Subgroups — #6915519

Order 512.

1420 conjugacy classes of subgroups.

The subgroup lattice has 1270 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#39385	C₂	1	1	yes	maximal, characteristic
2	#38217	C₂	1	1	yes	maximal, characteristic
3	#32801	C₂	1	1	yes	maximal, characteristic, complemented
4	#32768	C₂	1	1	yes	maximal, characteristic, complemented
5	#31505	C₂	1	1	yes	maximal, characteristic, complemented
6	#31501	C₂	1	1	yes	maximal, characteristic, complemented
7	#30864	C₂	1	1	yes	maximal, characteristic, complemented
8	#30853	C₂	1	1	yes	maximal, characteristic, complemented
9	#30726	C₂	1	1	yes	maximal, characteristic
10	#30721	C₂	1	1	yes	maximal, characteristic
11	#30712	C₂	1	1	yes	maximal, characteristic
12	#30707	C₂	1	1	yes	maximal, characteristic
13	#30331	C₂	1	1	yes	maximal, characteristic, complemented
14	#30156	C₂	1	1	yes	maximal, characteristic, complemented
15	#29799	C₂	1	1	yes	maximal, characteristic, complemented
16	#29766	C₂	1	1	yes	maximal, characteristic, complemented
17	#29674	C₂	1	1	yes	maximal, characteristic, complemented
18	#29399	C₂	1	1	yes	maximal, characteristic, complemented
19	#28588	C₂	1	1	yes	maximal, characteristic, complemented
20	#26952	C₂	1	1	yes	maximal, characteristic, complemented
21	#26937	C₂	1	1	yes	maximal, characteristic, complemented
22	#26774	C₂	1	1	yes	maximal, characteristic, complemented
23	#26759	C₂	1	1	yes	maximal, characteristic, complemented
24	#26636	C₂	1	1	yes	maximal, characteristic, complemented
25	#26621	C₂	1	1	yes	maximal, characteristic, complemented
26	#26607	C₂	1	1	yes	maximal, characteristic, complemented
27	#26590	C₂	1	1	yes	maximal, characteristic, complemented
28	#25512	C₂	1	1	yes	maximal, characteristic, complemented
29	#24071	C₂	1	1	yes	maximal, characteristic, complemented
30	#23586	C₂	1	1	yes	maximal, characteristic, complemented
31	#22005	C₂	1	1	yes	maximal, characteristic
32	C₂×#541	C₂²	1	1	yes	characteristic
33	C₂×#541	C₂²	1	1	yes	characteristic
34	C₂×#484	C₂²	1	1	yes	characteristic
35	C₂×#485	C₂²	1	1	yes	characteristic
36	C₂×#485	C₂²	1	1	yes	characteristic
37	C₂×#483	C₂²	1	1	yes	characteristic
38	C₂×#470	C₂²	1	1	yes	characteristic
39	C₂×#470	C₂²	1	1	yes	characteristic
40	C₂×#467	C₂²	1	1	yes	characteristic
41	C₂×#467	C₂²	1	1	yes	characteristic
42	C₂×#462	C₂²	1	1	yes	characteristic
43	C₂×#462	C₂²	1	1	yes	characteristic
44	C₂×#462	C₂²	1	1	yes	characteristic
45	C₂×#462	C₂²	1	1	yes	characteristic
46	C₂×#441	C₂²	1	1	yes	characteristic
47	C₂×C₄×Q₁₆	C₂²	1	1	yes	characteristic
48	#2868	C₂²	1	1	yes	characteristic
49	#2863	C₂²	1	1	yes	characteristic
50	#2793	—	2	1	no	—
51	#2787	—	2	1	no	—
52	#2766	—	2	1	no	—
53	#2757	—	2	1	no	—
54	#2721	—	2	1	no	—
55	#2721	—	2	1	no	—
56	#2721	—	2	1	no	—
57	#2721	—	2	1	no	—
58	#2625	C₂²	1	1	yes	characteristic
59	#2621	C₂²	1	1	yes	characteristic
60	#2621	C₂²	1	1	yes	characteristic
61	#2621	C₂²	1	1	yes	characteristic
62	#2595	—	2	1	no	—
63	#2552	—	2	1	no	—
64	#2552	—	2	1	no	—
65	#2542	C₂²	1	1	yes	characteristic
66	#2542	C₂²	1	1	yes	characteristic
67	#2530	—	2	1	no	—
68	#2529	—	2	1	no	—
69	#2512	—	2	1	no	—
70	#2512	—	2	1	no	—
71	#2509	C₂²	1	1	yes	characteristic
72	#2507	—	2	1	no	—
73	#2494	C₂²	1	1	yes	characteristic
74	#2446	C₂²	1	1	yes	characteristic
75	#2429	C₂²	1	1	yes	characteristic
76	#2429	C₂²	1	1	yes	characteristic
77	#2429	C₂²	1	1	yes	characteristic
78	#2429	C₂²	1	1	yes	characteristic
79	#2429	C₂²	1	1	yes	characteristic
80	#2417	C₂²	1	1	yes	characteristic
81	#2415	C₂²	1	1	yes	characteristic
82	#2365	C₂²	1	1	yes	characteristic
83	#2365	C₂²	1	1	yes	characteristic
84	#2362	C₂²	1	1	yes	characteristic
85	#2360	C₂²	1	1	yes	characteristic
86	#2323	C₂²	1	1	yes	characteristic
87	#2317	C₂²	1	1	yes	characteristic
88	C₄×#125	C₂²	1	1	yes	characteristic
89	#2295	C₂²	1	1	yes	characteristic
90	#2293	C₂²	1	1	yes	characteristic
91	#2088	C₂²	1	1	yes	characteristic
92	#2086	C₂²	1	1	yes	characteristic
93	#2085	C₂²	1	1	yes	characteristic
94	#2085	C₂²	1	1	yes	characteristic
95	#2074	C₂²	1	1	yes	characteristic
96	#2074	C₂²	1	1	yes	characteristic
97	#2074	C₂²	1	1	yes	characteristic
98	#2074	C₂²	1	1	yes	characteristic
99	#2068	C₂²	1	1	yes	characteristic
100	#2068	C₂²	1	1	yes	characteristic
101	#2068	C₂²	1	1	yes	characteristic
102	#2066	C₂²	1	1	yes	characteristic
103	#2066	C₂²	1	1	yes	characteristic
