no	—
1046	C₂³	—	2	1	no	—
1047	C₂³	—	2	1	no	—
1048	C₂³	—	2	2	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	—	4	1	no	—
1055	C₂³	C₂×C₄×D₄	1	2	yes	—
1056	C₂³	C₂³×D₄	1	1	yes	characteristic
1057	Q₈	—	2	2	no	—
1058	Q₈	—	2	2	no	—
1059	Q₈	—	2	2	no	—
1060	Q₈	—	2	2	no	—
1061	Q₈	—	2	2	no	—
1062	Q₈	—	2	2	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	—	8	4	no	—
1070	D₄	—	2	2	no	—
1071	D₄	—	2	2	no	—
1072	D₄	—	4	1	no	—
1073	D₄	—	4	1	no	—
1074	D₄	—	8	4	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	1	no	—
1080	C₂×C₄	—	2	1	no	—
1081	C₂×C₄	—	2	1	no	—
1082	C₂×C₄	—	2	1	no	—
1083	C₂×C₄	—	2	1	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	2	no	—
1090	C₂×C₄	—	2	2	no	—
1091	C₂×C₄	—	2	2	no	—
1092	C₂×C₄	—	2	2	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	1	no	—
1104	C₂×C₄	—	2	1	no	—
1105	C₂×C₄	—	2	2	no	—
1106	C₂×C₄	—	2	2	no	—
1107	C₂×C₄	—	2	2	no	—
1108	C₂×C₄	—	2	2	no	—
1109	C₂×C₄	—	2	2	no	—
1110	C₂×C₄	—	2	2	no	—
1111	C₂×C₄	—	2	2	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	—	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	—	4	1	no	—
1153	C₂×C₄	—	4	1	no	—
1154	C₂×C₄	—	4	1	no	—
1155	C₂×C₄	—	4	1	no	—
1156	C₂×C₄	—	8	2	no	—
1157	C₂×C₄	—	8	2	no	—
1158	C₂×C₄	—	8	4	no	—
1159	C₂×C₄	—	16	2	no	—
1160	C₂×C₄	—	16	2	no	—
1161	C₂×C₄	C₂×C₄×D₄	1	2	yes	—
1162	C₂×C₄	C₂×C₄×D₄	1	2	yes	—
1163	C₂×C₄	C₂×C₄×D₄	1	2	yes	—
1164	C₂×C₄	C₂×C₄×D₄	1	2	yes	—
1165	C₂×C₄	C₂×C₄×D₄	1	2	yes	—
1166	C₂×C₄	#537	1	2	yes	—
1167	C₂×C₄	#537	1	2	yes	—
1168	C₂×C₄	C₂⁴×C₄	1	1	yes	characteristic
1169	C₂×C₄	C₂²×#41	1	1	yes	characteristic
1170	C₂×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
1171	C₂×C₄	C₂×2₋¹⁺⁴	1	1	yes	characteristic
1172	C₂×C₄	#585	1	1	yes	characteristic
1173	C₂×C₄	#585	1	1	yes	characteristic
1174	C₈	—	2	2	no	—
1175	C₈	—	2	2	no	—
1176	C₈	—	2	2	no	—
1177	C₈	—	2	2	no	—
1178	C₈	—	4	1	no	—
1179	C₈	—	4	1	no	—
1180	C₈	—	4	1	no	—
1181	C₈	—	4	1	no	—
1182	C₂²	—	2	2	no	—
1183	C₂²	—	2	2	no	—
1184	C₂²	—	2	2	no	—
1185	C₂²	—	4	1	no	—
1186	C₂²	—	4	1	no	—
1187	C₂²	—	4	1	no	—
1188	C₂²	—	4	1	no	—
1189	C₂²	—	4	2	no	—
1190	C₂²	—	4	2	no	—
1191	C₂²	—	4	2	no	—
1192	C₂²	—	8	1	no	—
1193	C₂²	—	8	1	no	—
1194	C₂²	—	8	1	no	—
1195	C₂²	—	8	1	no	—
1196	C₂²	C₂²×C₄×D₄	1	1	yes	characteristic
1197	C₂²	C₂×#537	1	1	yes	characteristic
1198	C₂²	#3449	1	1	yes	characteristic
1199	C₂²	#3585	1	1	yes	characteristic
1200	C₂²	#3586	1	1	yes	characteristic
1201	C₂²	#3586	1	1	yes	characteristic
