Subgroups — #6554003

Order 512.

1430 conjugacy classes of subgroups.

The subgroup lattice has 1227 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#39078	C₂	1	1	yes	maximal, characteristic, complemented
2	#38254	C₂	1	1	yes	maximal, characteristic
3	#30390	C₂	1	1	yes	maximal, characteristic, complemented
4	#30341	C₂	1	1	yes	maximal, characteristic, complemented
5	#29786	C₂	1	1	yes	maximal, characteristic, complemented
6	#29449	C₂	1	1	yes	maximal, characteristic, complemented
7	#29443	C₂	1	1	yes	maximal, characteristic, complemented
8	#29199	C₂	1	1	yes	maximal, characteristic, complemented
9	#29025	C₂	1	1	yes	maximal, characteristic, complemented
10	#29008	C₂	1	1	yes	maximal, characteristic, complemented
11	#28951	C₂	1	1	yes	maximal, characteristic, complemented
12	#28889	C₂	1	1	yes	maximal, characteristic, complemented
13	#28658	C₂	1	1	yes	maximal, characteristic, complemented
14	#28361	C₂	1	1	yes	maximal, characteristic
15	#28038	C₂	1	1	yes	maximal, characteristic, complemented
16	#28010	C₂	1	1	yes	maximal, characteristic, complemented
17	#27716	C₂	1	1	yes	maximal, characteristic, complemented
18	#27262	C₂	1	1	yes	maximal, characteristic
19	#26846	C₂	1	1	yes	maximal, characteristic, complemented
20	#26487	C₂	1	1	yes	maximal, characteristic, complemented
21	#26078	C₂	1	1	yes	maximal, characteristic, complemented
22	#24619	C₂	1	1	yes	maximal, characteristic, complemented
23	#24516	C₂	1	1	yes	maximal, characteristic
24	#23775	C₂	1	1	yes	maximal, characteristic, complemented
25	#23694	C₂	1	1	yes	maximal, characteristic, complemented
26	#23614	C₂	1	1	yes	maximal, characteristic
27	#23038	C₂	1	1	yes	maximal, characteristic, complemented
28	#22919	C₂	1	1	yes	maximal, characteristic, complemented
29	#22874	C₂	1	1	yes	maximal, characteristic
30	#22580	C₂	1	1	yes	maximal, characteristic
31	#20553	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×#501	C₂²	1	1	yes	characteristic, complemented
33	C₂×#489	C₂²	1	1	yes	characteristic
34	C₂×#485	C₂²	1	1	yes	characteristic
35	C₂×#470	C₂²	1	1	yes	characteristic
36	C₂×#450	C₂²	1	1	yes	characteristic
37	C₂×#441	C₂²	1	1	yes	characteristic, complemented
38	C₂×C₄×SD₁₆	C₂²	1	1	yes	characteristic
39	C₂×#433	C₂²	1	1	yes	characteristic
40	C₂×#428	C₂²	1	1	yes	characteristic
41	C₂×#424	C₂²	1	1	yes	characteristic
42	C₂×#418	C₂²	1	1	yes	characteristic
43	C₂²×#102	C₂²	1	1	yes	characteristic
44	#2863	C₂²	1	1	yes	characteristic, complemented
45	#2861	C₂²	1	1	yes	characteristic
46	#2796	—	2	1	no	—
47	#2786	—	2	1	no	—
48	#2770	—	2	1	no	—
49	#2769	—	2	1	no	—
50	#2758	—	2	1	no	—
51	#2735	—	2	1	no	—
52	#2735	—	2	1	no	—
53	#2690	—	2	1	no	—
54	#2647	C₂²	1	1	yes	characteristic, complemented
55	#2644	C₂²	1	1	yes	characteristic
56	#2625	C₂²	1	1	yes	characteristic
57	#2625	C₂²	1	1	yes	characteristic
58	#2601	—	2	1	no	—
59	#2590	—	2	1	no	—
60	#2577	—	2	1	no	—
61	#2516	—	2	1	no	—
62	#2512	C₂²	1	1	yes	characteristic
63	#2511	C₂²	1	1	yes	characteristic, complemented
64	#2509	C₂²	1	1	yes	characteristic, complemented
65	#2506	C₂²	1	1	yes	characteristic, complemented
66	#2499	C₂²	1	1	yes	characteristic
67	#2482	—	2	1	no	—
68	#2480	—	2	1	no	—
69	#2462	—	2	1	no	—
70	#2454	C₂²	1	1	yes	characteristic
71	#2451	C₂²	1	1	yes	characteristic, complemented
72	#2448	C₂²	1	1	yes	characteristic
73	#2447	C₂²	1	1	yes	characteristic
74	#2441	C₂²	1	1	yes	characteristic
75	#2440	C₂²	1	1	yes	characteristic
76	#2435	C₂²	1	1	yes	characteristic
77	#2421	—	2	1	no	—
78	#2362	C₂²	1	1	yes	characteristic
79	#2360	C₂²	1	1	yes	characteristic
80	#2347	C₂²	1	1	yes	characteristic
81	D₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
82	#2326	C₂²	1	1	yes	characteristic
83	#2320	C₂²	1	1	yes	characteristic, complemented
84	#2316	C₂²	1	1	yes	characteristic
85	#2309	C₂²	1	1	yes	characteristic
86	C₄×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
87	#2298	C₂²	1	1	yes	characteristic
88	#2293	C₂²	1	1	yes	characteristic
89	#2101	C₂²	1	1	yes	characteristic, complemented
90	#2100	C₂²	1	1	yes	characteristic, complemented
91	#2094	C₂²	1	1	yes	characteristic
92	#2092	C₂²	1	1	yes	characteristic
93	#2088	C₂²	1	1	yes	characteristic, complemented
94	#2088	C₂²	1	1	yes	characteristic, complemented
95	#2088	C₂²	1	1	yes	characteristic, complemented
96	#2087	C₂²	1	1	yes	characteristic, complemented
97	#2084	C₂²	1	1	yes	characteristic, complemented
98	#2083	C₂²	1	1	yes	characteristic, complemented
99	#2072	C₂²	1	1	yes	characteristic, complemented
100	#2071	C₂²	1	1	yes	characteristic
101	#2068	C₂²	1	1	yes	characteristic, complemented
102	#2068	C₂²	1	1	yes	characteristic, complemented
103	#2067	C₂²	1	1	yes	characteristic
104	#2067	C₂²	1	1	yes	characteristic
105	#2067	C₂²	1	1	yes	characteristic
106	#2067	C₂²	1	1	yes	characteristic
107	#2067	C₂²	1	1	yes	characteristic
108	#2066	C₂²	1	1	yes	characteristic, complemented
109	#2066	C₂²	1	1	yes	characteristic, complemented
