Subgroups — #6755862

Order 512.

1473 conjugacy classes of subgroups.

The subgroup lattice has 1278 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#37799	C₂	1	1	yes	maximal, characteristic, complemented
2	#35266	C₂	1	1	yes	maximal, characteristic, complemented
3	#33101	C₂	1	1	yes	maximal, characteristic, complemented
4	#32257	C₂	1	1	yes	maximal, characteristic, complemented
5	#32241	C₂	1	1	yes	maximal, characteristic, complemented
6	#32183	C₂	1	1	yes	maximal, characteristic, complemented
7	#32167	C₂	1	1	yes	maximal, characteristic, complemented
8	#31928	C₂	1	1	yes	maximal, characteristic, complemented
9	#31899	C₂	1	1	yes	maximal, characteristic, complemented
10	#31821	C₂	1	1	yes	maximal, characteristic, complemented
11	#31816	C₂	1	1	yes	maximal, characteristic, complemented
12	#29917	C₂	1	1	yes	maximal, characteristic, complemented
13	#29727	C₂	1	1	yes	maximal, characteristic
14	#29342	C₂	1	1	yes	maximal, characteristic, complemented
15	#29252	C₂	1	1	yes	maximal, characteristic, complemented
16	#29096	C₂	1	1	yes	maximal, characteristic, complemented
17	#29080	C₂	1	1	yes	maximal, characteristic, complemented
18	#28900	C₂	1	1	yes	maximal, characteristic, complemented
19	#28883	C₂	1	1	yes	maximal, characteristic, complemented
20	#27572	C₂	1	1	yes	maximal, characteristic, complemented
21	#27567	C₂	1	1	yes	maximal, characteristic, complemented
22	#27089	C₂	1	1	yes	maximal, characteristic, complemented
23	#27086	C₂	1	1	yes	maximal, characteristic, complemented
24	#24512	C₂	1	1	yes	maximal, characteristic
25	#24507	C₂	1	1	yes	maximal, characteristic, complemented
26	#23942	C₂	1	1	yes	maximal, characteristic, complemented
27	#23936	C₂	1	1	yes	maximal, characteristic
28	#22605	C₂	1	1	yes	maximal, characteristic, complemented
29	#22052	C₂	1	1	yes	maximal, characteristic, complemented
30	#21873	C₂	1	1	yes	maximal, characteristic, complemented
31	#21396	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×#541	C₂²	1	1	yes	characteristic
33	C₂×#529	C₂²	1	1	yes	characteristic
34	C₂×#450	C₂²	1	1	yes	characteristic
35	C₂×#450	C₂²	1	1	yes	characteristic
36	C₂×#447	C₂²	1	1	yes	characteristic
37	C₂×#433	C₂²	1	1	yes	characteristic
38	C₂×#432	C₂²	1	1	yes	characteristic
39	#2860	—	2	1	no	—
40	#2860	—	2	1	no	—
41	#2855	C₂²	1	1	yes	characteristic
42	#2725	—	2	1	no	—
43	#2721	—	2	1	no	—
44	#2718	—	2	1	no	—
45	#2718	—	2	1	no	—
46	#2644	—	2	1	no	—
47	#2644	—	2	1	no	—
48	#2624	C₂²	1	1	yes	characteristic
49	#2620	C₂²	1	1	yes	characteristic
50	#2552	C₂²	1	1	yes	characteristic, complemented
51	#2545	C₂²	1	1	yes	characteristic, complemented
52	#2513	C₂²	1	1	yes	characteristic
53	#2513	C₂²	1	1	yes	characteristic
54	#2513	C₂²	1	1	yes	characteristic
55	#2513	C₂²	1	1	yes	characteristic
56	#2512	C₂²	1	1	yes	characteristic
57	#2512	C₂²	1	1	yes	characteristic
58	#2512	C₂²	1	1	yes	characteristic
59	#2512	C₂²	1	1	yes	characteristic
60	#2480	—	2	1	no	—
61	#2480	—	2	1	no	—
62	#2480	—	2	1	no	—
63	#2480	—	2	1	no	—
64	#2475	—	2	1	no	—
65	#2468	—	2	1	no	—
66	#2466	—	2	1	no	—
67	#2454	C₂²	1	1	yes	characteristic, complemented
68	#2453	C₂²	1	1	yes	characteristic, complemented
69	#2448	C₂²	1	1	yes	characteristic, complemented
70	#2446	C₂²	1	1	yes	characteristic, complemented
71	#2441	—	2	1	no	—
72	#2367	C₂²	1	1	yes	characteristic, complemented
73	Q₈×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
74	#2323	C₂²	1	1	yes	characteristic
75	#2317	C₂²	1	1	yes	characteristic
76	#2316	C₂²	1	1	yes	characteristic
77	#2309	C₂²	1	1	yes	characteristic
78	#2309	C₂²	1	1	yes	characteristic
79	#2296	C₂²	1	1	yes	characteristic
80	C₂×#390	C₂²	1	1	yes	characteristic
81	C₄×#117	C₂²	1	1	yes	characteristic
82	#2101	C₂²	1	1	yes	characteristic, complemented
83	#2100	C₂²	1	1	yes	characteristic, complemented
84	#2100	C₂²	1	1	yes	characteristic, complemented
85	#2099	C₂²	1	1	yes	characteristic, complemented
86	#2093	C₂²	1	1	yes	characteristic, complemented
87	#2092	C₂²	1	1	yes	characteristic, complemented
88	#2088	C₂²	1	1	yes	characteristic, complemented
89	#2086	C₂²	1	1	yes	characteristic, complemented
90	#2085	C₂²	1	1	yes	characteristic, complemented
91	#2083	C₂²	1	1	yes	characteristic, complemented
92	#2073	C₂²	1	1	yes	characteristic, complemented
93	#2071	C₂²	1	1	yes	characteristic
94	#2071	C₂²	1	1	yes	characteristic
95	#2071	C₂²	1	1	yes	characteristic, complemented
96	#2068	C₂²	1	1	yes	characteristic, complemented
97	#2068	C₂²	1	1	yes	characteristic, complemented