104	#2066	C₂²	1	1	yes	characteristic
105	#2059	C₂²	1	1	yes	characteristic
106	#2059	C₂²	1	1	yes	characteristic
107	#2043	C₂²	1	1	yes	characteristic
108	#2043	C₂²	1	1	yes	characteristic
109	#2043	C₂²	1	1	yes	characteristic
110	#2043	C₂²	1	1	yes	characteristic
111	#2043	C₂²	1	1	yes	characteristic
112	#2043	C₂²	1	1	yes	characteristic
113	#2043	C₂²	1	1	yes	characteristic
114	#2043	C₂²	1	1	yes	characteristic
115	#2043	C₂²	1	1	yes	characteristic
116	#2043	C₂²	1	1	yes	characteristic
117	#2036	C₂²	1	1	yes	characteristic
118	#2036	C₂²	1	1	yes	characteristic
119	#2035	C₂²	1	1	yes	characteristic
120	#2035	C₂²	1	1	yes	characteristic
121	#2026	C₂²	1	1	yes	characteristic
122	#2026	C₂²	1	1	yes	characteristic
123	#2016	C₂²	1	1	yes	characteristic
124	#2016	C₂²	1	1	yes	characteristic
125	#2016	C₂²	1	1	yes	characteristic
126	#2016	C₂²	1	1	yes	characteristic
127	#2016	C₂²	1	1	yes	characteristic
128	#2016	C₂²	1	1	yes	characteristic
129	#2016	C₂²	1	1	yes	characteristic
130	#2016	C₂²	1	1	yes	characteristic
131	#2016	C₂²	1	1	yes	characteristic
132	#2016	C₂²	1	1	yes	characteristic
133	#2016	C₂²	1	1	yes	characteristic
134	#2016	C₂²	1	1	yes	characteristic
135	#2001	C₂²	1	1	yes	characteristic
136	#2001	C₂²	1	1	yes	characteristic
137	#2001	C₂²	1	1	yes	characteristic
138	#2001	C₂²	1	1	yes	characteristic
139	#2001	C₂²	1	1	yes	characteristic
140	#2001	C₂²	1	1	yes	characteristic
141	#2001	C₂²	1	1	yes	characteristic
142	#2001	C₂²	1	1	yes	characteristic
143	#2001	C₂²	1	1	yes	characteristic
144	#2001	C₂²	1	1	yes	characteristic
145	#2001	C₂²	1	1	yes	characteristic
146	#2001	C₂²	1	1	yes	characteristic
147	#1981	C₂²	1	1	yes	characteristic
148	#1981	C₂²	1	1	yes	characteristic
149	#1971	C₂²	1	1	yes	characteristic
150	#1969	C₂²	1	1	yes	characteristic
151	#1935	C₂²	1	1	yes	characteristic
152	#1933	C₂²	1	1	yes	characteristic
153	#1928	C₂²	1	1	yes	characteristic
154	#1928	C₂²	1	1	yes	characteristic
155	#1928	C₂²	1	1	yes	characteristic
156	#1927	C₂²	1	1	yes	characteristic
157	#1927	C₂²	1	1	yes	characteristic
158	#1927	C₂²	1	1	yes	characteristic
159	#1924	C₂²	1	1	yes	characteristic
160	#1923	C₂²	1	1	yes	characteristic
161	#1921	C₂²	1	1	yes	characteristic
162	#1921	C₂²	1	1	yes	characteristic
163	#1920	C₂²	1	1	yes	characteristic
164	#1919	C₂²	1	1	yes	characteristic
165	#1919	C₂²	1	1	yes	characteristic
166	#1918	C₂²	1	1	yes	characteristic
167	#1917	C₂²	1	1	yes	characteristic
168	#1916	C₂²	1	1	yes	characteristic
169	#1894	C₂²	1	1	yes	characteristic
170	#1894	C₂²	1	1	yes	characteristic
171	#1892	C₂²	1	1	yes	characteristic
172	#1892	C₂²	1	1	yes	characteristic
173	#1878	C₂²	1	1	yes	characteristic
174	#1878	C₂²	1	1	yes	characteristic
175	#1878	C₂²	1	1	yes	characteristic
176	#1878	C₂²	1	1	yes	characteristic
177	#1873	C₂²	1	1	yes	characteristic
178	#1873	C₂²	1	1	yes	characteristic
179	#1872	C₂²	1	1	yes	characteristic
180	#1872	C₂²	1	1	yes	characteristic
181	#1870	C₂²	1	1	yes	characteristic
182	#1869	C₂²	1	1	yes	characteristic
183	#1865	C₂²	1	1	yes	characteristic
184	#1865	C₂²	1	1	yes	characteristic
185	#1865	C₂²	1	1	yes	characteristic
186	#1865	C₂²	1	1	yes	characteristic
187	#1863	C₂²	1	1	yes	characteristic
188	#1863	C₂²	1	1	yes	characteristic
189	#1863	C₂²	1	1	yes	characteristic
190	#1863	C₂²	1	1	yes	characteristic
191	#1851	C₂²	1	1	yes	characteristic
192	#1850	C₂²	1	1	yes	characteristic
193	#1839	C₂²	1	1	yes	characteristic
194	#1831	C₂²	1	1	yes	characteristic
195	#1818	C₂²	1	1	yes	characteristic
196	#1805	C₂²	1	1	yes	characteristic
197	#1805	C₂²	1	1	yes	characteristic
198	#1798	C₂²	1	1	yes	characteristic
199	#1763	C₂²	1	1	yes	characteristic
200	C₄×#103	C₂²	1	1	yes	characteristic
201	#1750	C₂²	1	1	yes	characteristic
202	#1729	C₂²	1	1	yes	characteristic
203	C₂²×Q₁₆	C₂³	1	1	yes	characteristic
204	C₂²×Q₁₆	C₂³	1	1	yes	characteristic
205	C₂²×Q₁₆	C₂³	1	1	yes	characteristic
206	C₂²×Q₁₆	C₂³	1	1	yes	characteristic
207	C₂²×Q₁₆	C₂³	1	1	yes	characteristic
208	C₂²×Q₁₆	C₂³	1	1	yes	characteristic
209	C₂²×Q₁₆	C₂³	1	1	yes	characteristic
210	C₂²×Q₁₆	C₂³	1	1	yes	characteristic
211	C₂²×M₁₆	C₂³	1	1	yes	characteristic
212	C₂³×C₈	C₂³	1	1	yes	characteristic
213	#541	—	4	2	no	—
214	#541	—	4	2	no	—
215	#541	—	4	2	no	—
216	#541	—	4	2	no	—
217	C₂×C₄⋊Q₈	C₂³	1	1	yes	characteristic
218	C₂×C₄⋊Q₈	C₂³	1	1	yes	characteristic