110	#2066	C₂²	1	1	yes	characteristic, complemented
111	#2066	C₂²	1	1	yes	characteristic, complemented
112	#2065	C₂²	1	1	yes	characteristic
113	#2065	C₂²	1	1	yes	characteristic
114	#2065	C₂²	1	1	yes	characteristic
115	#2065	C₂²	1	1	yes	characteristic
116	#2065	C₂²	1	1	yes	characteristic
117	#2059	C₂²	1	1	yes	characteristic, complemented
118	#2058	C₂²	1	1	yes	characteristic, complemented
119	#2056	C₂²	1	1	yes	characteristic, complemented
120	#2056	C₂²	1	1	yes	characteristic, complemented
121	#2055	C₂²	1	1	yes	characteristic
122	#2055	C₂²	1	1	yes	characteristic
123	#2042	C₂²	1	1	yes	characteristic
124	#2042	C₂²	1	1	yes	characteristic
125	#2026	C₂²	1	1	yes	characteristic, complemented
126	#2023	C₂²	1	1	yes	characteristic
127	#2015	C₂²	1	1	yes	characteristic
128	#2015	C₂²	1	1	yes	characteristic
129	#1992	C₂²	1	1	yes	characteristic, complemented
130	#1973	C₂²	1	1	yes	characteristic
131	#1973	C₂²	1	1	yes	characteristic
132	#1969	C₂²	1	1	yes	characteristic, complemented
133	#1968	C₂²	1	1	yes	characteristic
134	#1968	C₂²	1	1	yes	characteristic
135	#1968	C₂²	1	1	yes	characteristic
136	#1959	C₂²	1	1	yes	characteristic
137	#1959	C₂²	1	1	yes	characteristic
138	#1958	C₂²	1	1	yes	characteristic
139	#1944	C₂²	1	1	yes	characteristic, complemented
140	#1944	C₂²	1	1	yes	characteristic, complemented
141	#1943	C₂²	1	1	yes	characteristic, complemented
142	#1942	C₂²	1	1	yes	characteristic, complemented
143	#1942	C₂²	1	1	yes	characteristic, complemented
144	#1941	C₂²	1	1	yes	characteristic, complemented
145	#1936	C₂²	1	1	yes	characteristic
146	#1936	C₂²	1	1	yes	characteristic
147	#1936	C₂²	1	1	yes	characteristic
148	#1936	C₂²	1	1	yes	characteristic
149	#1935	C₂²	1	1	yes	characteristic, complemented
150	#1935	C₂²	1	1	yes	characteristic, complemented
151	#1935	C₂²	1	1	yes	characteristic, complemented
152	#1934	C₂²	1	1	yes	characteristic
153	#1934	C₂²	1	1	yes	characteristic
154	#1934	C₂²	1	1	yes	characteristic
155	#1933	C₂²	1	1	yes	characteristic, complemented
156	#1933	C₂²	1	1	yes	characteristic, complemented
157	#1928	C₂²	1	1	yes	characteristic, complemented
158	#1928	C₂²	1	1	yes	characteristic, complemented
159	#1927	C₂²	1	1	yes	characteristic, complemented
160	#1926	C₂²	1	1	yes	characteristic
161	#1926	C₂²	1	1	yes	characteristic
162	#1925	C₂²	1	1	yes	characteristic
163	#1919	C₂²	1	1	yes	characteristic, complemented
164	#1918	C₂²	1	1	yes	characteristic, complemented
165	#1892	C₂²	1	1	yes	characteristic
166	#1892	C₂²	1	1	yes	characteristic
167	#1880	C₂²	1	1	yes	characteristic
168	#1877	C₂²	1	1	yes	characteristic
169	#1873	C₂²	1	1	yes	characteristic
170	#1872	C₂²	1	1	yes	characteristic
171	#1865	C₂²	1	1	yes	characteristic, complemented
172	#1865	C₂²	1	1	yes	characteristic, complemented
173	#1864	C₂²	1	1	yes	characteristic
174	#1864	C₂²	1	1	yes	characteristic
175	#1863	C₂²	1	1	yes	characteristic, complemented
176	#1862	C₂²	1	1	yes	characteristic
177	#1854	C₂²	1	1	yes	characteristic
178	#1853	C₂²	1	1	yes	characteristic
179	#1844	C₂²	1	1	yes	characteristic, complemented
180	#1836	C₂²	1	1	yes	characteristic, complemented
181	#1825	C₂²	1	1	yes	characteristic
182	#1809	C₂²	1	1	yes	characteristic
183	#1786	C₂²	1	1	yes	characteristic
184	C₄×#106	C₂²	1	1	yes	characteristic, complemented
185	C₄×#106	C₂²	1	1	yes	characteristic, complemented
186	#1771	C₂²	1	1	yes	characteristic, complemented
187	#1771	C₂²	1	1	yes	characteristic, complemented
188	#1770	C₂²	1	1	yes	characteristic, complemented
189	C₈×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
190	#1768	C₂²	1	1	yes	characteristic, complemented
191	#1768	C₂²	1	1	yes	characteristic, complemented
192	#1767	C₂²	1	1	yes	characteristic, complemented
193	C₄×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
194	#1762	C₂²	1	1	yes	characteristic
195	C₄×#103	C₂²	1	1	yes	characteristic, complemented
196	C₄×#102	C₂²	1	1	yes	characteristic
197	C₄×#102	C₂²	1	1	yes	characteristic
198	#1753	C₂²	1	1	yes	characteristic
199	#1753	C₂²	1	1	yes	characteristic
200	#1752	C₂²	1	1	yes	characteristic
201	C₈×C₂²⋊C₄	C₂²	1	1	yes	characteristic
202	#1735	C₂²	1	1	yes	characteristic
203	C₂³×D₄	C₂³	1	1	yes	characteristic
204	C₂²×Q₁₆	C₂³	1	1	yes	characteristic
205	C₂²×SD₁₆	C₂³	1	1	yes	characteristic
206	C₂²×SD₁₆	C₂³	1	1	yes	characteristic
207	C₂²×M₁₆	C₂³	1	1	yes	characteristic
208	C₂³×C₈	C₂³	1	1	yes	characteristic
209	C₂×C₄⋊Q₈	C₂³	1	1	yes	characteristic
210	C₂×#126	—	2	1	no	—
211	C₂×#125	—	2	1	no	—
212	C₂×#125	C₂³	1	1	yes	characteristic
213	C₂×#124	C₂³	1	1	yes	characteristic
214	C₂×#124	C₂³	1	1	yes	characteristic
215	C₂×C₂²⋊Q₈	—	2	1	no	—
216	C₂×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
217	C₂×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
218	C₂×C₄×Q₈	—	2	1	no	—
219	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
220	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