98	#2067	C₂²	1	1	yes	characteristic
99	#2067	C₂²	1	1	yes	characteristic
100	#2067	C₂²	1	1	yes	characteristic
101	#2065	C₂²	1	1	yes	characteristic
102	#2055	C₂²	1	1	yes	characteristic
103	#2055	C₂²	1	1	yes	characteristic
104	#2055	C₂²	1	1	yes	characteristic
105	#2055	C₂²	1	1	yes	characteristic
106	#2054	C₂²	1	1	yes	characteristic
107	#2054	C₂²	1	1	yes	characteristic
108	#2054	C₂²	1	1	yes	characteristic
109	#2054	C₂²	1	1	yes	characteristic
110	#2042	C₂²	1	1	yes	characteristic, complemented
111	#2042	C₂²	1	1	yes	characteristic, complemented
112	#2025	C₂²	1	1	yes	characteristic
113	#2025	C₂²	1	1	yes	characteristic
114	#2025	C₂²	1	1	yes	characteristic
115	#2025	C₂²	1	1	yes	characteristic
116	#2013	C₂²	1	1	yes	characteristic
117	#2013	C₂²	1	1	yes	characteristic
118	#2012	C₂²	1	1	yes	characteristic
119	#2012	C₂²	1	1	yes	characteristic
120	#2012	C₂²	1	1	yes	characteristic
121	#2012	C₂²	1	1	yes	characteristic
122	#1992	C₂²	1	1	yes	characteristic, complemented
123	#1991	C₂²	1	1	yes	characteristic, complemented
124	#1989	C₂²	1	1	yes	characteristic, complemented
125	#1989	C₂²	1	1	yes	characteristic, complemented
126	#1983	C₂²	1	1	yes	characteristic, complemented
127	#1983	C₂²	1	1	yes	characteristic, complemented
128	#1973	C₂²	1	1	yes	characteristic
129	#1973	C₂²	1	1	yes	characteristic
130	#1973	C₂²	1	1	yes	characteristic
131	#1972	C₂²	1	1	yes	characteristic
132	#1970	C₂²	1	1	yes	characteristic
133	#1968	C₂²	1	1	yes	characteristic
134	#1960	C₂²	1	1	yes	characteristic, complemented
135	#1956	C₂²	1	1	yes	characteristic, complemented
136	#1940	C₂²	1	1	yes	characteristic, complemented
137	#1939	C₂²	1	1	yes	characteristic, complemented
138	#1936	C₂²	1	1	yes	characteristic
139	#1936	C₂²	1	1	yes	characteristic
140	#1936	C₂²	1	1	yes	characteristic
141	#1936	C₂²	1	1	yes	characteristic
142	#1936	C₂²	1	1	yes	characteristic, complemented
143	#1935	C₂²	1	1	yes	characteristic, complemented
144	#1934	C₂²	1	1	yes	characteristic
145	#1934	C₂²	1	1	yes	characteristic
146	#1934	C₂²	1	1	yes	characteristic, complemented
147	#1933	C₂²	1	1	yes	characteristic, complemented
148	#1928	C₂²	1	1	yes	characteristic, complemented
149	#1928	C₂²	1	1	yes	characteristic, complemented
150	#1927	C₂²	1	1	yes	characteristic, complemented
151	#1927	C₂²	1	1	yes	characteristic, complemented
152	#1926	C₂²	1	1	yes	characteristic
153	#1925	C₂²	1	1	yes	characteristic
154	#1921	C₂²	1	1	yes	characteristic, complemented
155	#1921	C₂²	1	1	yes	characteristic, complemented
156	#1920	C₂²	1	1	yes	characteristic, complemented
157	#1919	C₂²	1	1	yes	characteristic, complemented
158	#1918	C₂²	1	1	yes	characteristic, complemented
159	#1918	C₂²	1	1	yes	characteristic, complemented
160	#1917	C₂²	1	1	yes	characteristic, complemented
161	#1917	C₂²	1	1	yes	characteristic, complemented
162	#1917	C₂²	1	1	yes	characteristic, complemented
163	#1916	C₂²	1	1	yes	characteristic, complemented
164	#1880	C₂²	1	1	yes	characteristic
165	#1880	C₂²	1	1	yes	characteristic
166	#1880	C₂²	1	1	yes	characteristic
167	#1880	C₂²	1	1	yes	characteristic
168	#1880	C₂²	1	1	yes	characteristic
169	#1880	C₂²	1	1	yes	characteristic
170	#1880	C₂²	1	1	yes	characteristic
171	#1880	C₂²	1	1	yes	characteristic
172	#1879	C₂²	1	1	yes	characteristic
173	#1879	C₂²	1	1	yes	characteristic
174	#1875	C₂²	1	1	yes	characteristic
175	#1875	C₂²	1	1	yes	characteristic
176	#1874	C₂²	1	1	yes	characteristic
177	#1873	C₂²	1	1	yes	characteristic
178	#1873	C₂²	1	1	yes	characteristic
179	#1873	C₂²	1	1	yes	characteristic
180	#1873	C₂²	1	1	yes	characteristic
181	#1872	C₂²	1	1	yes	characteristic
182	#1872	C₂²	1	1	yes	characteristic
183	#1865	C₂²	1	1	yes	characteristic, complemented
184	#1863	C₂²	1	1	yes	characteristic, complemented
185	#1854	C₂²	1	1	yes	characteristic
186	#1854	C₂²	1	1	yes	characteristic
187	#1852	C₂²	1	1	yes	characteristic
188	#1818	C₂²	1	1	yes	characteristic
189	#1817	C₂²	1	1	yes	characteristic
190	#1805	C₂²	1	1	yes	characteristic, complemented
191	#1805	C₂²	1	1	yes	characteristic, complemented
192	#1803	C₂²	1	1	yes	characteristic, complemented
193	#1803	C₂²	1	1	yes	characteristic, complemented
194	#1798	C₂²	1	1	yes	characteristic
195	#1786	C₂²	1	1	yes	characteristic
196	#1771	C₂²	1	1	yes	characteristic, complemented
197	#1770	C₂²	1	1	yes	characteristic, complemented
198	#1763	C₂²	1	1	yes	characteristic, complemented
199	#1763	C₂²	1	1	yes	characteristic, complemented