219	C₂×C₄⋊Q₈	C₂³	1	1	yes	characteristic
220	C₂×C₄⋊Q₈	C₂³	1	1	yes	characteristic
221	C₂×C₄⋊Q₈	C₂³	1	1	yes	characteristic
222	C₂×C₄⋊Q₈	C₂³	1	1	yes	characteristic
223	C₂×C₄⋊Q₈	C₂³	1	1	yes	characteristic
224	C₂×#126	—	2	1	no	—
225	C₂×#126	—	2	1	no	—
226	C₂×#126	—	2	1	no	—
227	C₂×#126	—	2	1	no	—
228	C₂×#125	—	2	1	no	—
229	C₂×#125	—	2	1	no	—
230	C₂×#125	—	2	1	no	—
231	C₂×#125	—	2	1	no	—
232	C₂×#125	C₂³	1	1	yes	characteristic
233	C₂×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
234	C₂×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
235	C₂×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
236	C₂×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
237	C₂×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
238	C₂×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
239	C₂×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
240	C₂×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
241	C₂×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
242	C₂×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
243	C₂×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
244	C₂×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
245	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
246	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
247	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
248	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
249	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
250	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
251	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
252	C₂×#117	C₂³	1	1	yes	characteristic
253	C₂×#117	C₂³	1	1	yes	characteristic
254	C₂×#117	C₂³	1	1	yes	characteristic
255	C₂²×C₄⋊C₄	C₂³	1	1	yes	characteristic
256	#485	—	4	2	no	—
257	#485	—	4	2	no	—
258	#484	—	4	2	no	—
259	#483	—	4	2	no	—
260	#470	—	4	2	no	—
261	#470	—	4	2	no	—
262	#467	—	4	2	no	—
263	#467	—	4	2	no	—
264	#462	—	4	2	no	—
265	#462	—	4	2	no	—
266	#462	—	4	2	no	—
267	#462	—	4	2	no	—
268	#441	—	4	2	no	—
269	C₄×Q₁₆	—	4	2	no	—
270	C₂×#107	C₂³	1	1	yes	characteristic
271	C₂×#107	C₂³	1	1	yes	characteristic
272	C₂×#107	C₂³	1	1	yes	characteristic
273	C₂×#107	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	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
279	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
280	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
281	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
282	C₂×#103	C₂³	1	1	yes	characteristic
283	C₂×#103	C₂³	1	1	yes	characteristic
284	C₂×#103	C₂³	1	1	yes	characteristic
285	C₂×#103	C₂³	1	1	yes	characteristic
286	C₂×#103	C₂³	1	1	yes	characteristic
287	C₂×#103	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×#103	C₂³	1	1	yes	characteristic
307	C₂×#103	C₂³	1	1	yes	characteristic
308	C₂×#103	C₂³	1	1	yes	characteristic
309	C₂×#103	C₂³	1	1	yes	characteristic
310	C₂×#103	C₂³	1	1	yes	characteristic
311	C₂×#103	C₂³	1	1	yes	characteristic
312	C₂×#103	C₂³	1	1	yes	characteristic
313	C₂×#103	C₂³	1	1	yes	characteristic
314	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
315	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
316	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
317	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
318	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
319	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
320	C₂×#97	C₂³	1	1	yes	characteristic
321	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
322	#401	—	2	1	no	—
323	#400	—	2	1	no	—
324	#400	—	2	1	no	—
325	#400	—	2	1	no	—
326	#400	—	2	1	no	—
327	#399	—	2	1	no	—
328	#399	—	2	1	no	—
329	#399	—	2	1	no	—
330	#399	—	2	1	no	—
331	#398	—	2	1	no	—
332	#398	—	2	1	no	—
333	#398	—	2	1	no	—
334	#398	—	2	1	no	—
335	#398	—	2	1	no	—
336	#398	—	2	1	no	—
337	#398	—	2	1	no	—
338	#398	—	2	1	no	—
339	#398	—	2	1	no	—
340	#398	—	2	1	no	—
341	#398	—	2	1	no	—
342	#398	—	2	1	no	—
343	#398	—	2	1	no	—
344	#398	—	2	1	no	—
345	#397	—	2	1	no	—
346	#397	—	2	1	no	—
347	#397	—	2	1	no	—
348	#397	—	2	1	no	—
349	#397	—	2	1	no	—
350	#397	—	2	1	no	—
351	#397	—	2	1	no	—
352	#397	—	2	1	no	—
353	#397	—	2	1	no	—
354	#397	—	2	1	no	—
355	#396	—	2	1	no	—
356	#396	—	2	1	no	—
357	#396	—	2	1	no	—
358	#396	—	2	1	no	—
359	#396	—	2	1	no	—
360	#396	—	2	1	no	—
361	#394	—	2	1	no	—
362	#391	C₂³	1	1	yes	characteristic