221	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
222	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
223	C₂×#117	—	2	1	no	—
224	C₂×#117	C₂³	1	1	yes	characteristic
225	C₂×#117	C₂³	1	1	yes	characteristic
226	C₂×#117	C₂³	1	1	yes	characteristic
227	C₂²×C₄⋊C₄	C₂³	1	1	yes	characteristic
228	C₂²×C₂²⋊C₄	—	2	1	no	—
229	#501	—	4	2	no	—
230	#489	—	4	2	no	—
231	#485	—	2	4	no	—
232	#470	—	2	4	no	—
233	#450	—	2	4	no	—
234	#441	—	4	2	no	—
235	C₄×SD₁₆	—	4	2	no	—
236	#433	—	2	4	no	—
237	#428	—	4	2	no	—
238	C₂×#107	C₂³	1	1	yes	characteristic
239	C₂×#107	C₂³	1	1	yes	characteristic
240	C₂×#107	C₂³	1	1	yes	characteristic
241	C₂×#107	C₂³	1	1	yes	characteristic
242	C₂×#107	C₂³	1	1	yes	characteristic
243	C₂×#106	C₂³	1	1	yes	characteristic
244	C₂×#106	C₂³	1	1	yes	characteristic
245	C₂×#106	C₂³	1	1	yes	characteristic
246	C₂×#106	C₂³	1	1	yes	characteristic
247	C₂×#106	C₂³	1	1	yes	characteristic
248	C₂×#106	C₂³	1	1	yes	characteristic
249	C₂×#106	C₂³	1	1	yes	characteristic
250	C₂×#106	C₂³	1	1	yes	characteristic
251	#424	—	2	4	no	—
252	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
253	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
254	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
255	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
256	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
257	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
258	#418	—	2	4	no	—
259	C₂×#103	C₂³	1	1	yes	characteristic
260	C₂×#103	C₂³	1	1	yes	characteristic
261	C₂×#103	C₂³	1	1	yes	characteristic
262	C₂×#103	C₂³	1	1	yes	characteristic
263	C₂×#103	C₂³	1	1	yes	characteristic
264	C₂×#103	C₂³	1	1	yes	characteristic
265	C₂×#103	C₂³	1	1	yes	characteristic
266	C₂×#103	C₂³	1	1	yes	characteristic
267	C₂×#103	C₂³	1	1	yes	characteristic
268	C₂×#103	C₂³	1	1	yes	characteristic
269	C₂×#103	C₂³	1	1	yes	characteristic
270	C₂×#103	C₂³	1	1	yes	characteristic
271	C₂×#102	—	4	2	no	—
272	C₂×#102	C₂³	1	1	yes	characteristic
273	C₂×#102	C₂³	1	1	yes	characteristic
274	C₂×#102	C₂³	1	1	yes	characteristic
275	C₂×#102	C₂³	1	1	yes	characteristic
276	C₂×#102	C₂³	1	1	yes	characteristic
277	C₂×#102	C₂³	1	1	yes	characteristic
278	C₂×#102	C₂³	1	1	yes	characteristic
279	C₂×#102	C₂³	1	1	yes	characteristic
280	C₂×#102	C₂³	1	1	yes	characteristic
281	C₂×#102	C₂³	1	1	yes	characteristic
282	C₂×#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×C₂²⋊C₈	C₂³	1	1	yes	characteristic
287	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
288	C₂×#97	C₂³	1	1	yes	characteristic
289	C₂×#97	C₂³	1	1	yes	characteristic
290	C₂×#97	C₂³	1	1	yes	characteristic
291	C₂×#97	C₂³	1	1	yes	characteristic
292	C₂×#97	C₂³	1	1	yes	characteristic
293	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
294	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
295	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
296	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
297	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
298	#400	—	2	1	no	—
299	#400	—	2	1	no	—
300	#400	—	2	1	no	—
301	#400	—	2	1	no	—
302	#400	—	2	1	no	—
303	#400	—	2	1	no	—
304	#400	—	2	1	no	—
305	#400	—	2	1	no	—
306	#400	—	2	1	no	—
307	#399	—	2	1	no	—
308	#399	—	2	1	no	—
309	#399	—	2	1	no	—
310	#398	—	2	1	no	—
311	#398	—	2	1	no	—
312	#398	—	2	1	no	—
313	#398	—	2	1	no	—
314	#398	—	2	1	no	—
315	#398	—	2	1	no	—
316	#398	—	2	1	no	—
317	#397	—	2	1	no	—
318	#397	—	2	1	no	—
319	#397	—	2	1	no	—
320	#397	—	2	1	no	—
321	#397	—	2	1	no	—
322	#397	—	2	1	no	—
323	#397	—	2	1	no	—
324	#397	—	2	1	no	—
325	#397	—	2	1	no	—
326	#397	—	2	1	no	—
327	#397	—	2	1	no	—
328	#397	—	2	1	no	—
329	#397	—	2	1	no	—
330	#396	—	2	1	no	—
331	#396	—	2	1	no	—
332	#396	—	2	1	no	—
333	#396	—	2	1	no	—
334	#395	—	2	1	no	—
335	#395	—	2	1	no	—
336	#394	—	2	1	no	—
337	#394	—	2	1	no	—
338	#391	—	2	1	no	—
339	#391	—	2	1	no	—
340	#391	C₂³	1	1	yes	characteristic
341	#391	C₂³	1	1	yes	characteristic
342	#391	C₂³	1	1	yes	characteristic
343	#391	C₂³	1	1	yes	characteristic
344	#391	C₂³	1	1	yes	characteristic
345	#391	C₂³	1	1	yes	characteristic
346	#391	C₂³	1	1	yes	characteristic
347	#391	C₂³	1	1	yes	characteristic
348	#390	—	2	1	no	—
349	#390	—	2	1	no	—
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	#389	—	2	1	no	—
359	#389	—	2	1	no	—
360	#389	—	2	1	no	—
361	#389	—	2	1	no	—
362	#389	—	2	1	no	—
363	#389	—	2	1	no	—
364	#389	C₂³	1	1	yes	characteristic
365	#389	C₂³	1	1	yes	characteristic
366	#389	C₂³	1	1	yes	characteristic
367	#389	C₂³	1	1	yes	characteristic
368	#389	C₂³	1	1	yes	characteristic
369	#389	C₂³	1	1	yes	characteristic
370	#389	C₂³	1	1	yes	characteristic
371	#389	C₂³	1	1	yes	characteristic
372	#389	C₂³	1	1	yes	characteristic
373	#389	C₂³	1	1	yes	characteristic
374	#389	C₂³	1	1	yes	characteristic
375	#389	C₂³	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	#388	—	2	1	no	—
381	#388	—	2	1	no	—
382	#388	—	2	1	no	—
383	#388	—	2	1	no	—