200	#1762	C₂²	1	1	yes	characteristic, complemented
201	#1762	C₂²	1	1	yes	characteristic, complemented
202	#1750	C₂²	1	1	yes	characteristic
203	C₂³×D₄	C₂³	1	1	yes	characteristic
204	C₂²×SD₁₆	C₂³	1	1	yes	characteristic
205	C₂²×SD₁₆	C₂³	1	1	yes	characteristic
206	C₂²×SD₁₆	C₂³	1	1	yes	characteristic
207	C₂²×SD₁₆	C₂³	1	1	yes	characteristic
208	C₂²×D₈	C₂³	1	1	yes	characteristic
209	C₂²×D₈	C₂³	1	1	yes	characteristic
210	#541	—	2	4	no	—
211	#541	—	4	2	no	—
212	C₂×C₄⋊Q₈	C₂³	1	1	yes	characteristic
213	#529	—	2	4	no	—
214	#529	—	4	2	no	—
215	C₂×#126	—	2	1	no	—
216	C₂×#126	—	2	1	no	—
217	C₂×#126	—	2	1	no	—
218	C₂×#126	—	2	1	no	—
219	C₂×#126	—	2	1	no	—
220	C₂×#126	—	2	1	no	—
221	C₂×#126	—	2	1	no	—
222	C₂×#125	—	2	1	no	—
223	C₂×#125	—	2	1	no	—
224	C₂×#125	C₂³	1	1	yes	characteristic
225	C₂×#125	C₂³	1	1	yes	characteristic
226	C₂×#124	C₂³	1	1	yes	characteristic
227	C₂×#124	C₂³	1	1	yes	characteristic
228	C₂×#123	—	2	1	no	—
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	C₂³	1	1	yes	characteristic
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×D₄	—	2	1	no	—
237	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
238	C₂×#117	—	2	1	no	—
239	C₂×#117	C₂³	1	1	yes	characteristic
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	C₂²×C₄⋊C₄	C₂³	1	1	yes	characteristic
244	C₂²×C₂²⋊C₄	—	2	1	no	—
245	C₂²×C₂²⋊C₄	—	2	1	no	—
246	C₂²×C₄²	C₂³	1	1	yes	characteristic
247	#450	—	2	4	no	—
248	#450	—	4	2	no	—
249	#447	—	4	2	no	—
250	#433	—	4	2	no	—
251	#432	—	4	2	no	—
252	C₂×#107	C₂³	1	1	yes	characteristic
253	C₂×#107	C₂³	1	1	yes	characteristic
254	C₂×#107	C₂³	1	1	yes	characteristic
255	C₂×#107	C₂³	1	1	yes	characteristic
256	C₂×#106	C₂³	1	1	yes	characteristic
257	C₂×#106	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×#103	C₂³	1	1	yes	characteristic
265	C₂×#103	C₂³	1	1	yes	characteristic
266	C₂×#103	C₂³	1	1	yes	characteristic
267	C₂×#103	C₂³	1	1	yes	characteristic
268	C₂×#103	C₂³	1	1	yes	characteristic
269	C₂×#103	C₂³	1	1	yes	characteristic
270	C₂×#103	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×#102	C₂³	1	1	yes	characteristic
277	C₂×#102	C₂³	1	1	yes	characteristic
278	C₂×#102	C₂³	1	1	yes	characteristic
279	C₂×#102	C₂³	1	1	yes	characteristic
280	C₂×#102	C₂³	1	1	yes	characteristic
281	C₂×#102	C₂³	1	1	yes	characteristic
282	C₂×#102	C₂³	1	1	yes	characteristic
283	C₂×#102	C₂³	1	1	yes	characteristic
284	C₂×#102	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×C₂²⋊C₈	C₂³	1	1	yes	characteristic
293	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
294	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
295	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
296	C₂×#97	C₂³	1	1	yes	characteristic
297	C₂×#97	C₂³	1	1	yes	characteristic
298	C₂×#97	C₂³	1	1	yes	characteristic
299	C₂×#97	C₂³	1	1	yes	characteristic
300	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
301	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
302	#400	—	2	1	no	—
303	#400	—	2	1	no	—
304	#399	—	2	1	no	—
305	#399	—	2	1	no	—
306	#399	—	2	1	no	—
307	#398	—	2	1	no	—
308	#398	—	2	1	no	—
309	#398	—	2	1	no	—
310	#398	—	2	1	no	—
311	#397	—	2	1	no	—
312	#397	—	2	1	no	—
313	#397	—	2	1	no	—
314	#397	—	2	1	no	—
315	#397	—	2	1	no	—
316	#397	—	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	#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	#396	—	2	1	no	—
332	#396	—	2	1	no	—
333	#396	—	2	1	no	—
334	#394	—	2	1	no	—
335	#394	—	2	1	no	—
336	#394	—	2	1	no	—
337	#394	—	2	1	no	—
338	#391	C₂³	1	1	yes	characteristic
339	#391	C₂³	1	1	yes	characteristic
340	#391	C₂³	1	1	yes	characteristic
341	#391	C₂³	1	1	yes	characteristic
342	#390	—	2	1	no	—
343	#390	—	2	1	no	—
344	#390	—	2	1	no	—
345	#390	—	2	1	no	—
346	#390	—	2	1	no	—
347	#390	—	2	1	no	—
348	#390	C₂³	1	1	yes	characteristic
349	#390	C₂³	1	1	yes	characteristic
350	#390	C₂³	1	1	yes	characteristic
351	#390	C₂³	1	1	yes	characteristic
352	#390	C₂³	1	1	yes	characteristic
353	#390	C₂³	1	1	yes	characteristic
354	#390	C₂³	1	1	yes	characteristic
355	#390	C₂³	1	1	yes	characteristic
356	#390	C₂³	1	1	yes	characteristic
357	#390	C₂³	1	1	yes	characteristic
358	#390	C₂³	1	1	yes	characteristic
359	#390	C₂³	1	1	yes	characteristic
360	#390	C₂³	1	1	yes	characteristic
361	#390	C₂³	1	1	yes	characteristic
362	#390	C₂³	1	1	yes	characteristic
363	#389	—	2	1	no	—
364	#389	—	2	1	no	—
365	#389	—	2	1	no	—
366	#389	—	2	1	no	—
367	#389	—	2	1	no	—
368	#389	—	2	1	no	—
369	#389	—	2	1	no	—
370	#389	—	2	1	no	—