363	#391	C₂³	1	1	yes	characteristic
364	#391	C₂³	1	1	yes	characteristic
365	#391	C₂³	1	1	yes	characteristic
366	#391	C₂³	1	1	yes	characteristic
367	#391	C₂³	1	1	yes	characteristic
368	#391	C₂³	1	1	yes	characteristic
369	#391	C₂³	1	1	yes	characteristic
370	#391	C₂³	1	1	yes	characteristic
371	#391	C₂³	1	1	yes	characteristic
372	#390	—	2	1	no	—
373	#390	—	2	1	no	—
374	#390	D₄	1	1	yes	characteristic
375	#390	D₄	1	1	yes	characteristic
376	#389	—	2	1	no	—
377	#389	—	2	1	no	—
378	#389	—	2	1	no	—
379	#389	—	2	1	no	—
380	#389	—	2	1	no	—
381	#389	—	2	1	no	—
382	#389	—	2	1	no	—
383	#389	—	2	1	no	—
384	#389	—	2	1	no	—
385	#389	—	2	1	no	—
386	#389	—	2	1	no	—
387	#389	D₄	1	1	yes	characteristic
388	#389	D₄	1	1	yes	characteristic
389	#389	C₂³	1	1	yes	characteristic
390	#389	C₂³	1	1	yes	characteristic
391	#389	C₂³	1	1	yes	characteristic
392	#389	C₂³	1	1	yes	characteristic
393	#389	C₂³	1	1	yes	characteristic
394	#389	C₂³	1	1	yes	characteristic
395	#389	C₂³	1	1	yes	characteristic
396	#389	C₂³	1	1	yes	characteristic
397	#389	C₂³	1	1	yes	characteristic
398	#389	C₂³	1	1	yes	characteristic
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	#388	—	2	1	no	—
406	#388	—	2	1	no	—
407	#388	—	2	1	no	—
408	#388	—	2	1	no	—
409	#388	—	2	1	no	—
410	#388	D₄	1	1	yes	characteristic
411	#388	D₄	1	1	yes	characteristic
412	#388	D₄	1	1	yes	characteristic
413	#388	D₄	1	1	yes	characteristic
414	#387	—	2	1	no	—
415	#387	—	2	1	no	—
416	#387	—	2	1	no	—
417	#387	—	2	1	no	—
418	#387	—	2	1	no	—
419	#387	—	2	1	no	—
420	#387	—	2	1	no	—
421	#387	—	2	1	no	—
422	#387	—	2	1	no	—
423	#387	—	2	1	no	—
424	#387	—	2	1	no	—
425	#387	—	2	1	no	—
426	#387	—	2	1	no	—
427	#387	—	2	1	no	—
428	#387	—	2	1	no	—
429	#387	—	2	1	no	—
430	#387	—	2	1	no	—
431	#387	—	2	1	no	—
432	#386	—	2	1	no	—
433	#385	—	2	1	no	—
434	#385	—	2	1	no	—
435	#385	—	2	1	no	—
436	#384	—	2	1	no	—
437	#384	—	2	1	no	—
438	#384	—	2	1	no	—
439	#384	—	2	1	no	—
440	#384	—	2	1	no	—
441	#384	—	2	1	no	—
442	#384	—	2	1	no	—
443	#383	—	2	1	no	—
444	#382	—	2	1	no	—
445	#382	C₂³	1	1	yes	characteristic
446	#382	C₂³	1	1	yes	characteristic
447	#380	—	2	1	no	—
448	#380	C₂³	1	1	yes	characteristic
449	#380	C₂³	1	1	yes	characteristic
450	C₄×C₄⋊C₄	—	2	1	no	—
451	C₄×C₄⋊C₄	—	2	1	no	—
452	C₄×C₄⋊C₄	—	2	1	no	—
453	C₄×C₄⋊C₄	—	2	1	no	—
454	C₄×C₄⋊C₄	—	2	1	no	—
455	C₄×C₄⋊C₄	—	2	1	no	—
456	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
457	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
458	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
459	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
460	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
461	C₄×C₂²⋊C₄	—	2	1	no	—
462	C₄×C₂²⋊C₄	C₂³	1	1	yes	characteristic
463	C₄×C₂²⋊C₄	C₂³	1	1	yes	characteristic
464	#376	—	2	1	no	—
465	C₄³	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	#336	C₂³	1	1	yes	characteristic
491	#336	C₂³	1	1	yes	characteristic
492	#336	C₂³	1	1	yes	characteristic
493	#336	C₂³	1	1	yes	characteristic
494	#336	C₂³	1	1	yes	characteristic
495	#336	C₂³	1	1	yes	characteristic
496	C₂²×Q₈	C₂⁴	1	1	yes	characteristic
497	C₂²×Q₈	C₂⁴	1	1	yes	characteristic
498	C₂²×Q₈	C₂⁴	1	1	yes	characteristic
499	C₂²×Q₈	C₂⁴	1	1	yes	characteristic
500	C₂²×Q₈	C₂⁴	1	1	yes	characteristic
501	C₂²×Q₈	C₂⁴	1	1	yes	characteristic
502	C₂²×D₄	C₂×D₄	1	1	yes	characteristic
503	C₂³×C₄	—	2	1	no	—
504	C₂³×C₄	C₂⁴	1	1	yes	characteristic
505	C₂³×C₄	C₂⁴	1	1	yes	characteristic
506	C₂×Q₁₆	—	4	1	no	—
507	C₂×Q₁₆	—	4	1	no	—
508	C₂×Q₁₆	—	4	1	no	—
509	C₂×Q₁₆	—	4	1	no	—
510	C₂×Q₁₆	—	4	1	no	—
511	C₂×Q₁₆	—	4	1	no	—
512	C₂×Q₁₆	—	4	1	no	—
513	C₂×Q₁₆	—	4	1	no	—
514	C₂×Q₁₆	—	4	1	no	—
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	—	4	1	no	—
520	C₂×Q₁₆	—	4	1	no	—
521	C₂×Q₁₆	—	4	1	no	—
522	C₂×Q₁₆	—	4	1	no	—
523	C₂×Q₁₆	—	4	1	no	—
524	C₂×Q₁₆	—	4	1	no	—
525	C₂×Q₁₆	—	4	1	no	—
526	C₂×Q₁₆	—	4	1	no	—
527	C₂×Q₁₆	—	4	1	no	—
528	C₂×Q₁₆	—	4	1	no	—
529	C₂×Q₁₆	—	4	1	no	—
530	C₂×M₁₆	—	4	1	no	—
531	C₂×M₁₆	—	4	1	no	—
532	C₂×M₁₆	—	4	1	no	—
533	C₂²×C₈	—	4	1	no	—
534	C₂²×C₈	—	4	1	no	—
535	C₂²×C₈	—	4	1	no	—
536	C₂²×C₈	C₂⁴	1	1	yes	characteristic
537	C₂²×C₈	C₂⁴	1	1	yes	characteristic
538	C₂²×C₈	C₂⁴	1	1	yes	characteristic
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	C₄⋊Q₈	—	4	1	no	—
545	C₄⋊Q₈	—	4	1	no	—
546	C₄⋊Q₈	—	4	1	no	—
547	C₄⋊Q₈	—	4	1	no	—