384	#388	—	2	1	no	—
385	#388	—	2	1	no	—
386	#388	—	2	1	no	—
387	#388	—	2	1	no	—
388	#388	—	2	1	no	—
389	#388	—	2	1	no	—
390	#388	—	2	1	no	—
391	#388	—	2	1	no	—
392	#388	—	2	1	no	—
393	#388	—	2	1	no	—
394	#388	—	2	1	no	—
395	#388	D₄	1	1	yes	characteristic
396	#388	D₄	1	1	yes	characteristic
397	#388	D₄	1	1	yes	characteristic
398	#388	D₄	1	1	yes	characteristic
399	#387	—	2	1	no	—
400	#387	—	2	1	no	—
401	#387	—	2	1	no	—
402	#387	—	2	1	no	—
403	#387	—	2	1	no	—
404	#387	—	2	1	no	—
405	#387	—	2	1	no	—
406	#387	—	2	1	no	—
407	#387	—	2	1	no	—
408	#387	—	2	1	no	—
409	#387	—	2	1	no	—
410	#387	—	2	1	no	—
411	#387	—	2	1	no	—
412	#387	—	2	1	no	—
413	#387	—	2	1	no	—
414	#387	D₄	1	1	yes	characteristic
415	#387	D₄	1	1	yes	characteristic
416	#387	D₄	1	1	yes	characteristic
417	#387	D₄	1	1	yes	characteristic
418	#386	—	2	1	no	—
419	#386	—	2	1	no	—
420	#385	—	2	1	no	—
421	#385	—	2	1	no	—
422	#385	—	2	1	no	—
423	#385	—	2	1	no	—
424	#385	—	2	1	no	—
425	#385	—	2	1	no	—
426	#384	C₂³	1	1	yes	characteristic
427	#384	C₂³	1	1	yes	characteristic
428	#384	C₂³	1	1	yes	characteristic
429	#383	—	2	1	no	—
430	#383	—	2	1	no	—
431	#383	—	2	1	no	—
432	#382	—	2	1	no	—
433	#382	C₂³	1	1	yes	characteristic
434	#381	—	2	1	no	—
435	#380	—	2	1	no	—
436	#380	—	2	1	no	—
437	#380	—	2	1	no	—
438	#380	C₂³	1	1	yes	characteristic
439	#380	C₂³	1	1	yes	characteristic
440	#379	—	2	1	no	—
441	#379	—	2	1	no	—
442	#379	—	2	1	no	—
443	#379	—	2	1	no	—
444	#379	—	2	1	no	—
445	C₄×C₄⋊C₄	—	2	1	no	—
446	C₄×C₄⋊C₄	—	2	1	no	—
447	C₄×C₄⋊C₄	—	2	1	no	—
448	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
449	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
450	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
451	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
452	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
453	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
454	C₄×C₂²⋊C₄	—	2	1	no	—
455	C₄×C₂²⋊C₄	—	2	1	no	—
456	C₄×C₂²⋊C₄	C₂³	1	1	yes	characteristic
457	C₄×C₂²⋊C₄	C₂³	1	1	yes	characteristic
458	#376	C₂³	1	1	yes	characteristic
459	C₄³	C₂³	1	1	yes	characteristic
460	#340	C₂³	1	1	yes	characteristic
461	#340	C₂³	1	1	yes	characteristic
462	#340	C₂³	1	1	yes	characteristic
463	#340	C₂³	1	1	yes	characteristic
464	#340	C₂³	1	1	yes	characteristic
465	#340	C₂³	1	1	yes	characteristic
466	#340	C₂³	1	1	yes	characteristic
467	#340	C₂³	1	1	yes	characteristic
468	#340	C₂³	1	1	yes	characteristic
469	#340	C₂³	1	1	yes	characteristic
470	#340	C₂³	1	1	yes	characteristic
471	#340	C₂³	1	1	yes	characteristic
472	#340	C₂³	1	1	yes	characteristic
473	#340	C₂³	1	1	yes	characteristic
474	#340	C₂³	1	1	yes	characteristic
475	#340	C₂³	1	1	yes	characteristic
476	#340	C₂³	1	1	yes	characteristic
477	#340	C₂³	1	1	yes	characteristic
478	#340	C₂³	1	1	yes	characteristic
479	#340	C₂³	1	1	yes	characteristic
480	#340	C₂³	1	1	yes	characteristic
481	#340	C₂³	1	1	yes	characteristic
482	#336	C₂³	1	1	yes	characteristic
483	#336	C₂³	1	1	yes	characteristic
484	#336	C₂³	1	1	yes	characteristic
485	#336	C₂³	1	1	yes	characteristic
486	#336	C₂³	1	1	yes	characteristic
487	#336	C₂³	1	1	yes	characteristic
488	#336	C₂³	1	1	yes	characteristic
489	#336	C₂³	1	1	yes	characteristic
490	C₂⁵	—	2	1	no	—
491	C₂²×Q₈	—	2	1	no	—
492	C₂²×Q₈	C₂⁴	1	1	yes	characteristic
493	C₂²×Q₈	C₂⁴	1	1	yes	characteristic
494	C₂²×D₄	—	2	2	no	—
495	C₂²×D₄	—	2	1	no	—
496	C₂²×D₄	—	2	2	no	—
497	C₂²×D₄	—	2	2	no	—
498	C₂²×D₄	—	4	1	no	—
499	C₂²×D₄	—	4	1	no	—
500	C₂²×D₄	—	4	1	no	—
501	C₂²×D₄	C₂⁴	1	1	yes	characteristic
502	C₂²×D₄	C₂⁴	1	1	yes	characteristic
503	C₂³×C₄	—	2	1	no	—
504	C₂³×C₄	—	2	1	no	—
505	C₂³×C₄	—	2	1	no	—
506	C₂³×C₄	C₂⁴	1	1	yes	characteristic
507	C₂×Q₁₆	—	2	2	no	—
508	C₂×Q₁₆	—	4	1	no	—
509	C₂×Q₁₆	—	4	1	no	—
510	C₂×SD₁₆	—	2	2	no	—
511	C₂×SD₁₆	—	2	2	no	—
512	C₂×SD₁₆	—	2	2	no	—
513	C₂×SD₁₆	—	4	1	no	—
514	C₂×SD₁₆	—	4	1	no	—
515	C₂×SD₁₆	—	4	1	no	—
516	C₂×M₁₆	—	4	1	no	—
517	C₂×M₁₆	—	4	1	no	—
518	C₂×M₁₆	#41	1	4	yes	—
519	C₂²×C₈	—	2	2	no	—
520	C₂²×C₈	—	4	1	no	—
521	C₂²×C₈	—	4	1	no	—
522	C₂²×C₈	C₂⁴	1	1	yes	characteristic
523	C₂²×C₈	C₂⁴	1	1	yes	characteristic
524	C₂²×C₈	C₂⁴	1	1	yes	characteristic
525	C₂²×C₈	C₂⁴	1	1	yes	characteristic
526	C₂²×C₈	C₂⁴	1	1	yes	characteristic
527	C₂²×C₈	C₂⁴	1	1	yes	characteristic
528	C₂²×C₈	C₂⁴	1	1	yes	characteristic
529	C₂²×C₈	C₂⁴	1	1	yes	characteristic
530	C₄⋊Q₈	—	2	2	no	—
531	C₄⋊Q₈	—	4	1	no	—
532	#126	—	8	2	no	—
533	#125	—	4	1	no	—
534	#125	—	4	1	no	—
535	#125	—	8	2	no	—
536	#124	—	2	2	no	—
537	#124	—	4	1	no	—
538	#124	—	4	1	no	—
539	#124	—	4	1	no	—
540	C₂²⋊Q₈	—	2	2	no	—
541	C₂²⋊Q₈	—	2	2	no	—
542	C₂²⋊Q₈	—	2	2	no	—
543	C₂²⋊Q₈	—	2	2	no	—
544	C₂²⋊Q₈	—	8	2	no	—
545	C₄×Q₈	—	2	2	no	—
546	C₄×Q₈	—	4	1	no	—
547	C₄×Q₈	—	4	1	no	—
548	C₄×Q₈	—	4	1	no	—
549	C₄×Q₈	—	8	2	no	—
550	C₄×D₄	—	2	2	no	—
551	C₄×D₄	—	4	1	no	—
552	C₄×D₄	—	4	1	no	—
553	C₄×D₄	—	4	1	no	—
554	#117	—	2	2	no	—
555	#117	—	2	2	no	—
556	#117	—	2	2	no	—