371	#389	—	2	1	no	—
372	#389	D₄	1	1	yes	characteristic
373	#389	D₄	1	1	yes	characteristic
374	#389	D₄	1	1	yes	characteristic
375	#389	D₄	1	1	yes	characteristic
376	#389	C₂³	1	1	yes	characteristic
377	#389	C₂³	1	1	yes	characteristic
378	#389	C₂³	1	1	yes	characteristic
379	#389	C₂³	1	1	yes	characteristic
380	#389	C₂³	1	1	yes	characteristic
381	#389	C₂³	1	1	yes	characteristic
382	#389	C₂³	1	1	yes	characteristic
383	#389	C₂³	1	1	yes	characteristic
384	#389	C₂³	1	1	yes	characteristic
385	#388	—	2	1	no	—
386	#388	—	2	1	no	—
387	#388	—	2	1	no	—
388	#388	—	2	1	no	—
389	#388	—	2	1	no	—
390	#388	—	2	1	no	—
391	#388	—	2	1	no	—
392	#388	—	2	1	no	—
393	#388	—	2	1	no	—
394	#388	—	2	1	no	—
395	#388	—	2	1	no	—
396	#388	—	2	1	no	—
397	#388	—	2	1	no	—
398	#388	—	2	1	no	—
399	#388	—	2	1	no	—
400	#388	—	2	1	no	—
401	#388	—	2	1	no	—
402	#388	—	2	1	no	—
403	#388	—	2	1	no	—
404	#388	—	2	1	no	—
405	#387	—	2	1	no	—
406	#387	—	2	1	no	—
407	#387	—	2	1	no	—
408	#387	—	2	1	no	—
409	#387	—	2	1	no	—
410	#387	—	2	1	no	—
411	#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	D₄	1	1	yes	characteristic
417	#385	D₄	1	1	yes	characteristic
418	#385	D₄	1	1	yes	characteristic
419	#385	D₄	1	1	yes	characteristic
420	#384	—	2	1	no	—
421	#384	—	2	1	no	—
422	#384	C₂³	1	1	yes	characteristic
423	#384	C₂³	1	1	yes	characteristic
424	#384	C₂³	1	1	yes	characteristic
425	#382	C₂³	1	1	yes	characteristic
426	#382	C₂³	1	1	yes	characteristic
427	#381	—	2	1	no	—
428	#380	—	2	1	no	—
429	#380	—	2	1	no	—
430	#380	—	2	1	no	—
431	#380	C₂³	1	1	yes	characteristic
432	#379	—	2	1	no	—
433	#379	—	2	1	no	—
434	#379	—	2	1	no	—
435	#379	—	2	1	no	—
436	C₄×C₄⋊C₄	—	2	1	no	—
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	#376	—	2	1	no	—
450	C₄³	—	2	1	no	—
451	#340	C₂³	1	1	yes	characteristic
452	#340	C₂³	1	1	yes	characteristic
453	#340	C₂³	1	1	yes	characteristic
454	#340	C₂³	1	1	yes	characteristic
455	#340	C₂³	1	1	yes	characteristic
456	#340	C₂³	1	1	yes	characteristic
457	#340	C₂³	1	1	yes	characteristic
458	#340	C₂³	1	1	yes	characteristic
459	#340	C₂³	1	1	yes	characteristic
460	#340	C₂³	1	1	yes	characteristic
461	#340	C₂³	1	1	yes	characteristic
462	#340	C₂³	1	1	yes	characteristic
463	#340	C₂³	1	1	yes	characteristic
464	#340	C₂³	1	1	yes	characteristic
465	#340	C₂³	1	1	yes	characteristic
466	#340	C₂³	1	1	yes	characteristic
467	#340	C₂³	1	1	yes	characteristic
468	#340	C₂³	1	1	yes	characteristic
469	#340	C₂³	1	1	yes	characteristic
470	#340	C₂³	1	1	yes	characteristic
471	#340	C₂³	1	1	yes	characteristic
472	#340	C₂³	1	1	yes	characteristic
473	#340	C₂³	1	1	yes	characteristic
474	#340	C₂³	1	1	yes	characteristic
475	#336	C₂³	1	1	yes	characteristic
476	#336	C₂³	1	1	yes	characteristic
477	#336	C₂³	1	1	yes	characteristic
478	#336	C₂³	1	1	yes	characteristic
479	#336	C₂³	1	1	yes	characteristic
480	#336	C₂³	1	1	yes	characteristic
481	#336	C₂³	1	1	yes	characteristic
482	#336	C₂³	1	1	yes	characteristic
483	#336	C₂³	1	1	yes	characteristic
484	#336	C₂³	1	1	yes	characteristic
485	#336	C₂³	1	1	yes	characteristic
486	#336	C₂³	1	1	yes	characteristic
487	C₂⁵	—	2	1	no	—
488	C₂²×Q₈	C₂⁴	1	1	yes	characteristic
489	C₂²×Q₈	C₂⁴	1	1	yes	characteristic
490	C₂²×D₄	—	2	1	no	—
491	C₂²×D₄	—	2	1	no	—
492	C₂²×D₄	—	2	2	no	—
493	C₂²×D₄	—	2	2	no	—
494	C₂²×D₄	—	4	1	no	—
495	C₂²×D₄	—	4	1	no	—
496	C₂²×D₄	—	4	1	no	—
497	C₂²×D₄	—	4	1	no	—
498	C₂²×D₄	C₂⁴	1	1	yes	characteristic
499	C₂²×D₄	C₂⁴	1	1	yes	characteristic
500	C₂²×D₄	C₂⁴	1	1	yes	characteristic
501	C₂³×C₄	—	2	1	no	—
502	C₂³×C₄	—	2	1	no	—
503	C₂³×C₄	C₂×D₄	1	1	yes	characteristic
504	C₂³×C₄	C₂×D₄	1	1	yes	characteristic
505	C₂³×C₄	C₂⁴	1	1	yes	characteristic
506	C₂×SD₁₆	—	2	2	no	—
507	C₂×SD₁₆	—	2	2	no	—
508	C₂×SD₁₆	—	4	1	no	—
509	C₂×SD₁₆	—	4	1	no	—
510	C₂×SD₁₆	—	4	1	no	—
511	C₂×SD₁₆	—	4	1	no	—
512	C₂×SD₁₆	—	4	1	no	—
513	C₂×SD₁₆	—	4	1	no	—
514	C₂×SD₁₆	—	4	1	no	—
515	C₂×SD₁₆	—	4	1	no	—
516	C₂×SD₁₆	—	4	1	no	—
517	C₂×SD₁₆	—	4	1	no	—
518	C₂×D₈	—	4	1	no	—
519	C₂×D₈	—	4	1	no	—
520	C₂×D₈	—	4	1	no	—
521	C₂×D₈	—	4	1	no	—
522	C₂×D₈	—	4	1	no	—
523	C₂×D₈	—	4	1	no	—
524	C₂²×C₈	C₂⁴	1	1	yes	characteristic
525	C₂²×C₈	C₂⁴	1	1	yes	characteristic
526	C₂²×C₈	C₂⁴	1	1	yes	characteristic
527	C₂²×C₈	C₂⁴	1	1	yes	characteristic
528	C₂²×C₈	C₂⁴	1	1	yes	characteristic
529	C₂²×C₈	C₂⁴	1	1	yes	characteristic
530	C₂²×C₈	C₂⁴	1	1	yes	characteristic
531	C₂²×C₈	C₂⁴	1	1	yes	characteristic
532	C₄⋊Q₈	—	2	2	no	—
533	C₄⋊Q₈	—	4	1	no	—
534	#126	—	4	4	no	—
535	#126	—	4	4	no	—
536	#126	—	4	4	no	—