548	C₄⋊Q₈	—	4	1	no	—
549	C₄⋊Q₈	—	4	1	no	—
550	C₄⋊Q₈	—	4	1	no	—
551	C₄⋊Q₈	—	4	1	no	—
552	C₄⋊Q₈	—	4	1	no	—
553	C₄⋊Q₈	—	4	1	no	—
554	C₄⋊Q₈	—	4	1	no	—
555	C₄⋊Q₈	—	4	1	no	—
556	C₄⋊Q₈	—	4	1	no	—
557	C₄⋊Q₈	—	4	1	no	—
558	#126	—	4	4	no	—
559	#126	—	4	4	no	—
560	#126	—	4	4	no	—
561	#126	—	4	4	no	—
562	#125	—	2	2	no	—
563	#125	—	2	2	no	—
564	#125	—	4	4	no	—
565	#125	—	4	4	no	—
566	#125	—	4	4	no	—
567	#125	—	4	4	no	—
568	C₂²⋊Q₈	—	2	2	no	—
569	C₂²⋊Q₈	—	2	2	no	—
570	C₂²⋊Q₈	—	2	2	no	—
571	C₂²⋊Q₈	—	2	2	no	—
572	C₂²⋊Q₈	—	2	2	no	—
573	C₂²⋊Q₈	—	4	1	no	—
574	C₂²⋊Q₈	—	4	1	no	—
575	C₂²⋊Q₈	—	4	1	no	—
576	C₂²⋊Q₈	—	4	1	no	—
577	C₂²⋊Q₈	—	4	1	no	—
578	C₂²⋊Q₈	—	4	1	no	—
579	C₂²⋊Q₈	—	4	1	no	—
580	C₂²⋊Q₈	—	4	1	no	—
581	C₂²⋊Q₈	—	4	1	no	—
582	C₂²⋊Q₈	—	4	1	no	—
583	C₂²⋊Q₈	—	4	1	no	—
584	C₂²⋊Q₈	—	4	1	no	—
585	C₂²⋊Q₈	—	4	1	no	—
586	C₂²⋊Q₈	—	4	1	no	—
587	C₂²⋊Q₈	—	4	1	no	—
588	C₂²⋊Q₈	—	4	1	no	—
589	C₂²⋊Q₈	—	4	1	no	—
590	C₂²⋊Q₈	—	4	1	no	—
591	C₂²⋊Q₈	—	4	1	no	—
592	C₄×Q₈	—	2	2	no	—
593	C₄×Q₈	—	2	2	no	—
594	C₄×Q₈	—	2	2	no	—
595	C₄×Q₈	—	2	2	no	—
596	C₄×Q₈	—	2	2	no	—
597	C₄×Q₈	—	4	1	no	—
598	C₄×Q₈	—	4	1	no	—
599	C₄×Q₈	—	4	1	no	—
600	C₄×Q₈	—	4	1	no	—
601	C₄×Q₈	—	4	1	no	—
602	C₄×Q₈	—	4	1	no	—
603	C₄×Q₈	—	4	1	no	—
604	C₄×D₄	—	4	1	no	—
605	C₄×D₄	—	4	1	no	—
606	#117	—	2	2	no	—
607	#117	—	4	1	no	—
608	#117	—	4	1	no	—
609	#117	—	4	1	no	—
610	#117	—	4	1	no	—
611	#117	—	4	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	—	2	1	no	—
632	C₂×C₄⋊C₄	—	2	1	no	—
633	C₂×C₄⋊C₄	—	2	1	no	—
634	C₂×C₄⋊C₄	—	2	1	no	—
635	C₂×C₄⋊C₄	—	2	1	no	—
636	C₂×C₄⋊C₄	—	2	1	no	—
637	C₂×C₄⋊C₄	—	2	1	no	—
638	C₂×C₄⋊C₄	—	2	1	no	—
639	C₂×C₄⋊C₄	—	2	1	no	—
640	C₂×C₄⋊C₄	—	2	1	no	—
641	C₂×C₄⋊C₄	—	2	1	no	—
642	C₂×C₄⋊C₄	—	2	1	no	—
643	C₂×C₄⋊C₄	—	2	1	no	—
644	C₂×C₄⋊C₄	—	2	1	no	—
645	C₂×C₄⋊C₄	—	2	1	no	—
646	C₂×C₄⋊C₄	—	2	1	no	—
647	C₂×C₄⋊C₄	—	2	1	no	—
648	C₂×C₄⋊C₄	—	2	1	no	—
649	C₂×C₄⋊C₄	—	2	1	no	—
650	C₂×C₄⋊C₄	—	2	1	no	—
651	C₂×C₄⋊C₄	—	2	1	no	—
652	C₂×C₄⋊C₄	—	2	1	no	—
653	C₂×C₄⋊C₄	—	2	1	no	—
654	C₂×C₄⋊C₄	—	2	1	no	—
655	C₂×C₄⋊C₄	—	2	1	no	—
656	C₂×C₄⋊C₄	—	2	1	no	—
657	C₂×C₄⋊C₄	—	4	1	no	—
658	C₂×C₄⋊C₄	—	4	1	no	—
659	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
660	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
661	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
662	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
663	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
664	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
665	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
666	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
667	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
668	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
669	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
670	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
671	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
672	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
673	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
674	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
675	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
676	C₂×C₂²⋊C₄	—	2	1	no	—
677	C₂×C₂²⋊C₄	—	2	1	no	—
678	C₂×C₂²⋊C₄	—	2	1	no	—
679	C₂×C₂²⋊C₄	—	2	1	no	—
680	C₂×C₂²⋊C₄	—	2	1	no	—
681	C₂×C₂²⋊C₄	—	2	1	no	—
682	C₂×C₂²⋊C₄	—	2	1	no	—
683	C₂×C₂²⋊C₄	—	2	1	no	—
684	C₂×C₂²⋊C₄	—	2	1	no	—
685	C₂×C₂²⋊C₄	—	2	1	no	—
686	C₂×C₂²⋊C₄	—	2	1	no	—
687	C₂×C₂²⋊C₄	—	2	1	no	—
688	C₂×C₂²⋊C₄	—	2	1	no	—
689	C₂×C₂²⋊C₄	—	2	1	no	—
690	C₂×C₂²⋊C₄	—	2	1	no	—
691	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
692	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
693	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
694	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
695	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
696	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
697	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
698	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
699	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
700	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
701	C₂×C₄²	—	2	1	no	—
702	C₂×C₄²	—	2	1	no	—
703	C₂×C₄²	—	2	1	no	—
704	C₂×C₄²	—	2	1	no	—
705	C₂×C₄²	—	2	1	no	—
706	C₂×C₄²	—	2	1	no	—
707	C₂×C₄²	—	2	1	no	—
708	C₂×C₄²	—	2	1	no	—
709	C₂×C₄²	—	2	1	no	—
710	C₂×C₄²	—	2	1	no	—
711	C₂×C₄²	—	2	1	no	—