1202	C₂²	#3586	1	1	yes	characteristic
1203	C₄	—	2	2	no	—
1204	C₄	—	2	2	no	—
1205	C₄	—	2	2	no	—
1206	C₄	—	2	2	no	—
1207	C₄	—	2	2	no	—
1208	C₄	—	2	2	no	—
1209	C₄	—	2	2	no	—
1210	C₄	—	4	1	no	—
1211	C₄	—	4	1	no	—
1212	C₄	—	4	2	no	—
1213	C₄	—	4	2	no	—
1214	C₄	—	4	2	no	—
1215	C₄	—	4	2	no	—
1216	C₄	—	4	2	no	—
1217	C₄	—	4	2	no	—
1218	C₄	—	4	2	no	—
1219	C₄	—	4	1	no	—
1220	C₄	—	4	1	no	—
1221	C₄	—	4	1	no	—
1222	C₄	—	4	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	C₄×H(5,𝔽₂)	1	1	yes	characteristic
1232	C₄	C₄×2₋¹⁺⁴	1	1	yes	characteristic
1233	C₄	#3460	1	1	yes	characteristic
1234	C₄	#3461	1	1	yes	characteristic
1235	C₂	—	4	2	no	—
1236	C₂	—	8	2	no	—
1237	C₂	C₄×#537	1	1	yes	characteristic
1238	C₂	#60174	1	1	yes	characteristic
1239	C₂	#60175	1	1	yes	characteristic
1240	C₂	#60938	1	1	yes	characteristic
1241	C₂	#60939	1	1	yes	characteristic
1242	C₂	#61018	1	1	yes	characteristic
1243	C₂	#61021	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³	C₂³×D₄
commutator	C₂×C₄	C₂⁴×C₄
Frattini, cosocle	C₂²×C₄	C₂⁵
prime radical	C₂×#121	C₂³
LCS	G ▷ C₂×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. #34281	C₂	semidirect
4. #22203	C₂	semidirect
6. #22197	C₂	semidirect
8. #22156	C₂	semidirect
9. #22156	C₂	semidirect
10. #22154	C₂	semidirect
11. #22152	C₂	semidirect
12. #22121	C₂	semidirect
13. #22120	C₂	semidirect
14. #22119	C₂	semidirect
15. #22118	C₂	semidirect
16. #21966	C₂	semidirect
17. #21898	C₂	semidirect
19. #21626	C₂	semidirect
20. #21625	C₂	semidirect
21. #21621	C₂	semidirect
22. #21619	C₂	semidirect
23. C₄×#470	C₂	semidirect
26. #21527	C₂	semidirect
27. #21516	C₂	semidirect
28. #21514	C₂	semidirect
29. #21512	C₂	semidirect
30. #21511	C₂	semidirect
31. #20427	C₂	semidirect
34. #3258	C₄	semidirect
215. #541	C₂×C₄	semidirect
250. #479	C₂×C₄	semidirect
251. #478	C₂×C₄	semidirect
252. #477	C₂×C₄	semidirect
253. #475	C₂×C₄	semidirect
254. #470	C₂×C₄	semidirect
256. #467	C₂×C₄	semidirect
258. #464	C₂×C₄	semidirect
259. #464	C₂×C₄	semidirect
260. #462	C₂×C₄	semidirect
261. #461	C₂×C₄	semidirect
279. #424	C₂×C₄	semidirect

Maximal subgroups

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

subgroup	index
C₂×#3258	2
#34281	2
#34279	2
#22203	2
#22201	2
#22197	2
#22195	2
#22156	2
#22154	2
#22152	2
#22121	2
#22120	2
#22119	2
#22118	2
#21966	2
#21898	2
#21896	2
#21626	2
#21625	2
#21621	2
#21619	2
C₄×#470	2
C₄×#468	2
#21528	2
#21527	2
#21516	2
#21514	2
#21512	2
#21511	2
#20427	2