537	#126	—	8	2	no	—
538	#126	—	8	2	no	—
539	#126	—	8	2	no	—
540	#126	—	8	2	no	—
541	#125	—	2	2	no	—
542	#125	—	2	2	no	—
543	#125	—	4	1	no	—
544	#125	—	4	1	no	—
545	#125	—	4	4	no	—
546	#125	—	4	4	no	—
547	#124	—	2	2	no	—
548	#124	—	4	1	no	—
549	#124	—	4	1	no	—
550	#124	—	4	1	no	—
551	#123	—	4	4	no	—
552	C₂²⋊Q₈	—	2	2	no	—
553	C₂²⋊Q₈	—	2	2	no	—
554	C₂²⋊Q₈	—	2	2	no	—
555	C₂²⋊Q₈	#41	1	4	yes	—
556	#121	—	2	2	no	—
557	#121	—	2	2	no	—
558	C₄×Q₈	—	2	2	no	—
559	C₄×Q₈	—	2	2	no	—
560	C₄×Q₈	—	2	2	no	—
561	C₄×Q₈	—	4	1	no	—
562	C₄×Q₈	—	4	1	no	—
563	C₄×Q₈	—	4	1	no	—
564	C₄×Q₈	—	4	1	no	—
565	C₄×Q₈	—	4	1	no	—
566	C₄×D₄	—	2	2	no	—
567	C₄×D₄	—	4	1	no	—
568	C₄×D₄	—	4	4	no	—
569	#117	—	2	2	no	—
570	#117	—	2	2	no	—
571	#117	—	4	1	no	—
572	#117	—	4	1	no	—
573	#117	—	4	4	no	—
574	#117	—	4	1	no	—
575	#117	—	4	1	no	—
576	#117	—	4	1	no	—
577	#117	—	4	1	no	—
578	C₂×C₄⋊C₄	—	2	1	no	—
579	C₂×C₄⋊C₄	—	2	1	no	—
580	C₂×C₄⋊C₄	—	2	1	no	—
581	C₂×C₄⋊C₄	—	2	1	no	—
582	C₂×C₄⋊C₄	—	2	1	no	—
583	C₂×C₄⋊C₄	—	2	1	no	—
584	C₂×C₄⋊C₄	—	2	1	no	—
585	C₂×C₄⋊C₄	—	2	1	no	—
586	C₂×C₄⋊C₄	—	2	1	no	—
587	C₂×C₄⋊C₄	—	2	1	no	—
588	C₂×C₄⋊C₄	—	2	1	no	—
589	C₂×C₄⋊C₄	—	2	1	no	—
590	C₂×C₄⋊C₄	—	2	1	no	—
591	C₂×C₄⋊C₄	—	2	1	no	—
592	C₂×C₄⋊C₄	—	2	1	no	—
593	C₂×C₄⋊C₄	—	2	1	no	—
594	C₂×C₄⋊C₄	—	2	1	no	—
595	C₂×C₄⋊C₄	—	2	1	no	—
596	C₂×C₄⋊C₄	—	2	1	no	—
597	C₂×C₄⋊C₄	—	2	1	no	—
598	C₂×C₄⋊C₄	—	2	1	no	—
599	C₂×C₄⋊C₄	—	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	—	4	1	no	—
607	C₂×C₄⋊C₄	—	4	1	no	—
608	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
609	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
610	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
611	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
612	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
613	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
614	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
615	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
616	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
617	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
618	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
619	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
620	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
621	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
622	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
623	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
624	C₂×C₄⋊C₄	C₂⁴	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×C₂²⋊C₄	—	2	1	no	—
632	C₂×C₂²⋊C₄	—	2	1	no	—
633	C₂×C₂²⋊C₄	—	2	1	no	—
634	C₂×C₂²⋊C₄	—	2	1	no	—
635	C₂×C₂²⋊C₄	—	2	1	no	—
636	C₂×C₂²⋊C₄	—	2	1	no	—
637	C₂×C₂²⋊C₄	—	2	1	no	—
638	C₂×C₂²⋊C₄	—	2	1	no	—
639	C₂×C₂²⋊C₄	—	2	1	no	—
640	C₂×C₂²⋊C₄	—	2	1	no	—
641	C₂×C₂²⋊C₄	—	2	1	no	—
642	C₂×C₂²⋊C₄	—	2	1	no	—
643	C₂×C₂²⋊C₄	—	2	1	no	—
644	C₂×C₂²⋊C₄	—	2	1	no	—
645	C₂×C₂²⋊C₄	—	2	1	no	—
646	C₂×C₂²⋊C₄	—	2	1	no	—
647	C₂×C₂²⋊C₄	—	2	1	no	—
648	C₂×C₂²⋊C₄	—	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	—	2	1	no	—
669	C₂×C₂²⋊C₄	—	2	1	no	—
670	C₂×C₂²⋊C₄	—	2	1	no	—
671	C₂×C₂²⋊C₄	—	2	1	no	—
672	C₂×C₂²⋊C₄	—	8	2	no	—
673	C₂×C₂²⋊C₄	—	8	2	no	—
674	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
675	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
676	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
677	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
678	C₂×C₄²	—	2	2	no	—
679	C₂×C₄²	—	2	2	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	C₂⁴	1	1	yes	characteristic
694	C₂×C₄²	C₂⁴	1	1	yes	characteristic
695	C₂×C₄²	C₂⁴	1	1	yes	characteristic
696	C₂×C₄²	C₂⁴	1	1	yes	characteristic
697	C₂×C₄²	C₂⁴	1	1	yes	characteristic
698	C₂×C₄²	C₂⁴	1	1	yes	characteristic
699	#107	—	4	1	no	—
700	#107	—	4	1	no	—
701	#107	—	4	1	no	—
702	#107	—	4	1	no	—
703	#106	—	4	1	no	—
704	#106	—	4	1	no	—
705	C₄⋊C₈	—	4	1	no	—
706	C₄⋊C₈	—	4	1	no	—
707	C₄⋊C₈	—	4	1	no	—
708	C₄⋊C₈	—	4	1	no	—
709	C₄⋊C₈	—	4	1	no	—
710	C₄⋊C₈	—	4	1	no	—
711	#103	—	4	1	no	—
712	#103	—	4	1	no	—
713	#103	—	4	1	no	—
714	#103	—	4	1	no	—
715	#103	—	4	1	no	—
716	#103	—	4	1	no	—
717	#103	—	4	1	no	—
718	#103	—	4	1	no	—
719	#103	—	4	1	no	—
720	#103	—	4	1	no	—
721	#103	—	4	1	no	—
722	#103	—	4	1	no	—
723	#102	—	2	2	no	—
724	#102	—	2	2	no	—
725	#102	—	4	1	no	—
726	#102	—	4	1	no	—
727	#102	—	4	1	no	—
728	#102	—	4	1	no	—
729	#102	—	4	1	no	—
730	#102	—	4	1	no	—
731	#102	—	4	1	no	—
732	#102	—	4	1	no	—
733	#102	—	4	1	no	—
734	#102	—	4	1	no	—
735	#102	—	4	1	no	—