712	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
713	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
714	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
715	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
716	C₂×C₄²	C₂⁴	1	1	yes	characteristic
717	C₂×C₄²	C₂⁴	1	1	yes	characteristic
718	C₂×C₄²	C₂⁴	1	1	yes	characteristic
719	C₂×C₄²	C₂⁴	1	1	yes	characteristic
720	C₂×C₄²	C₂⁴	1	1	yes	characteristic
721	#107	—	2	2	no	—
722	#107	—	2	2	no	—
723	#107	—	2	2	no	—
724	#107	—	4	1	no	—
725	#106	—	2	2	no	—
726	#106	—	2	2	no	—
727	#106	—	2	2	no	—
728	#106	—	4	1	no	—
729	C₄⋊C₈	—	4	1	no	—
730	C₄⋊C₈	—	4	1	no	—
731	C₄⋊C₈	—	4	1	no	—
732	C₄⋊C₈	—	4	1	no	—
733	#103	—	2	2	no	—
734	#103	—	2	2	no	—
735	#103	—	2	2	no	—
736	#103	—	2	2	no	—
737	#103	—	2	2	no	—
738	#103	—	2	2	no	—
739	#103	—	2	2	no	—
740	#103	—	2	2	no	—
741	#103	—	4	1	no	—
742	#103	—	4	1	no	—
743	#103	—	4	1	no	—
744	#103	—	4	1	no	—
745	#103	—	4	1	no	—
746	#103	—	4	1	no	—
747	#103	—	4	1	no	—
748	#103	—	4	1	no	—
749	#103	—	4	1	no	—
750	#103	—	4	1	no	—
751	#103	—	4	1	no	—
752	#103	—	4	1	no	—
753	#103	—	4	1	no	—
754	#103	—	4	1	no	—
755	#103	—	4	1	no	—
756	#103	—	4	1	no	—
757	#103	—	4	1	no	—
758	#103	—	4	1	no	—
759	#103	—	4	1	no	—
760	#103	—	4	1	no	—
761	#103	—	4	1	no	—
762	#103	—	4	1	no	—
763	#103	—	4	1	no	—
764	#103	—	4	1	no	—
765	C₂²⋊C₈	—	4	1	no	—
766	C₂²⋊C₈	—	4	1	no	—
767	C₂²⋊C₈	—	4	1	no	—
768	C₂²⋊C₈	—	4	1	no	—
769	C₂²⋊C₈	—	4	1	no	—
770	C₂²⋊C₈	—	4	1	no	—
771	#97	—	4	1	no	—
772	C₄×C₈	—	4	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	—	2	1	no	—
800	#95	—	2	1	no	—
801	#95	—	2	1	no	—
802	#95	—	2	1	no	—
803	#95	—	2	1	no	—
804	#95	—	2	1	no	—
805	#95	—	2	1	no	—
806	#95	—	2	1	no	—
807	#95	—	2	1	no	—
808	#95	—	2	1	no	—
809	#95	—	2	1	no	—
810	#95	—	2	1	no	—
811	#95	—	2	1	no	—
812	#95	—	2	1	no	—
813	#95	C₂×D₄	1	1	yes	characteristic
814	#95	C₂×D₄	1	1	yes	characteristic
815	#95	C₂×D₄	1	1	yes	characteristic
816	#95	C₂×D₄	1	1	yes	characteristic
817	#95	C₂×D₄	1	1	yes	characteristic
818	#95	C₂×D₄	1	1	yes	characteristic
819	C₂⁴	C₂²×D₄	1	1	yes	characteristic
820	C₂⁴	C₂²×D₄	1	1	yes	characteristic
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	—	2	1	no	—
826	C₂×Q₈	—	2	1	no	—
827	C₂×Q₈	—	2	1	no	—
828	C₂×Q₈	—	2	1	no	—
829	C₂×Q₈	—	2	1	no	—
830	C₂×Q₈	—	2	1	no	—
831	C₂×Q₈	—	2	1	no	—
832	C₂×Q₈	—	2	1	no	—
833	C₂×Q₈	—	2	1	no	—
834	C₂×Q₈	—	2	1	no	—
835	C₂×Q₈	—	2	1	no	—
836	C₂×Q₈	—	2	1	no	—
837	C₂×Q₈	—	2	1	no	—
838	C₂×Q₈	—	2	1	no	—
839	C₂×Q₈	—	2	1	no	—
840	C₂×Q₈	—	2	1	no	—
841	C₂×Q₈	—	2	1	no	—
842	C₂×Q₈	—	2	1	no	—
843	C₂×Q₈	—	2	1	no	—
844	C₂×Q₈	—	2	1	no	—
845	C₂×Q₈	—	2	1	no	—
846	C₂×Q₈	—	2	1	no	—
847	C₂×Q₈	—	2	1	no	—
848	C₂×Q₈	—	2	1	no	—
849	C₂×Q₈	—	2	1	no	—
850	C₂×Q₈	—	2	1	no	—
851	C₂×Q₈	—	2	1	no	—
852	C₂×Q₈	—	2	1	no	—
853	C₂×Q₈	—	2	1	no	—
854	C₂×Q₈	—	2	1	no	—
855	C₂×Q₈	—	2	1	no	—
856	C₂×Q₈	—	2	1	no	—
857	C₂×D₄	—	2	2	no	—
858	C₂×D₄	—	4	1	no	—
859	C₂×D₄	—	4	1	no	—
860	C₂²×C₄	—	2	1	no	—
861	C₂²×C₄	—	2	1	no	—
862	C₂²×C₄	—	2	1	no	—
863	C₂²×C₄	—	2	1	no	—
864	C₂²×C₄	—	2	1	no	—
865	C₂²×C₄	—	2	1	no	—
866	C₂²×C₄	—	2	1	no	—
867	C₂²×C₄	—	2	1	no	—
868	C₂²×C₄	—	2	1	no	—
869	C₂²×C₄	—	2	1	no	—
870	C₂²×C₄	—	2	1	no	—
871	C₂²×C₄	—	2	1	no	—
872	C₂²×C₄	—	2	1	no	—
873	C₂²×C₄	—	2	1	no	—
874	C₂²×C₄	—	2	1	no	—
875	C₂²×C₄	—	2	1	no	—
876	C₂²×C₄	—	2	1	no	—
877	C₂²×C₄	—	2	1	no	—
878	C₂²×C₄	—	2	1	no	—
879	C₂²×C₄	—	2	1	no	—
880	C₂²×C₄	—	2	1	no	—
881	C₂²×C₄	—	2	1	no	—
882	C₂²×C₄	—	2	1	no	—
883	C₂²×C₄	—	2	1	no	—
884	C₂²×C₄	—	2	1	no	—
885	C₂²×C₄	—	2	1	no	—
886	C₂²×C₄	—	2	1	no	—
887	C₂²×C₄	—	2	1	no	—
888	C₂²×C₄	—	8	1	no	—
889	C₂²×C₄	—	8	1	no	—
890	C₂²×C₄	—	8	1	no	—
891	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
892	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
893	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
894	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
895	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
896	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
897	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
898	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
899	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
900	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
901	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
902	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