557	#117	—	2	2	no	—
558	#117	—	4	1	no	—
559	#117	—	4	1	no	—
560	#117	—	8	2	no	—
561	C₂×C₄⋊C₄	—	2	2	no	—
562	C₂×C₄⋊C₄	—	2	1	no	—
563	C₂×C₄⋊C₄	—	2	1	no	—
564	C₂×C₄⋊C₄	—	2	1	no	—
565	C₂×C₄⋊C₄	—	2	1	no	—
566	C₂×C₄⋊C₄	—	2	1	no	—
567	C₂×C₄⋊C₄	—	2	1	no	—
568	C₂×C₄⋊C₄	—	2	1	no	—
569	C₂×C₄⋊C₄	—	2	1	no	—
570	C₂×C₄⋊C₄	—	2	1	no	—
571	C₂×C₄⋊C₄	—	2	1	no	—
572	C₂×C₄⋊C₄	—	2	1	no	—
573	C₂×C₄⋊C₄	—	2	1	no	—
574	C₂×C₄⋊C₄	—	2	1	no	—
575	C₂×C₄⋊C₄	—	2	1	no	—
576	C₂×C₄⋊C₄	—	2	1	no	—
577	C₂×C₄⋊C₄	—	2	1	no	—
578	C₂×C₄⋊C₄	—	2	1	no	—
579	C₂×C₄⋊C₄	—	2	1	no	—
580	C₂×C₄⋊C₄	—	2	1	no	—
581	C₂×C₄⋊C₄	—	2	1	no	—
582	C₂×C₄⋊C₄	—	2	1	no	—
583	C₂×C₄⋊C₄	—	2	1	no	—
584	C₂×C₄⋊C₄	—	2	1	no	—
585	C₂×C₄⋊C₄	—	2	1	no	—
586	C₂×C₄⋊C₄	—	2	1	no	—
587	C₂×C₄⋊C₄	—	2	1	no	—
588	C₂×C₄⋊C₄	—	2	1	no	—
589	C₂×C₄⋊C₄	—	2	1	no	—
590	C₂×C₄⋊C₄	—	2	1	no	—
591	C₂×C₄⋊C₄	—	2	1	no	—
592	C₂×C₄⋊C₄	—	4	1	no	—
593	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
594	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
595	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
596	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
597	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
598	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
599	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
600	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
601	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
602	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
603	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
604	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
605	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
606	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
607	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
608	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
609	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
610	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
611	C₂×C₂²⋊C₄	—	2	1	no	—
612	C₂×C₂²⋊C₄	—	2	1	no	—
613	C₂×C₂²⋊C₄	—	2	1	no	—
614	C₂×C₂²⋊C₄	—	2	1	no	—
615	C₂×C₂²⋊C₄	—	2	1	no	—
616	C₂×C₂²⋊C₄	—	2	1	no	—
617	C₂×C₂²⋊C₄	—	2	1	no	—
618	C₂×C₂²⋊C₄	—	2	1	no	—
619	C₂×C₂²⋊C₄	—	2	1	no	—
620	C₂×C₂²⋊C₄	—	2	1	no	—
621	C₂×C₂²⋊C₄	—	2	1	no	—
622	C₂×C₂²⋊C₄	—	2	1	no	—
623	C₂×C₂²⋊C₄	—	2	1	no	—
624	C₂×C₂²⋊C₄	—	2	1	no	—
625	C₂×C₂²⋊C₄	—	2	1	no	—
626	C₂×C₂²⋊C₄	—	2	1	no	—
627	C₂×C₂²⋊C₄	—	2	1	no	—
628	C₂×C₂²⋊C₄	—	2	1	no	—
629	C₂×C₂²⋊C₄	—	2	1	no	—
630	C₂×C₂²⋊C₄	—	2	1	no	—
631	C₂×C₂²⋊C₄	—	2	1	no	—
632	C₂×C₂²⋊C₄	—	2	1	no	—
633	C₂×C₂²⋊C₄	—	2	1	no	—
634	C₂×C₂²⋊C₄	—	2	1	no	—
635	C₂×C₂²⋊C₄	—	2	1	no	—
636	C₂×C₂²⋊C₄	—	2	1	no	—
637	C₂×C₂²⋊C₄	—	2	1	no	—
638	C₂×C₂²⋊C₄	—	2	1	no	—
639	C₂×C₂²⋊C₄	—	8	2	no	—
640	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
641	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
642	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
643	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
644	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
645	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
646	C₂×C₄²	—	2	1	no	—
647	C₂×C₄²	—	2	1	no	—
648	C₂×C₄²	—	2	1	no	—
649	C₂×C₄²	—	2	1	no	—
650	C₂×C₄²	—	2	1	no	—
651	C₂×C₄²	—	2	1	no	—
652	C₂×C₄²	—	2	1	no	—
653	C₂×C₄²	—	2	1	no	—
654	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
655	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
656	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
657	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
658	C₂×C₄²	C₂⁴	1	1	yes	characteristic
659	C₂×C₄²	C₂⁴	1	1	yes	characteristic
660	C₂×C₄²	C₂⁴	1	1	yes	characteristic
661	C₂×C₄²	C₂⁴	1	1	yes	characteristic
662	C₂×C₄²	C₂⁴	1	1	yes	characteristic
663	C₂×C₄²	C₂⁴	1	1	yes	characteristic
664	#107	—	2	2	no	—
665	#107	—	2	2	no	—
666	#107	—	4	1	no	—
667	#107	—	4	1	no	—
668	#107	—	4	1	no	—
669	#106	—	2	2	no	—
670	#106	—	2	2	no	—
671	#106	—	2	2	no	—
672	#106	—	2	2	no	—
673	#106	—	4	1	no	—
674	#106	—	4	1	no	—
675	#106	—	4	1	no	—
676	#106	—	4	1	no	—
677	C₄⋊C₈	—	2	2	no	—
678	C₄⋊C₈	—	2	2	no	—
679	C₄⋊C₈	—	2	2	no	—
680	C₄⋊C₈	—	2	2	no	—
681	C₄⋊C₈	—	2	2	no	—
682	C₄⋊C₈	—	2	2	no	—
683	#103	—	2	2	no	—
684	#103	—	2	2	no	—
685	#103	—	2	2	no	—
686	#103	—	2	2	no	—
687	#103	—	2	2	no	—
688	#103	—	4	1	no	—
689	#103	—	4	1	no	—
690	#103	—	4	1	no	—
691	#103	—	4	1	no	—
692	#103	—	4	1	no	—
693	#103	—	4	1	no	—
694	#103	—	4	1	no	—
695	#102	—	2	2	no	—
696	#102	—	2	2	no	—
697	#102	—	2	2	no	—
698	#102	—	2	2	no	—
699	#102	—	2	2	no	—
700	#102	—	2	2	no	—
701	#102	—	2	2	no	—
702	#102	—	2	2	no	—
703	#102	—	2	2	no	—
704	#102	—	4	1	no	—
705	#102	—	4	1	no	—
706	#102	—	4	1	no	—
707	#102	—	4	1	no	—
708	#102	—	4	1	no	—
709	C₂²⋊C₈	—	2	2	no	—
710	C₂²⋊C₈	#41	1	4	yes	—
711	#97	—	2	2	no	—
712	#97	—	4	1	no	—
713	#97	—	4	1	no	—
714	#97	—	4	1	no	—
715	#97	—	4	1	no	—
716	C₄×C₈	—	2	2	no	—
717	C₄×C₈	—	4	1	no	—
718	C₄×C₈	—	4	1	no	—
719	C₄×C₈	—	4	1	no	—
720	C₄×C₈	—	4	1	no	—
721	#95	—	2	1	no	—
722	#95	—	2	1	no	—