736	#102	—	4	1	no	—
737	#102	—	4	1	no	—
738	#102	—	4	1	no	—
739	C₂²⋊C₈	—	2	2	no	—
740	C₂²⋊C₈	—	2	2	no	—
741	C₂²⋊C₈	—	2	2	no	—
742	C₂²⋊C₈	—	2	2	no	—
743	#97	—	4	1	no	—
744	#97	—	4	1	no	—
745	#97	—	4	1	no	—
746	#97	—	4	1	no	—
747	C₄×C₈	—	4	1	no	—
748	C₄×C₈	—	4	1	no	—
749	#95	—	2	1	no	—
750	#95	—	2	1	no	—
751	#95	—	2	1	no	—
752	#95	—	2	1	no	—
753	#95	—	2	1	no	—
754	#95	—	2	1	no	—
755	#95	—	2	1	no	—
756	#95	—	2	1	no	—
757	#95	—	2	1	no	—
758	#95	—	2	1	no	—
759	#95	—	2	1	no	—
760	#95	—	2	1	no	—
761	#95	—	2	1	no	—
762	#95	—	2	1	no	—
763	#95	—	2	1	no	—
764	#95	—	2	1	no	—
765	#95	—	2	1	no	—
766	#95	—	2	1	no	—
767	#95	—	2	1	no	—
768	#95	—	2	1	no	—
769	#95	—	2	1	no	—
770	#95	—	2	1	no	—
771	#95	—	2	1	no	—
772	#95	—	2	1	no	—
773	#95	—	2	1	no	—
774	#95	—	2	1	no	—
775	#95	—	2	1	no	—
776	#95	C₂×D₄	1	1	yes	characteristic
777	#95	C₂×D₄	1	1	yes	characteristic
778	#95	C₂×D₄	1	1	yes	characteristic
779	#95	C₂×D₄	1	1	yes	characteristic
780	#95	C₂×D₄	1	1	yes	characteristic
781	#95	C₂×D₄	1	1	yes	characteristic
782	#95	C₂×D₄	1	1	yes	characteristic
783	#95	C₂×D₄	1	1	yes	characteristic
784	C₂⁴	—	2	1	no	—
785	C₂⁴	—	2	1	no	—
786	C₂⁴	—	2	1	no	—
787	C₂⁴	—	4	2	no	—
788	C₂⁴	—	4	2	no	—
789	C₂⁴	—	4	2	no	—
790	C₂⁴	—	8	1	no	—
791	C₂⁴	—	8	1	no	—
792	C₂⁴	—	8	1	no	—
793	C₂⁴	—	8	1	no	—
794	C₂⁴	C₂²×D₄	1	1	yes	characteristic
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	—	2	1	no	—
801	C₂×Q₈	—	2	1	no	—
802	C₂×Q₈	—	2	1	no	—
803	C₂×Q₈	—	2	1	no	—
804	C₂×Q₈	—	2	1	no	—
805	C₂×Q₈	—	2	1	no	—
806	C₂×Q₈	C₂×#41	1	2	yes	—
807	C₂×D₄	—	2	1	no	—
808	C₂×D₄	—	2	1	no	—
809	C₂×D₄	—	2	1	no	—
810	C₂×D₄	—	2	1	no	—
811	C₂×D₄	—	2	1	no	—
812	C₂×D₄	—	2	1	no	—
813	C₂×D₄	—	2	1	no	—
814	C₂×D₄	—	2	1	no	—
815	C₂×D₄	—	2	1	no	—
816	C₂×D₄	—	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	—	2	1	no	—
825	C₂×D₄	—	4	2	no	—
826	C₂×D₄	—	4	2	no	—
827	C₂×D₄	—	4	2	no	—
828	C₂×D₄	—	4	2	no	—
829	C₂×D₄	—	8	2	no	—
830	C₂×D₄	—	8	2	no	—
831	C₂×D₄	—	8	2	no	—
832	C₂×D₄	—	8	2	no	—
833	C₂×D₄	—	8	1	no	—
834	C₂×D₄	—	8	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	2	no	—
842	C₂²×C₄	—	2	2	no	—
843	C₂²×C₄	—	2	1	no	—
844	C₂²×C₄	—	2	1	no	—
845	C₂²×C₄	—	2	1	no	—
846	C₂²×C₄	—	2	1	no	—
847	C₂²×C₄	—	2	1	no	—
848	C₂²×C₄	—	2	1	no	—
849	C₂²×C₄	—	2	1	no	—
850	C₂²×C₄	—	2	1	no	—
851	C₂²×C₄	—	2	1	no	—
852	C₂²×C₄	—	2	1	no	—
853	C₂²×C₄	—	2	1	no	—
854	C₂²×C₄	—	4	1	no	—
855	C₂²×C₄	—	4	1	no	—
856	C₂²×C₄	—	4	1	no	—
857	C₂²×C₄	—	4	1	no	—
858	C₂²×C₄	—	4	2	no	—
859	C₂²×C₄	—	4	2	no	—
860	C₂²×C₄	—	4	2	no	—
861	C₂²×C₄	—	8	1	no	—
862	C₂²×C₄	—	8	1	no	—
863	C₂²×C₄	—	8	1	no	—
864	C₂²×C₄	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	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	C₂×#41	1	2	yes	—
878	C₂²×C₄	H(5,𝔽₂)	1	2	yes	—
879	C₂²×C₄	C₂⁵	1	1	yes	characteristic
880	SD₁₆	—	8	2	no	—
881	SD₁₆	—	8	2	no	—
882	SD₁₆	—	8	2	no	—
883	SD₁₆	—	8	2	no	—
884	D₈	—	8	2	no	—
885	D₈	—	8	2	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	—	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	C₄⋊C₄	—	2	4	no	—
911	C₄⋊C₄	—	2	2	no	—
912	C₄⋊C₄	—	2	2	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	—	2	1	no	—
934	C₄⋊C₄	—	4	1	no	—
935	C₄⋊C₄	—	4	1	no	—
936	C₄⋊C₄	—	4	1	no	—
937	C₄⋊C₄	—	4	1	no	—
938	C₄⋊C₄	—	4	1	no	—
939	C₄⋊C₄	—	4	1	no	—
940	C₄⋊C₄	—	4	1	no	—
941	C₄⋊C₄	—	4	1	no	—
942	C₄⋊C₄	—	4	1	no	—
943	C₄⋊C₄	—	4	1	no	—
944	C₄⋊C₄	—	4	2	no	—
945	C₄⋊C₄	—	4	2	no	—
946	C₄⋊C₄	—	4	2	no	—
947	C₄⋊C₄	—	4	2	no	—
948	C₄⋊C₄	—	4	2	no	—
949	C₄⋊C₄	—	4	2	no	—
950	C₄⋊C₄	—	4	2	no	—
951	C₄⋊C₄	—	4	2	no	—
952	C₄⋊C₄	—	4	2	no	—
953	C₄⋊C₄	—	4	2	no	—
954	C₄⋊C₄	—	4	2	no	—
955	C₄⋊C₄	—	4	2	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	—	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	C₂×#41	1	2	yes	—
972	C₂²⋊C₄	—	2	4	no	—
973	C₂²⋊C₄	—	2	2	no	—
974	C₂²⋊C₄	—	2	2	no	—
975	C₂²⋊C₄	—	4	1	no	—
976	C₂²⋊C₄	—	4	1	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	—	4	2	no	—
985	C₂²⋊C₄	—	4	2	no	—
986	C₂²⋊C₄	—	4	2	no	—
987	C₂²⋊C₄	—	4	2	no	—
988	C₂²⋊C₄	—	4	2	no	—
989	C₂²⋊C₄	—	4	2	no	—
990	C₂²⋊C₄	—	8	1	no	—
991	C₂²⋊C₄	—	8	1	no	—
992	C₂²⋊C₄	—	8	1	no	—
993	C₂²⋊C₄	—	8	1	no	—
994	C₂²⋊C₄	—	8	1	no	—
995	C₂²⋊C₄	—	8	1	no	—
996	C₂²⋊C₄	—	8	1	no	—
997	C₂²⋊C₄	—	8	1	no	—
998	C₂²⋊C₄	—	8	1	no	—
999	C₂²⋊C₄	—	8	1	no	—
1000	C₂²⋊C₄	—	8	1	no	—
1001	C₂²⋊C₄	—	8	1	no	—
1002	C₂²⋊C₄	—	8	1	no	—
1003	C₂²⋊C₄	—	8	1	no	—
1004	C₂²⋊C₄	—	8	1	no	—
1005	C₂²⋊C₄	—	8	1	no	—
1006	C₂²⋊C₄	—	8	1	no	—
1007	C₂²⋊C₄	—	8	1	no	—
1008	C₂²⋊C₄	—	8	1	no	—
1009	C₂²⋊C₄	—	8	1	no	—