903	C₂²×C₄	C₂⁵	1	1	yes	characteristic
904	Q₁₆	—	4	4	no	—
905	Q₁₆	—	4	4	no	—
906	Q₁₆	—	8	2	no	—
907	Q₁₆	—	8	2	no	—
908	Q₁₆	—	8	2	no	—
909	Q₁₆	—	8	2	no	—
910	Q₁₆	—	8	2	no	—
911	Q₁₆	—	8	2	no	—
912	M₁₆	—	8	2	no	—
913	C₂×C₈	—	2	1	no	—
914	C₂×C₈	—	2	1	no	—
915	C₂×C₈	—	2	1	no	—
916	C₂×C₈	—	2	1	no	—
917	C₂×C₈	—	2	1	no	—
918	C₂×C₈	—	2	1	no	—
919	C₂×C₈	—	2	1	no	—
920	C₂×C₈	—	2	1	no	—
921	C₂×C₈	—	2	1	no	—
922	C₂×C₈	—	2	1	no	—
923	C₂×C₈	—	2	1	no	—
924	C₂×C₈	—	2	1	no	—
925	C₂×C₈	—	2	1	no	—
926	C₂×C₈	—	2	1	no	—
927	C₂×C₈	—	2	1	no	—
928	C₂×C₈	—	2	1	no	—
929	C₂×C₈	—	2	1	no	—
930	C₂×C₈	—	2	1	no	—
931	C₂×C₈	—	2	1	no	—
932	C₂×C₈	—	2	1	no	—
933	C₂×C₈	—	2	1	no	—
934	C₂×C₈	—	2	1	no	—
935	C₂×C₈	—	2	1	no	—
936	C₂×C₈	—	2	1	no	—
937	C₂×C₈	—	8	2	no	—
938	C₄⋊C₄	—	2	4	no	—
939	C₄⋊C₄	—	2	4	no	—
940	C₄⋊C₄	—	2	2	no	—
941	C₄⋊C₄	—	2	1	no	—
942	C₄⋊C₄	—	2	1	no	—
943	C₄⋊C₄	—	2	1	no	—
944	C₄⋊C₄	—	2	1	no	—
945	C₄⋊C₄	—	2	1	no	—
946	C₄⋊C₄	—	2	1	no	—
947	C₄⋊C₄	—	2	1	no	—
948	C₄⋊C₄	—	2	1	no	—
949	C₄⋊C₄	—	2	1	no	—
950	C₄⋊C₄	—	2	1	no	—
951	C₄⋊C₄	—	2	1	no	—
952	C₄⋊C₄	—	2	1	no	—
953	C₄⋊C₄	—	2	1	no	—
954	C₄⋊C₄	—	2	1	no	—
955	C₄⋊C₄	—	2	1	no	—
956	C₄⋊C₄	—	2	1	no	—
957	C₄⋊C₄	—	2	1	no	—
958	C₄⋊C₄	—	4	1	no	—
959	C₄⋊C₄	—	4	1	no	—
960	C₄⋊C₄	—	4	1	no	—
961	C₄⋊C₄	—	4	1	no	—
962	C₄⋊C₄	—	4	1	no	—
963	C₄⋊C₄	—	4	1	no	—
964	C₄⋊C₄	—	4	2	no	—
965	C₄⋊C₄	—	4	2	no	—
966	C₄⋊C₄	—	4	2	no	—
967	C₄⋊C₄	—	4	2	no	—
968	C₄⋊C₄	—	4	2	no	—
969	C₄⋊C₄	—	4	2	no	—
970	C₄⋊C₄	—	4	2	no	—
971	C₄⋊C₄	—	4	2	no	—
972	C₄⋊C₄	—	4	2	no	—
973	C₄⋊C₄	—	4	2	no	—
974	C₄⋊C₄	—	4	2	no	—
975	C₄⋊C₄	—	4	2	no	—
976	C₄⋊C₄	—	4	2	no	—
977	C₄⋊C₄	—	4	2	no	—
978	C₄⋊C₄	—	4	2	no	—
979	C₄⋊C₄	—	4	2	no	—
980	C₄⋊C₄	—	4	2	no	—
981	C₄⋊C₄	—	4	2	no	—
982	C₄⋊C₄	—	4	2	no	—
983	C₄⋊C₄	—	4	2	no	—
984	C₄⋊C₄	—	4	2	no	—
985	C₄⋊C₄	—	4	2	no	—
986	C₄⋊C₄	—	4	2	no	—
987	C₄⋊C₄	—	4	2	no	—
988	C₄⋊C₄	—	8	1	no	—
989	C₄⋊C₄	—	8	1	no	—
990	C₄⋊C₄	—	8	1	no	—
991	C₄⋊C₄	—	8	1	no	—
992	C₄⋊C₄	—	8	1	no	—
993	C₄⋊C₄	—	8	1	no	—
994	C₄⋊C₄	—	8	1	no	—
995	C₄⋊C₄	—	8	1	no	—
996	C₄⋊C₄	—	8	1	no	—
997	C₄⋊C₄	—	8	1	no	—
998	C₄⋊C₄	—	8	1	no	—
999	C₄⋊C₄	—	8	1	no	—
1000	C₄⋊C₄	—	8	1	no	—
1001	C₄⋊C₄	—	8	1	no	—
1002	C₄⋊C₄	—	8	1	no	—
1003	C₄⋊C₄	—	8	1	no	—
1004	C₄⋊C₄	—	8	1	no	—
1005	C₄⋊C₄	—	8	1	no	—
1006	C₄⋊C₄	—	8	1	no	—
1007	C₄⋊C₄	H(5,𝔽₂)	1	2	yes	—
1008	C₄⋊C₄	H(5,𝔽₂)	1	2	yes	—
1009	C₄⋊C₄	H(5,𝔽₂)	1	2	yes	—
1010	C₂²⋊C₄	—	2	2	no	—
1011	C₂²⋊C₄	—	2	2	no	—
1012	C₂²⋊C₄	—	4	1	no	—
1013	C₂²⋊C₄	—	4	1	no	—
1014	C₂²⋊C₄	—	4	1	no	—
1015	C₂²⋊C₄	—	4	1	no	—
1016	C₂²⋊C₄	—	4	1	no	—
1017	C₂²⋊C₄	—	4	1	no	—
1018	C₂²⋊C₄	—	4	1	no	—
1019	C₂²⋊C₄	—	4	1	no	—
1020	C₂²⋊C₄	—	4	2	no	—
1021	C₂²⋊C₄	—	4	2	no	—
1022	C₂²⋊C₄	—	4	2	no	—
1023	C₂²⋊C₄	—	4	2	no	—
1024	C₂²⋊C₄	—	4	2	no	—
1025	C₂²⋊C₄	—	4	2	no	—
1026	C₂²⋊C₄	—	4	2	no	—
1027	C₂²⋊C₄	—	4	2	no	—
1028	C₂²⋊C₄	—	8	1	no	—
1029	C₂²⋊C₄	—	8	1	no	—
1030	C₂²⋊C₄	—	8	1	no	—
1031	C₂²⋊C₄	—	8	1	no	—
1032	C₂²⋊C₄	—	8	1	no	—
1033	C₂²⋊C₄	—	8	1	no	—
1034	C₂²⋊C₄	—	8	1	no	—
1035	C₄²	—	2	2	no	—
1036	C₄²	—	2	2	no	—
1037	C₄²	—	2	1	no	—
1038	C₄²	—	2	1	no	—
1039	C₄²	—	2	1	no	—
1040	C₄²	—	2	1	no	—
1041	C₄²	—	2	1	no	—
1042	C₄²	—	2	1	no	—
1043	C₄²	—	2	1	no	—
1044	C₄²	—	2	1	no	—
1045	C₄²	—	2	1	no	—
1046	C₄²	—	2	1	no	—
1047	C₄²	—	4	1	no	—
1048	C₄²	—	4	1	no	—
1049	C₄²	—	4	2	no	—
1050	C₄²	—	4	2	no	—
1051	C₄²	—	4	2	no	—
1052	C₄²	—	4	2	no	—
1053	C₄²	—	4	2	no	—
1054	C₄²	—	4	2	no	—
1055	C₄²	—	4	2	no	—
1056	C₄²	—	4	2	no	—
1057	C₄²	—	8	1	no	—
1058	C₄²	—	8	1	no	—
1059	C₄²	—	8	1	no	—
1060	C₂³	—	2	1	no	—
1061	C₂³	—	2	1	no	—
1062	C₂³	—	2	1	no	—
1063	C₂³	—	2	1	no	—
1064	C₂³	—	2	1	no	—
1065	C₂³	—	2	1	no	—
1066	C₂³	—	2	1	no	—
1067	C₂³	—	2	1	no	—
1068	C₂³	—	2	1	no	—
1069	C₂³	—	2	1	no	—
1070	C₂³	—	2	1	no	—
1071	C₂³	—	2	1	no	—
1072	C₂³	—	2	1	no	—
1073	C₂³	—	2	1	no	—
1074	C₂³	C₂³×D₄	1	1	yes	characteristic
1075	Q₈	—	4	1	no	—
1076	Q₈	—	4	1	no	—
1077	Q₈	—	4	1	no	—
1078	Q₈	—	4	1	no	—
1079	Q₈	—	4	1	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	Q₈	—	4	1	no	—
1087	Q₈	—	4	1	no	—
1088	Q₈	—	4	1	no	—
1089	Q₈	—	4	1	no	—
1090	Q₈	—	4	1	no	—
1091	Q₈	—	4	1	no	—
1092	Q₈	—	4	1	no	—
1093	Q₈	—	4	1	no	—
1094	Q₈	—	4	1	no	—
1095	Q₈	—	4	1	no	—
1096	Q₈	—	4	1	no	—
1097	Q₈	—	4	1	no	—
1098	Q₈	—	4	1	no	—
1099	D₄	—	8	2	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	1	no	—
1106	C₂×C₄	—	2	1	no	—
1107	C₂×C₄	—	2	1	no	—
1108	C₂×C₄	—	2	1	no	—
1109	C₂×C₄	—	2	1	no	—
1110	C₂×C₄	—	2	1	no	—