723	#95	—	2	1	no	—
724	#95	—	2	1	no	—
725	#95	—	2	1	no	—
726	#95	—	2	1	no	—
727	#95	—	2	1	no	—
728	#95	—	2	1	no	—
729	#95	—	2	1	no	—
730	#95	—	2	1	no	—
731	#95	—	2	1	no	—
732	#95	—	2	1	no	—
733	#95	—	2	1	no	—
734	#95	—	2	1	no	—
735	#95	—	2	1	no	—
736	#95	—	2	1	no	—
737	#95	—	2	1	no	—
738	#95	—	2	1	no	—
739	#95	—	2	1	no	—
740	#95	—	2	1	no	—
741	#95	—	2	1	no	—
742	#95	—	2	1	no	—
743	#95	—	2	1	no	—
744	#95	—	2	1	no	—
745	#95	—	2	1	no	—
746	#95	—	2	1	no	—
747	#95	—	2	1	no	—
748	#95	—	2	1	no	—
749	#95	—	2	1	no	—
750	#95	—	2	1	no	—
751	#95	—	2	1	no	—
752	#95	—	2	1	no	—
753	#95	—	2	1	no	—
754	#95	—	2	1	no	—
755	#95	—	2	1	no	—
756	#95	—	2	1	no	—
757	#95	—	2	1	no	—
758	#95	—	2	1	no	—
759	#95	—	2	1	no	—
760	#95	—	2	1	no	—
761	#95	C₂×D₄	1	1	yes	characteristic
762	#95	C₂×D₄	1	1	yes	characteristic
763	#95	C₂×D₄	1	1	yes	characteristic
764	#95	C₂×D₄	1	1	yes	characteristic
765	#95	C₂×D₄	1	1	yes	characteristic
766	#95	C₂×D₄	1	1	yes	characteristic
767	#95	C₂×D₄	1	1	yes	characteristic
768	#95	C₂×D₄	1	1	yes	characteristic
769	#95	C₂×D₄	1	1	yes	characteristic
770	#95	C₂×D₄	1	1	yes	characteristic
771	#95	C₂×D₄	1	1	yes	characteristic
772	#95	C₂×D₄	1	1	yes	characteristic
773	C₂⁴	—	2	1	no	—
774	C₂⁴	—	2	1	no	—
775	C₂⁴	—	4	2	no	—
776	C₂⁴	—	4	2	no	—
777	C₂⁴	—	8	1	no	—
778	C₂⁴	—	8	1	no	—
779	C₂⁴	—	8	1	no	—
780	C₂⁴	—	8	1	no	—
781	C₂⁴	—	8	1	no	—
782	C₂⁴	C₂²×D₄	1	1	yes	characteristic
783	C₂×Q₈	—	2	1	no	—
784	C₂×Q₈	—	2	1	no	—
785	C₂×Q₈	—	2	1	no	—
786	C₂×Q₈	—	2	1	no	—
787	C₂×Q₈	—	2	1	no	—
788	C₂×Q₈	—	2	1	no	—
789	C₂×Q₈	—	2	1	no	—
790	C₂×Q₈	—	2	1	no	—
791	C₂×Q₈	—	2	1	no	—
792	C₂×Q₈	—	2	1	no	—
793	C₂×Q₈	—	2	1	no	—
794	C₂×Q₈	—	2	1	no	—
795	C₂×Q₈	—	4	2	no	—
796	C₂×Q₈	—	4	2	no	—
797	C₂×Q₈	—	8	1	no	—
798	C₂×D₄	—	2	1	no	—
799	C₂×D₄	—	2	1	no	—
800	C₂×D₄	—	2	1	no	—
801	C₂×D₄	—	2	1	no	—
802	C₂×D₄	—	2	1	no	—
803	C₂×D₄	—	2	1	no	—
804	C₂×D₄	—	2	1	no	—
805	C₂×D₄	—	2	1	no	—
806	C₂×D₄	—	2	1	no	—
807	C₂×D₄	—	2	1	no	—
808	C₂×D₄	—	2	1	no	—
809	C₂×D₄	—	4	4	no	—
810	C₂×D₄	—	4	4	no	—
811	C₂×D₄	—	4	2	no	—
812	C₂×D₄	—	4	2	no	—
813	C₂×D₄	—	8	2	no	—
814	C₂×D₄	—	8	2	no	—
815	C₂×D₄	—	8	1	no	—
816	C₂×D₄	2₋¹⁺⁴	1	2	yes	—
817	C₂²×C₄	—	2	1	no	—
818	C₂²×C₄	—	2	1	no	—
819	C₂²×C₄	—	2	1	no	—
820	C₂²×C₄	—	2	1	no	—
821	C₂²×C₄	—	2	1	no	—
822	C₂²×C₄	—	2	1	no	—
823	C₂²×C₄	—	2	1	no	—
824	C₂²×C₄	—	2	1	no	—
825	C₂²×C₄	—	2	1	no	—
826	C₂²×C₄	—	2	1	no	—
827	C₂²×C₄	—	2	1	no	—
828	C₂²×C₄	—	2	1	no	—
829	C₂²×C₄	—	2	1	no	—
830	C₂²×C₄	—	2	1	no	—
831	C₂²×C₄	—	2	1	no	—
832	C₂²×C₄	—	2	1	no	—
833	C₂²×C₄	—	2	1	no	—
834	C₂²×C₄	—	2	1	no	—
835	C₂²×C₄	—	4	2	no	—
836	C₂²×C₄	—	4	2	no	—
837	C₂²×C₄	—	4	2	no	—
838	C₂²×C₄	—	8	1	no	—
839	C₂²×C₄	—	8	1	no	—
840	C₂²×C₄	—	8	1	no	—
841	C₂²×C₄	—	8	1	no	—
842	C₂²×C₄	—	8	1	no	—
843	C₂²×C₄	—	8	1	no	—
844	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
845	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
846	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
847	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
848	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
849	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
850	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
851	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
852	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
853	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
854	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
855	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
856	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
857	C₂²×C₄	C₂×#41	1	2	yes	—
858	C₂²×C₄	C₂×#41	1	2	yes	—
859	C₂²×C₄	C₂⁵	1	1	yes	characteristic
860	Q₁₆	—	4	4	no	—
861	SD₁₆	—	4	4	no	—
862	SD₁₆	—	8	2	no	—
863	M₁₆	—	4	4	no	—
864	C₂×C₈	—	2	1	no	—
865	C₂×C₈	—	2	1	no	—
866	C₂×C₈	—	2	1	no	—
867	C₂×C₈	—	2	1	no	—
868	C₂×C₈	—	2	1	no	—
869	C₂×C₈	—	2	1	no	—
870	C₂×C₈	—	2	1	no	—
871	C₂×C₈	—	2	1	no	—
872	C₂×C₈	—	2	1	no	—
873	C₂×C₈	—	2	1	no	—
874	C₂×C₈	—	2	1	no	—
875	C₂×C₈	—	2	1	no	—
876	C₂×C₈	—	2	1	no	—
877	C₂×C₈	—	2	1	no	—
878	C₂×C₈	—	2	1	no	—
879	C₂×C₈	—	2	1	no	—
880	C₂×C₈	—	2	1	no	—
881	C₂×C₈	—	2	1	no	—
882	C₂×C₈	—	2	1	no	—
883	C₂×C₈	—	2	1	no	—
884	C₂×C₈	—	8	2	no	—
885	C₂×C₈	C₂×#41	1	2	yes	—
886	C₂×C₈	C₂×#41	1	2	yes	—
887	C₂×C₈	C₂×#41	1	2	yes	—
888	C₂×C₈	C₂×#41	1	2	yes	—
889	C₄⋊C₄	—	2	2	no	—
890	C₄⋊C₄	—	2	2	no	—
891	C₄⋊C₄	—	2	2	no	—
892	C₄⋊C₄	—	2	1	no	—
893	C₄⋊C₄	—	2	1	no	—
894	C₄⋊C₄	—	2	1	no	—
895	C₄⋊C₄	—	2	1	no	—
896	C₄⋊C₄	—	2	1	no	—
897	C₄⋊C₄	—	2	1	no	—
898	C₄⋊C₄	—	2	1	no	—
899	C₄⋊C₄	—	2	1	no	—
900	C₄⋊C₄	—	2	1	no	—
901	C₄⋊C₄	—	2	1	no	—
902	C₄⋊C₄	—	2	1	no	—
903	C₄⋊C₄	—	2	1	no	—
904	C₄⋊C₄	—	2	1	no	—
905	C₄⋊C₄	—	2	1	no	—
906	C₄⋊C₄	—	2	1	no	—
907	C₄⋊C₄	—	2	1	no	—
908	C₄⋊C₄	—	2	1	no	—
909	C₄⋊C₄	—	2	1	no	—
910	C₄⋊C₄	—	2	1	no	—
911	C₄⋊C₄	—	2	1	no	—
912	C₄⋊C₄	—	2	1	no	—
913	C₄⋊C₄	—	2	1	no	—
914	C₄⋊C₄	—	2	1	no	—
915	C₄⋊C₄	—	4	1	no	—
916	C₄⋊C₄	—	4	1	no	—
917	C₄⋊C₄	—	4	1	no	—
918	C₄⋊C₄	—	4	2	no	—