1010	C₂²⋊C₄	—	8	1	no	—
1011	C₂²⋊C₄	—	8	1	no	—
1012	C₂²⋊C₄	—	8	1	no	—
1013	C₂²⋊C₄	—	8	1	no	—
1014	C₂²⋊C₄	—	8	1	no	—
1015	C₂²⋊C₄	—	8	1	no	—
1016	C₂²⋊C₄	—	8	1	no	—
1017	C₄²	—	2	2	no	—
1018	C₄²	—	2	2	no	—
1019	C₄²	—	2	1	no	—
1020	C₄²	—	2	1	no	—
1021	C₄²	—	2	1	no	—
1022	C₄²	—	2	1	no	—
1023	C₄²	—	2	1	no	—
1024	C₄²	—	2	1	no	—
1025	C₄²	—	2	1	no	—
1026	C₄²	—	2	1	no	—
1027	C₄²	—	2	1	no	—
1028	C₄²	—	2	1	no	—
1029	C₄²	—	2	1	no	—
1030	C₄²	—	2	1	no	—
1031	C₄²	—	4	2	no	—
1032	C₄²	—	4	2	no	—
1033	C₄²	—	4	2	no	—
1034	C₄²	—	4	2	no	—
1035	C₄²	—	4	2	no	—
1036	C₄²	—	4	2	no	—
1037	C₄²	—	4	2	no	—
1038	C₄²	—	4	2	no	—
1039	C₄²	—	8	1	no	—
1040	C₄²	—	8	1	no	—
1041	C₄²	—	8	1	no	—
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	—	4	1	no	—
1049	C₂³	—	4	1	no	—
1050	C₂³	—	4	1	no	—
1051	C₂³	—	4	1	no	—
1052	C₂³	—	4	1	no	—
1053	C₂³	—	4	1	no	—
1054	C₂³	—	4	1	no	—
1055	C₂³	—	4	1	no	—
1056	C₂³	—	4	1	no	—
1057	C₂³	—	4	1	no	—
1058	C₂³	—	4	1	no	—
1059	C₂³	—	4	1	no	—
1060	C₂³	—	4	1	no	—
1061	C₂³	—	4	1	no	—
1062	C₂³	—	4	1	no	—
1063	C₂³	—	4	1	no	—
1064	C₂³	—	4	1	no	—
1065	C₂³	—	4	1	no	—
1066	C₂³	—	4	1	no	—
1067	C₂³	—	4	1	no	—
1068	C₂³	—	4	1	no	—
1069	C₂³	—	8	4	no	—
1070	C₂³	—	8	4	no	—
1071	C₂³	—	8	4	no	—
1072	C₂³	—	16	2	no	—
1073	C₂³	—	16	2	no	—
1074	C₂³	—	16	2	no	—
1075	C₂³	—	16	2	no	—
1076	C₂³	#546	1	2	yes	—
1077	C₂³	C₂³×D₄	1	1	yes	characteristic
1078	Q₈	—	2	2	no	—
1079	Q₈	—	2	2	no	—
1080	Q₈	—	4	1	no	—
1081	Q₈	—	4	1	no	—
1082	Q₈	—	4	1	no	—
1083	Q₈	—	4	1	no	—
1084	Q₈	—	4	1	no	—
1085	Q₈	—	4	1	no	—
1086	D₄	—	4	1	no	—
1087	D₄	—	4	1	no	—
1088	D₄	—	4	1	no	—
1089	D₄	—	4	1	no	—
1090	D₄	—	4	1	no	—
1091	D₄	—	4	1	no	—
1092	D₄	—	4	1	no	—
1093	D₄	—	4	1	no	—
1094	D₄	—	4	1	no	—
1095	D₄	—	4	1	no	—
1096	D₄	—	4	1	no	—
1097	D₄	—	4	1	no	—
1098	D₄	—	8	4	no	—
1099	D₄	—	8	4	no	—
1100	C₂×C₄	—	2	1	no	—
1101	C₂×C₄	—	2	1	no	—
1102	C₂×C₄	—	2	2	no	—
1103	C₂×C₄	—	2	2	no	—
1104	C₂×C₄	—	2	2	no	—
1105	C₂×C₄	—	2	2	no	—
1106	C₂×C₄	—	2	1	no	—
1107	C₂×C₄	—	2	1	no	—
1108	C₂×C₄	—	2	1	no	—
1109	C₂×C₄	—	2	1	no	—
1110	C₂×C₄	—	2	1	no	—
1111	C₂×C₄	—	2	1	no	—
1112	C₂×C₄	—	2	1	no	—
1113	C₂×C₄	—	2	1	no	—
1114	C₂×C₄	—	2	1	no	—
1115	C₂×C₄	—	2	1	no	—
1116	C₂×C₄	—	2	1	no	—
1117	C₂×C₄	—	2	1	no	—
1118	C₂×C₄	—	2	1	no	—
1119	C₂×C₄	—	2	1	no	—
1120	C₂×C₄	—	2	1	no	—
1121	C₂×C₄	—	2	1	no	—
1122	C₂×C₄	—	2	1	no	—
1123	C₂×C₄	—	2	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	1	no	—
1131	C₂×C₄	—	2	1	no	—
1132	C₂×C₄	—	2	1	no	—
1133	C₂×C₄	—	2	1	no	—
1134	C₂×C₄	—	2	1	no	—
1135	C₂×C₄	—	2	1	no	—
1136	C₂×C₄	—	2	1	no	—
1137	C₂×C₄	—	2	1	no	—
1138	C₂×C₄	—	2	1	no	—
1139	C₂×C₄	—	2	1	no	—
1140	C₂×C₄	—	2	1	no	—
1141	C₂×C₄	—	2	1	no	—
1142	C₂×C₄	—	2	2	no	—
1143	C₂×C₄	—	2	2	no	—
1144	C₂×C₄	—	4	1	no	—
1145	C₂×C₄	—	4	1	no	—
1146	C₂×C₄	—	4	1	no	—
1147	C₂×C₄	—	4	1	no	—
1148	C₂×C₄	—	4	1	no	—
1149	C₂×C₄	—	4	1	no	—
1150	C₂×C₄	—	4	1	no	—
1151	C₂×C₄	—	4	1	no	—
1152	C₂×C₄	—	4	1	no	—
1153	C₂×C₄	—	4	1	no	—
1154	C₂×C₄	—	4	1	no	—
1155	C₂×C₄	—	4	1	no	—
1156	C₂×C₄	—	4	1	no	—
1157	C₂×C₄	—	4	1	no	—
1158	C₂×C₄	—	4	1	no	—
1159	C₂×C₄	—	4	1	no	—
1160	C₂×C₄	—	4	1	no	—
1161	C₂×C₄	—	4	1	no	—
1162	C₂×C₄	—	4	1	no	—
1163	C₂×C₄	—	4	1	no	—
1164	C₂×C₄	—	4	1	no	—
1165	C₂×C₄	—	4	1	no	—
1166	C₂×C₄	—	4	1	no	—
1167	C₂×C₄	—	4	1	no	—
1168	C₂×C₄	—	4	1	no	—
1169	C₂×C₄	—	4	1	no	—
1170	C₂×C₄	—	4	1	no	—
1171	C₂×C₄	—	4	1	no	—
1172	C₂×C₄	—	4	1	no	—
1173	C₂×C₄	—	4	1	no	—
1174	C₂×C₄	—	4	1	no	—
1175	C₂×C₄	—	4	1	no	—
1176	C₂×C₄	—	4	1	no	—
1177	C₂×C₄	—	4	1	no	—
1178	C₂×C₄	—	4	1	no	—
1179	C₂×C₄	—	4	1	no	—
1180	C₂×C₄	—	4	1	no	—
1181	C₂×C₄	—	8	2	no	—
1182	C₂×C₄	—	8	2	no	—
1183	C₂×C₄	—	8	4	no	—
1184	C₂×C₄	—	16	2	no	—
1185	C₂×C₄	#546	1	2	yes	—
1186	C₂×C₄	C₂²×#41	1	1	yes	characteristic
1187	C₂×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
1188	C₂×C₄	#585	1	1	yes	characteristic
1189	C₂×C₄	#585	1	1	yes	characteristic
1190	C₂×C₄	#585	1	1	yes	characteristic
1191	C₂×C₄	#585	1	1	yes	characteristic
1192	C₈	—	4	1	no	—
1193	C₈	—	4	1	no	—
1194	C₈	—	4	1	no	—
1195	C₈	—	4	1	no	—
1196	C₈	—	4	1	no	—
1197	C₈	—	4	1	no	—
1198	C₈	—	4	1	no	—
1199	C₈	—	4	1	no	—
1200	C₂²	—	2	2	no	—
1201	C₂²	—	2	2	no	—
1202	C₂²	—	2	2	no	—
1203	C₂²	—	4	1	no	—
1204	C₂²	—	4	1	no	—
1205	C₂²	—	4	1	no	—
1206	C₂²	—	4	1	no	—
1207	C₂²	—	8	1	no	—
1208	C₂²	—	8	1	no	—
1209	C₂²	—	8	1	no	—
1210	C₂²	—	8	1	no	—
1211	C₂²	—	8	1	no	—
1212	C₂²	—	8	1	no	—
1213	C₂²	—	8	1	no	—
1214	C₂²	—	8	1	no	—
1215	C₂²	—	8	1	no	—
1216	C₂²	—	8	1	no	—
1217	C₂²	—	8	1	no	—
1218	C₂²	—	8	1	no	—
1219	C₂²	—	8	1	no	—