1111	C₂×C₄	—	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	2	no	—
1122	C₂×C₄	—	2	2	no	—
1123	C₂×C₄	—	2	1	no	—
1124	C₂×C₄	—	2	1	no	—
1125	C₂×C₄	—	2	1	no	—
1126	C₂×C₄	—	2	2	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	—	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	—	4	1	no	—
1157	C₂×C₄	—	4	1	no	—
1158	C₂×C₄	—	4	1	no	—
1159	C₂×C₄	—	4	1	no	—
1160	C₂×C₄	—	4	1	no	—
1161	C₂×C₄	—	4	1	no	—
1162	C₂×C₄	—	4	1	no	—
1163	C₂×C₄	—	4	1	no	—
1164	C₂×C₄	—	4	1	no	—
1165	C₂×C₄	—	4	1	no	—
1166	C₂×C₄	—	4	1	no	—
1167	C₂×C₄	—	4	1	no	—
1168	C₂×C₄	—	4	1	no	—
1169	C₂×C₄	—	4	1	no	—
1170	C₂×C₄	—	4	1	no	—
1171	C₂×C₄	—	4	1	no	—
1172	C₂×C₄	—	4	1	no	—
1173	C₂×C₄	—	4	1	no	—
1174	C₂×C₄	—	4	1	no	—
1175	C₂×C₄	—	4	1	no	—
1176	C₂×C₄	—	4	1	no	—
1177	C₂×C₄	—	4	1	no	—
1178	C₂×C₄	—	4	1	no	—
1179	C₂×C₄	—	4	1	no	—
1180	C₂×C₄	—	4	1	no	—
1181	C₂×C₄	—	4	1	no	—
1182	C₂×C₄	—	4	1	no	—
1183	C₂×C₄	—	4	1	no	—
1184	C₂×C₄	—	4	1	no	—
1185	C₂×C₄	—	4	1	no	—
1186	C₂×C₄	—	4	1	no	—
1187	C₂×C₄	—	4	1	no	—
1188	C₂×C₄	—	4	1	no	—
1189	C₂×C₄	—	4	1	no	—
1190	C₂×C₄	—	16	2	no	—
1191	C₂×C₄	#578	1	2	yes	—
1192	C₂×C₄	#578	1	2	yes	—
1193	C₂×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
1194	C₂×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
1195	C₂×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
1196	C₂×C₄	#585	1	1	yes	characteristic
1197	C₂×C₄	#585	1	1	yes	characteristic
1198	C₂×C₄	#585	1	1	yes	characteristic
1199	C₈	—	4	1	no	—
1200	C₈	—	4	1	no	—
1201	C₈	—	4	1	no	—
1202	C₈	—	4	1	no	—
1203	C₈	—	4	1	no	—
1204	C₈	—	4	1	no	—
1205	C₈	—	4	1	no	—
1206	C₈	—	4	1	no	—
1207	C₂²	—	4	1	no	—
1208	C₂²	—	4	1	no	—
1209	C₂²	—	4	1	no	—
1210	C₂²	—	4	1	no	—
1211	C₂²	—	4	1	no	—
1212	C₂²	—	4	1	no	—
1213	C₂²	—	4	1	no	—
1214	C₂²	—	4	1	no	—
1215	C₂²	—	4	1	no	—
1216	C₂²	—	4	1	no	—
1217	C₂²	—	4	1	no	—
1218	C₂²	—	4	1	no	—
1219	C₂²	—	4	1	no	—
1220	C₂²	—	4	1	no	—
1221	C₂²	#3449	1	1	yes	characteristic
1222	C₂²	#3484	1	1	yes	characteristic
1223	C₂²	#3488	1	1	yes	characteristic
1224	C₂²	C₂×#578	1	1	yes	characteristic
1225	C₂²	C₂×#578	1	1	yes	characteristic
1226	C₂²	#3586	1	1	yes	characteristic
1227	C₂²	#3586	1	1	yes	characteristic
1228	C₄	—	2	2	no	—
1229	C₄	—	2	2	no	—
1230	C₄	—	4	1	no	—
1231	C₄	—	4	1	no	—
1232	C₄	—	4	2	no	—
1233	C₄	—	4	1	no	—
1234	C₄	—	4	1	no	—
1235	C₄	—	4	1	no	—
1236	C₄	—	4	1	no	—
1237	C₄	—	4	1	no	—
1238	C₄	—	4	2	no	—
1239	C₄	—	4	1	no	—
1240	C₄	—	4	1	no	—
1241	C₄	—	4	1	no	—
1242	C₄	—	4	2	no	—
1243	C₄	—	8	1	no	—
1244	C₄	—	8	1	no	—
1245	C₄	—	8	1	no	—
1246	C₄	—	8	1	no	—
1247	C₄	—	8	1	no	—
1248	C₄	—	8	1	no	—
1249	C₄	—	8	1	no	—
1250	C₄	—	8	1	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	#3539	1	1	yes	characteristic
1257	C₄	#3539	1	1	yes	characteristic
1258	C₄	#3546	1	1	yes	characteristic
1259	C₄	#3546	1	1	yes	characteristic
1260	C₂	—	8	1	no	—
1261	C₂	—	8	1	no	—
1262	C₂	#40605	1	1	yes	characteristic
1263	C₂	#60983	1	1	yes	characteristic
1264	C₂	#60995	1	1	yes	characteristic
1265	C₂	#61665	1	1	yes	characteristic
1266	C₂	#61676	1	1	yes	characteristic
1267	C₂	#62010	1	1	yes	characteristic
1268	C₂	#62034	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³	C₂³×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁵
prime radical	C₂²×D₄	C₂×D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³ ◁ #2293 ◁ G
LECS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
3. #32801	C₂	semidirect
4. #32768	C₂	semidirect
5. #31505	C₂	semidirect
6. #31501	C₂	semidirect
7. #30864	C₂	semidirect
8. #30853	C₂	semidirect
13. #30331	C₂	semidirect
14. #30156	C₂	semidirect
15. #29799	C₂	semidirect
16. #29766	C₂	semidirect
17. #29674	C₂	semidirect
18. #29399	C₂	semidirect
19. #28588	C₂	semidirect
20. #26952	C₂	semidirect
21. #26937	C₂	semidirect
22. #26774	C₂	semidirect
23. #26759	C₂	semidirect
24. #26636	C₂	semidirect
25. #26621	C₂	semidirect
26. #26607	C₂	semidirect
27. #26590	C₂	semidirect
28. #25512	C₂	semidirect
29. #24071	C₂	semidirect
30. #23586	C₂	semidirect

Maximal subgroups

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

subgroup	index
#39385	2
#38217	2
#32801	2
#32768	2
#31505	2
#31501	2
#30864	2
#30853	2
#30726	2
#30721	2
#30712	2
#30707	2
#30331	2
#30156	2
#29799	2
#29766	2
#29674	2
#29399	2
#28588	2
#26952	2
#26937	2
#26774	2
#26759	2
#26636	2
#26621	2
#26607	2
#26590	2
#25512	2
#24071	2
#23586	2
#22005	2