919	C₄⋊C₄	—	4	2	no	—
920	C₄⋊C₄	—	4	2	no	—
921	C₄⋊C₄	—	4	2	no	—
922	C₄⋊C₄	—	4	2	no	—
923	C₄⋊C₄	—	4	2	no	—
924	C₄⋊C₄	—	4	2	no	—
925	C₄⋊C₄	—	4	2	no	—
926	C₄⋊C₄	—	4	2	no	—
927	C₄⋊C₄	—	8	1	no	—
928	C₄⋊C₄	—	8	1	no	—
929	C₄⋊C₄	—	8	1	no	—
930	C₄⋊C₄	—	8	1	no	—
931	C₄⋊C₄	—	8	1	no	—
932	C₄⋊C₄	—	8	1	no	—
933	C₄⋊C₄	—	8	1	no	—
934	C₄⋊C₄	—	8	1	no	—
935	C₄⋊C₄	—	8	1	no	—
936	C₄⋊C₄	—	8	1	no	—
937	C₄⋊C₄	—	8	1	no	—
938	C₄⋊C₄	—	8	1	no	—
939	C₄⋊C₄	—	8	1	no	—
940	C₄⋊C₄	—	8	1	no	—
941	C₄⋊C₄	—	8	1	no	—
942	C₄⋊C₄	—	8	1	no	—
943	C₄⋊C₄	—	8	1	no	—
944	C₄⋊C₄	—	8	1	no	—
945	C₄⋊C₄	—	8	1	no	—
946	C₄⋊C₄	—	8	1	no	—
947	C₄⋊C₄	—	8	1	no	—
948	C₄⋊C₄	H(5,𝔽₂)	1	2	yes	—
949	C₂²⋊C₄	—	2	2	no	—
950	C₂²⋊C₄	—	2	2	no	—
951	C₂²⋊C₄	—	2	2	no	—
952	C₂²⋊C₄	—	4	1	no	—
953	C₂²⋊C₄	—	4	1	no	—
954	C₂²⋊C₄	—	4	1	no	—
955	C₂²⋊C₄	—	4	2	no	—
956	C₂²⋊C₄	—	4	2	no	—
957	C₂²⋊C₄	—	4	2	no	—
958	C₂²⋊C₄	—	4	2	no	—
959	C₂²⋊C₄	—	4	2	no	—
960	C₂²⋊C₄	—	4	2	no	—
961	C₂²⋊C₄	—	4	2	no	—
962	C₂²⋊C₄	—	8	1	no	—
963	C₂²⋊C₄	—	8	1	no	—
964	C₂²⋊C₄	—	8	1	no	—
965	C₂²⋊C₄	—	8	1	no	—
966	C₂²⋊C₄	—	8	1	no	—
967	C₂²⋊C₄	—	8	1	no	—
968	C₂²⋊C₄	—	8	1	no	—
969	C₂²⋊C₄	—	8	1	no	—
970	C₂²⋊C₄	—	8	1	no	—
971	C₂²⋊C₄	—	8	1	no	—
972	C₂²⋊C₄	—	8	1	no	—
973	C₂²⋊C₄	—	8	1	no	—
974	C₂²⋊C₄	—	8	1	no	—
975	C₂²⋊C₄	—	8	1	no	—
976	C₂²⋊C₄	—	8	1	no	—
977	C₂²⋊C₄	—	8	1	no	—
978	C₂²⋊C₄	—	8	1	no	—
979	C₂²⋊C₄	—	8	1	no	—
980	C₂²⋊C₄	—	8	1	no	—
981	C₂²⋊C₄	—	8	1	no	—
982	C₂²⋊C₄	—	8	1	no	—
983	C₄²	—	2	2	no	—
984	C₄²	—	2	1	no	—
985	C₄²	—	2	1	no	—
986	C₄²	—	2	1	no	—
987	C₄²	—	2	1	no	—
988	C₄²	—	2	1	no	—
989	C₄²	—	2	1	no	—
990	C₄²	—	2	1	no	—
991	C₄²	—	2	1	no	—
992	C₄²	—	2	1	no	—
993	C₄²	—	2	1	no	—
994	C₄²	—	2	1	no	—
995	C₄²	—	2	1	no	—
996	C₄²	—	4	1	no	—
997	C₄²	—	4	1	no	—
998	C₄²	—	4	1	no	—
999	C₄²	—	4	2	no	—
1000	C₄²	—	4	2	no	—
1001	C₄²	—	4	2	no	—
1002	C₄²	—	8	1	no	—
1003	C₄²	—	8	1	no	—
1004	C₄²	—	8	1	no	—
1005	C₄²	—	8	1	no	—
1006	C₄²	—	8	1	no	—
1007	C₂³	—	2	1	no	—
1008	C₂³	—	2	1	no	—
1009	C₂³	—	2	1	no	—
1010	C₂³	—	2	1	no	—
1011	C₂³	—	2	1	no	—
1012	C₂³	—	2	1	no	—
1013	C₂³	—	2	2	no	—
1014	C₂³	—	4	1	no	—
1015	C₂³	—	4	1	no	—
1016	C₂³	—	4	1	no	—
1017	C₂³	—	4	1	no	—
1018	C₂³	—	4	1	no	—
1019	C₂³	—	4	1	no	—
1020	C₂³	—	4	1	no	—
1021	C₂³	—	4	1	no	—
1022	C₂³	—	4	1	no	—
1023	C₂³	—	4	1	no	—
1024	C₂³	—	4	1	no	—
1025	C₂³	—	4	1	no	—
1026	C₂³	—	4	1	no	—
1027	C₂³	—	8	4	no	—
1028	C₂³	—	8	4	no	—
1029	C₂³	—	16	2	no	—
1030	C₂³	—	16	2	no	—
1031	C₂³	—	16	2	no	—
1032	C₂³	—	16	2	no	—
1033	C₂³	—	16	2	no	—
1034	C₂³	#532	1	2	yes	—
1035	C₂³	C₂³×D₄	1	1	yes	characteristic
1036	Q₈	—	4	1	no	—
1037	Q₈	—	4	1	no	—
1038	Q₈	—	4	1	no	—
1039	Q₈	—	4	1	no	—
1040	Q₈	—	4	1	no	—
1041	Q₈	—	4	1	no	—
1042	Q₈	—	4	1	no	—
1043	Q₈	—	4	1	no	—
1044	Q₈	—	8	4	no	—
1045	D₄	—	2	2	no	—
1046	D₄	—	2	2	no	—
1047	D₄	—	4	1	no	—
1048	D₄	—	4	1	no	—
1049	D₄	—	4	1	no	—
1050	D₄	—	4	1	no	—
1051	D₄	—	4	1	no	—
1052	D₄	—	4	1	no	—
1053	D₄	—	8	4	no	—
1054	C₂×C₄	—	2	1	no	—
1055	C₂×C₄	—	2	1	no	—
1056	C₂×C₄	—	2	1	no	—
1057	C₂×C₄	—	2	1	no	—
1058	C₂×C₄	—	2	2	no	—
1059	C₂×C₄	—	2	2	no	—
1060	C₂×C₄	—	2	2	no	—
1061	C₂×C₄	—	2	2	no	—
1062	C₂×C₄	—	2	1	no	—
1063	C₂×C₄	—	2	1	no	—
1064	C₂×C₄	—	2	1	no	—
1065	C₂×C₄	—	2	1	no	—
1066	C₂×C₄	—	2	1	no	—
1067	C₂×C₄	—	2	1	no	—
1068	C₂×C₄	—	2	1	no	—
1069	C₂×C₄	—	2	1	no	—
1070	C₂×C₄	—	2	1	no	—
1071	C₂×C₄	—	2	1	no	—
1072	C₂×C₄	—	2	1	no	—
1073	C₂×C₄	—	2	1	no	—
1074	C₂×C₄	—	2	1	no	—
1075	C₂×C₄	—	2	1	no	—
1076	C₂×C₄	—	2	1	no	—
1077	C₂×C₄	—	2	1	no	—
1078	C₂×C₄	—	2	1	no	—
1079	C₂×C₄	—	2	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	2	no	—
1088	C₂×C₄	—	2	1	no	—
1089	C₂×C₄	—	2	1	no	—
1090	C₂×C₄	—	2	1	no	—
1091	C₂×C₄	—	2	1	no	—
1092	C₂×C₄	—	2	1	no	—
1093	C₂×C₄	—	2	1	no	—
1094	C₂×C₄	—	2	1	no	—
1095	C₂×C₄	—	2	1	no	—
1096	C₂×C₄	—	4	1	no	—
1097	C₂×C₄	—	4	1	no	—
1098	C₂×C₄	—	4	1	no	—
1099	C₂×C₄	—	4	1	no	—
1100	C₂×C₄	—	4	1	no	—
1101	C₂×C₄	—	4	1	no	—
1102	C₂×C₄	—	4	1	no	—
1103	C₂×C₄	—	4	1	no	—
1104	C₂×C₄	—	4	1	no	—
1105	C₂×C₄	—	4	1	no	—
1106	C₂×C₄	—	4	1	no	—
1107	C₂×C₄	—	4	1	no	—
1108	C₂×C₄	—	4	1	no	—
1109	C₂×C₄	—	4	1	no	—
1110	C₂×C₄	—	4	1	no	—
1111	C₂×C₄	—	4	1	no	—
1112	C₂×C₄	—	4	1	no	—
1113	C₂×C₄	—	4	1	no	—
1114	C₂×C₄	—	4	1	no	—
1115	C₂×C₄	—	4	1	no	—
1116	C₂×C₄	—	4	1	no	—
1117	C₂×C₄	—	4	1	no	—
1118	C₂×C₄	—	4	1	no	—
1119	C₂×C₄	—	4	1	no	—
1120	C₂×C₄	—	4	1	no	—
1121	C₂×C₄	—	4	1	no	—
1122	C₂×C₄	—	4	1	no	—
1123	C₂×C₄	—	4	1	no	—
1124	C₂×C₄	—	4	1	no	—
1125	C₂×C₄	—	4	1	no	—
1126	C₂×C₄	—	4	1	no	—
1127	C₂×C₄	—	4	1	no	—
1128	C₂×C₄	—	4	1	no	—
1129	C₂×C₄	—	4	1	no	—
1130	C₂×C₄	—	4	1	no	—
1131	C₂×C₄	—	4	1	no	—
1132	C₂×C₄	—	4	1	no	—
1133	C₂×C₄	—	4	1	no	—
1134	C₂×C₄	—	4	1	no	—
1135	C₂×C₄	—	4	1	no	—
1136	C₂×C₄	—	4	1	no	—
1137	C₂×C₄	—	8	4	no	—
1138	C₂×C₄	—	16	2	no	—
1139	C₂×C₄	—	16	2	no	—
1140	C₂×C₄	#532	1	2	yes	—
1141	C₂×C₄	#577	1	2	yes	—
1142	C₂×C₄	C₂²×#41	1	1	yes	characteristic
1143	C₂×C₄	C₂²×#41	1	1	yes	characteristic
1144	C₂×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
1145	C₂×C₄	C₂×2₋¹⁺⁴	1	1	yes	characteristic