1220	C₂²	—	8	1	no	—
1221	C₂²	—	8	1	no	—
1222	C₂²	—	8	1	no	—
1223	C₂²	—	8	1	no	—
1224	C₂²	—	8	1	no	—
1225	C₂²	—	8	1	no	—
1226	C₂²	—	8	1	no	—
1227	C₂²	—	8	1	no	—
1228	C₂²	—	16	8	no	—
1229	C₂²	#3449	1	1	yes	characteristic
1230	C₂²	C₂×#546	1	1	yes	characteristic
1231	C₂²	#3487	1	1	yes	characteristic
1232	C₂²	#3584	1	1	yes	characteristic
1233	C₂²	#3585	1	1	yes	characteristic
1234	C₂²	#3585	1	1	yes	characteristic
1235	C₂²	#3586	1	1	yes	characteristic
1236	C₄	—	2	2	no	—
1237	C₄	—	4	1	no	—
1238	C₄	—	4	1	no	—
1239	C₄	—	4	1	no	—
1240	C₄	—	4	1	no	—
1241	C₄	—	4	1	no	—
1242	C₄	—	4	1	no	—
1243	C₄	—	4	1	no	—
1244	C₄	—	4	1	no	—
1245	C₄	—	4	2	no	—
1246	C₄	—	4	1	no	—
1247	C₄	—	4	1	no	—
1248	C₄	—	4	1	no	—
1249	C₄	—	4	1	no	—
1250	C₄	—	4	2	no	—
1251	C₄	—	8	1	no	—
1252	C₄	—	8	1	no	—
1253	C₄	—	8	1	no	—
1254	C₄	—	8	1	no	—
1255	C₄	—	8	1	no	—
1256	C₄	—	8	1	no	—
1257	C₄	—	8	1	no	—
1258	C₄	—	8	1	no	—
1259	C₄	—	8	1	no	—
1260	C₄	—	8	1	no	—
1261	C₄	—	8	1	no	—
1262	C₄	#3521	1	1	yes	characteristic
1263	C₄	#3521	1	1	yes	characteristic
1264	C₄	#3560	1	1	yes	characteristic
1265	C₄	#3560	1	1	yes	characteristic
1266	C₂	—	4	2	no	—
1267	C₂	—	16	1	no	—
1268	C₂	—	16	1	no	—
1269	C₂	—	16	1	no	—
1270	C₂	#38031	1	1	yes	characteristic
1271	C₂	#60973	1	1	yes	characteristic
1272	C₂	#60997	1	1	yes	characteristic
1273	C₂	#61182	1	1	yes	characteristic
1274	C₂	#61189	1	1	yes	characteristic
1275	C₂	#61925	1	1	yes	characteristic
1276	C₂	#61945	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³	C₂³×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁵
prime radical	C₂×#447	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³ ◁ #2296 ◁ G
LECS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #37799	C₂	semidirect
2. #35266	C₂	semidirect
3. #33101	C₂	semidirect
4. #32257	C₂	semidirect
5. #32241	C₂	semidirect
6. #32183	C₂	semidirect
7. #32167	C₂	semidirect
8. #31928	C₂	semidirect
9. #31899	C₂	semidirect
10. #31821	C₂	semidirect
11. #31816	C₂	semidirect
12. #29917	C₂	semidirect
14. #29342	C₂	semidirect
15. #29252	C₂	semidirect
16. #29096	C₂	semidirect
17. #29080	C₂	semidirect
18. #28900	C₂	semidirect
19. #28883	C₂	semidirect
20. #27572	C₂	semidirect
21. #27567	C₂	semidirect
22. #27089	C₂	semidirect
23. #27086	C₂	semidirect
25. #24507	C₂	semidirect
26. #23942	C₂	semidirect
28. #22605	C₂	semidirect
29. #22052	C₂	semidirect
30. #21873	C₂	semidirect
31. #21396	C₂	semidirect
50. #2552	C₂²	semidirect
51. #2545	C₂²	semidirect
67. #2454	C₂²	semidirect
68. #2453	C₂²	semidirect
69. #2448	C₂²	semidirect
70. #2446	C₂²	semidirect
72. #2367	C₂²	semidirect
73. Q₈×C₄⋊C₄	C₂²	semidirect
82. #2101	C₂²	semidirect
83. #2100	C₂²	semidirect
84. #2100	C₂²	semidirect
85. #2099	C₂²	semidirect
86. #2093	C₂²	semidirect
87. #2092	C₂²	semidirect
88. #2088	C₂²	semidirect
89. #2086	C₂²	semidirect
90. #2085	C₂²	semidirect
91. #2083	C₂²	semidirect
92. #2073	C₂²	semidirect
95. #2071	C₂²	semidirect
96. #2068	C₂²	semidirect
97. #2068	C₂²	semidirect
110. #2042	C₂²	semidirect
111. #2042	C₂²	semidirect
122. #1992	C₂²	semidirect
123. #1991	C₂²	semidirect
124. #1989	C₂²	semidirect
125. #1989	C₂²	semidirect
126. #1983	C₂²	semidirect
127. #1983	C₂²	semidirect
134. #1960	C₂²	semidirect
135. #1956	C₂²	semidirect
136. #1940	C₂²	semidirect
137. #1939	C₂²	semidirect
142. #1936	C₂²	semidirect
143. #1935	C₂²	semidirect
146. #1934	C₂²	semidirect
147. #1933	C₂²	semidirect
148. #1928	C₂²	semidirect
149. #1928	C₂²	semidirect
150. #1927	C₂²	semidirect
151. #1927	C₂²	semidirect
154. #1921	C₂²	semidirect
155. #1921	C₂²	semidirect
156. #1920	C₂²	semidirect
157. #1919	C₂²	semidirect
158. #1918	C₂²	semidirect
159. #1918	C₂²	semidirect
160. #1917	C₂²	semidirect
161. #1917	C₂²	semidirect
162. #1917	C₂²	semidirect
163. #1916	C₂²	semidirect
183. #1865	C₂²	semidirect
184. #1863	C₂²	semidirect
190. #1805	C₂²	semidirect
191. #1805	C₂²	semidirect
192. #1803	C₂²	semidirect
193. #1803	C₂²	semidirect
196. #1771	C₂²	semidirect
197. #1770	C₂²	semidirect
198. #1763	C₂²	semidirect
199. #1763	C₂²	semidirect
200. #1762	C₂²	semidirect
201. #1762	C₂²	semidirect

Maximal subgroups

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

subgroup	index
#37799	2
#35266	2
#33101	2
#32257	2
#32241	2
#32183	2
#32167	2
#31928	2
#31899	2
#31821	2
#31816	2
#29917	2
#29727	2
#29342	2
#29252	2
#29096	2
#29080	2
#28900	2
#28883	2
#27572	2
#27567	2
#27089	2
#27086	2
#24512	2
#24507	2
#23942	2
#23936	2
#22605	2
#22052	2
#21873	2
#21396	2