1146	C₂×C₄	#585	1	1	yes	characteristic
1147	C₂×C₄	#585	1	1	yes	characteristic
1148	C₈	—	2	2	no	—
1149	C₈	—	2	2	no	—
1150	C₈	—	2	2	no	—
1151	C₈	—	2	2	no	—
1152	C₈	—	4	1	no	—
1153	C₈	—	4	1	no	—
1154	C₈	—	4	1	no	—
1155	C₈	—	4	1	no	—
1156	C₂²	—	2	2	no	—
1157	C₂²	—	2	2	no	—
1158	C₂²	—	2	2	no	—
1159	C₂²	—	4	1	no	—
1160	C₂²	—	4	1	no	—
1161	C₂²	—	4	1	no	—
1162	C₂²	—	4	1	no	—
1163	C₂²	—	4	2	no	—
1164	C₂²	—	4	2	no	—
1165	C₂²	—	4	2	no	—
1166	C₂²	—	8	1	no	—
1167	C₂²	—	8	1	no	—
1168	C₂²	—	8	1	no	—
1169	C₂²	—	8	1	no	—
1170	C₂²	—	8	1	no	—
1171	C₂²	—	8	1	no	—
1172	C₂²	—	8	1	no	—
1173	C₂²	—	8	1	no	—
1174	C₂²	—	8	1	no	—
1175	C₂²	—	8	1	no	—
1176	C₂²	—	8	1	no	—
1177	C₂²	—	16	8	no	—
1178	C₂²	C₂×#532	1	1	yes	characteristic
1179	C₂²	#3488	1	1	yes	characteristic
1180	C₂²	#3489	1	1	yes	characteristic
1181	C₂²	C₂×#577	1	1	yes	characteristic
1182	C₂²	#3584	1	1	yes	characteristic
1183	C₂²	#3585	1	1	yes	characteristic
1184	C₂²	#3586	1	1	yes	characteristic
1185	C₄	—	2	2	no	—
1186	C₄	—	2	2	no	—
1187	C₄	—	4	1	no	—
1188	C₄	—	4	1	no	—
1189	C₄	—	4	1	no	—
1190	C₄	—	4	1	no	—
1191	C₄	—	4	1	no	—
1192	C₄	—	4	1	no	—
1193	C₄	—	4	2	no	—
1194	C₄	—	4	1	no	—
1195	C₄	—	4	1	no	—
1196	C₄	—	4	1	no	—
1197	C₄	—	4	1	no	—
1198	C₄	—	4	1	no	—
1199	C₄	—	8	1	no	—
1200	C₄	—	8	1	no	—
1201	C₄	—	8	1	no	—
1202	C₄	—	8	1	no	—
1203	C₄	—	8	1	no	—
1204	C₄	—	8	1	no	—
1205	C₄	—	8	1	no	—
1206	C₄	—	8	1	no	—
1207	C₄	—	8	1	no	—
1208	C₄	—	8	1	no	—
1209	C₄	—	8	1	no	—
1210	C₄	—	8	1	no	—
1211	C₄	—	8	1	no	—
1212	C₄	#3495	1	1	yes	characteristic
1213	C₄	#3505	1	1	yes	characteristic
1214	C₄	#3520	1	1	yes	characteristic
1215	C₄	#3521	1	1	yes	characteristic
1216	C₂	—	4	2	no	—
1217	C₂	—	8	2	no	—
1218	C₂	—	16	1	no	—
1219	C₂	#35825	1	1	yes	characteristic
1220	C₂	#60694	1	1	yes	characteristic
1221	C₂	#60727	1	1	yes	characteristic
1222	C₂	#62028	1	1	yes	characteristic
1223	C₂	#62044	1	1	yes	characteristic
1224	C₂	#62156	1	1	yes	characteristic
1225	C₂	#62172	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³	C₂³×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁵
prime radical	C₂³×D₄	C₂³
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³ ◁ #2298 ◁ G
LECS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #39078	C₂	semidirect
3. #30390	C₂	semidirect
4. #30341	C₂	semidirect
5. #29786	C₂	semidirect
6. #29449	C₂	semidirect
7. #29443	C₂	semidirect
8. #29199	C₂	semidirect
9. #29025	C₂	semidirect
10. #29008	C₂	semidirect
11. #28951	C₂	semidirect
12. #28889	C₂	semidirect
13. #28658	C₂	semidirect
15. #28038	C₂	semidirect
16. #28010	C₂	semidirect
17. #27716	C₂	semidirect
19. #26846	C₂	semidirect
20. #26487	C₂	semidirect
21. #26078	C₂	semidirect
22. #24619	C₂	semidirect
24. #23775	C₂	semidirect
25. #23694	C₂	semidirect
27. #23038	C₂	semidirect
28. #22919	C₂	semidirect
31. #20553	C₂	semidirect
32. C₂×#501	C₂²	semidirect
37. C₂×#441	C₂²	semidirect
44. #2863	C₂²	semidirect
54. #2647	C₂²	semidirect
63. #2511	C₂²	semidirect
64. #2509	C₂²	semidirect
65. #2506	C₂²	semidirect
71. #2451	C₂²	semidirect
83. #2320	C₂²	semidirect
86. C₄×C₄⋊Q₈	C₂²	semidirect
89. #2101	C₂²	semidirect
90. #2100	C₂²	semidirect
93. #2088	C₂²	semidirect
94. #2088	C₂²	semidirect
95. #2088	C₂²	semidirect
96. #2087	C₂²	semidirect
97. #2084	C₂²	semidirect
98. #2083	C₂²	semidirect
99. #2072	C₂²	semidirect
101. #2068	C₂²	semidirect
102. #2068	C₂²	semidirect
108. #2066	C₂²	semidirect
109. #2066	C₂²	semidirect
110. #2066	C₂²	semidirect
111. #2066	C₂²	semidirect
117. #2059	C₂²	semidirect
118. #2058	C₂²	semidirect
119. #2056	C₂²	semidirect
120. #2056	C₂²	semidirect
125. #2026	C₂²	semidirect
129. #1992	C₂²	semidirect
132. #1969	C₂²	semidirect
139. #1944	C₂²	semidirect
140. #1944	C₂²	semidirect
141. #1943	C₂²	semidirect
142. #1942	C₂²	semidirect
143. #1942	C₂²	semidirect
144. #1941	C₂²	semidirect
149. #1935	C₂²	semidirect
150. #1935	C₂²	semidirect
151. #1935	C₂²	semidirect
155. #1933	C₂²	semidirect
156. #1933	C₂²	semidirect
157. #1928	C₂²	semidirect
158. #1928	C₂²	semidirect
159. #1927	C₂²	semidirect
163. #1919	C₂²	semidirect
164. #1918	C₂²	semidirect
171. #1865	C₂²	semidirect
172. #1865	C₂²	semidirect
175. #1863	C₂²	semidirect
179. #1844	C₂²	semidirect
180. #1836	C₂²	semidirect
184. C₄×#106	C₂²	semidirect
185. C₄×#106	C₂²	semidirect
186. #1771	C₂²	semidirect
187. #1771	C₂²	semidirect
188. #1770	C₂²	semidirect
189. C₈×C₄⋊C₄	C₂²	semidirect
190. #1768	C₂²	semidirect
191. #1768	C₂²	semidirect
192. #1767	C₂²	semidirect
193. C₄×C₄⋊C₈	C₂²	semidirect
195. C₄×#103	C₂²	semidirect

Maximal subgroups

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

subgroup	index
#39078	2
#38254	2
#30390	2
#30341	2
#29786	2
#29449	2
#29443	2
#29199	2
#29025	2
#29008	2
#28951	2
#28889	2
#28658	2
#28361	2
#28038	2
#28010	2
#27716	2
#27262	2
#26846	2
#26487	2
#26078	2
#24619	2
#24516	2
#23775	2
#23694	2
#23614	2
#23038	2
#22919	2
#22874	2
#22580	2
#20553	2