Subgroups — #6592504

Order 512.

1718 conjugacy classes of subgroups.

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

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#39546	C₂	1	1	yes	maximal, characteristic, complemented
2	#34309	C₂	1	1	yes	maximal, characteristic
3	#33066	C₂	1	1	yes	maximal, characteristic, complemented
4	#32968	C₂	1	1	yes	maximal, characteristic, complemented
5	#32966	C₂	1	1	yes	maximal, characteristic, complemented
6	#29122	C₂	1	1	yes	maximal, characteristic, complemented
7	#28208	C₂	1	1	yes	maximal, characteristic, complemented
8	#27656	C₂	1	1	yes	maximal, characteristic, complemented
9	#27640	C₂	1	1	yes	maximal, characteristic, complemented
10	#27531	C₂	1	1	yes	maximal, characteristic, complemented
11	#27528	C₂	1	1	yes	maximal, characteristic, complemented
12	#27323	C₂	1	1	yes	maximal, characteristic, complemented
13	#27309	C₂	1	1	yes	maximal, characteristic, complemented
14	#27097	C₂	1	1	yes	maximal, characteristic, complemented
15	#27094	C₂	1	1	yes	maximal, characteristic, complemented
16	#26782	C₂	1	1	yes	maximal, characteristic, complemented
17	#26764	C₂	1	1	yes	maximal, characteristic, complemented
18	#24956	C₂	1	1	yes	maximal, characteristic, complemented
19	#24934	C₂	1	1	yes	maximal, characteristic, complemented
20	#24850	C₂	1	1	yes	maximal, characteristic, complemented
21	#24713	C₂	1	1	yes	maximal, characteristic, complemented
22	#24050	C₂	1	1	yes	maximal, characteristic
23	#24039	C₂	1	1	yes	maximal, characteristic
24	#22947	C₂	1	1	yes	maximal, characteristic, complemented
25	#22919	C₂	1	1	yes	maximal, characteristic, complemented
26	#22756	C₂	1	1	yes	maximal, characteristic, complemented
27	#22580	C₂	1	1	yes	maximal, characteristic, complemented
28	#22570	C₂	1	1	yes	maximal, characteristic, complemented
29	C₄×#478	C₂	1	1	yes	maximal, characteristic, complemented
30	#20746	C₂	1	1	yes	maximal, characteristic, complemented
31	#20650	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×#546	C₂²	1	1	yes	characteristic
33	C₂×#520	C₂²	1	1	yes	characteristic
34	C₂×#518	C₂²	1	1	yes	characteristic
35	C₂×#484	C₂²	1	1	yes	characteristic
36	C₂×#485	C₂²	1	1	yes	characteristic
37	C₂×#479	C₂²	1	1	yes	characteristic, complemented
38	C₂×#478	C₂²	1	1	yes	characteristic
39	C₂×#478	C₂²	1	1	yes	characteristic
40	C₂×#433	C₂²	1	1	yes	characteristic, complemented
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	#2859	C₂²	1	1	yes	characteristic, complemented
45	#2777	—	2	1	no	—
46	#2766	—	2	1	no	—
47	#2765	—	2	1	no	—
48	#2761	—	2	1	no	—
49	#2629	C₂²	1	1	yes	characteristic
50	#2629	C₂²	1	1	yes	characteristic, complemented
51	#2601	—	2	1	no	—
52	#2590	—	2	1	no	—
53	#2519	—	2	1	no	—
54	#2508	C₂²	1	1	yes	characteristic, complemented
55	#2507	C₂²	1	1	yes	characteristic, complemented
56	#2496	C₂²	1	1	yes	characteristic, complemented
57	#2494	C₂²	1	1	yes	characteristic, complemented
58	#2487	C₂²	1	1	yes	characteristic
59	#2485	C₂²	1	1	yes	characteristic
60	#2475	—	2	1	no	—
61	#2367	C₂²	1	1	yes	characteristic
62	#2364	—	2	1	no	—
63	#2362	C₂²	1	1	yes	characteristic
64	#2361	C₂²	1	1	yes	characteristic
65	#2359	—	2	1	no	—
66	#2358	—	2	1	no	—
67	#2352	C₂²	1	1	yes	characteristic
68	#2349	C₂²	1	1	yes	characteristic
69	#2347	C₂²	1	1	yes	characteristic
70	#2344	C₂²	1	1	yes	characteristic
71	#2342	—	2	1	no	—
72	#2339	C₂²	1	1	yes	characteristic
73	D₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
74	#2324	C₂²	1	1	yes	characteristic
75	#2323	C₂²	1	1	yes	characteristic
76	#2322	—	2	1	no	—
77	#2321	—	2	1	no	—
78	#2317	C₂²	1	1	yes	characteristic
79	#2314	C₂²	1	1	yes	characteristic, complemented
80	C₄×#125	C₂²	1	1	yes	characteristic, complemented
81	C₄×#124	C₂²	1	1	yes	characteristic
82	C₄×#121	—	2	1	no	—
83	#2293	C₂²	1	1	yes	characteristic
84	C₂×#388	—	2	1	no	—
85	C₄²×D₄	C₂²	1	1	yes	characteristic
86	#2101	C₂²	1	1	yes	characteristic, complemented
87	#2101	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	#2085	C₂²	1	1	yes	characteristic, complemented
92	#2085	C₂²	1	1	yes	characteristic, complemented
93	#2083	C₂²	1	1	yes	characteristic, complemented
94	#2077	C₂²	1	1	yes	characteristic, complemented
95	#2076	C₂²	1	1	yes	characteristic, complemented
96	#2076	C₂²	1	1	yes	characteristic, complemented
97	#2075	C₂²	1	1	yes	characteristic, complemented
98	#2074	C₂²	1	1	yes	characteristic, complemented
99	#2072	C₂²	1	1	yes	characteristic, complemented
100	#2068	C₂²	1	1	yes	characteristic, complemented
101	#2068	C₂²	1	1	yes	characteristic, complemented
102	#2042	C₂²	1	1	yes	characteristic
103	#2042	C₂²	1	1	yes	characteristic
104	#2042	C₂²	1	1	yes	characteristic
105	#2042	C₂²	1	1	yes	characteristic
106	#2034	C₂²	1	1	yes	characteristic
107	#2033	C₂²	1	1	yes	characteristic
108	#2033	C₂²	1	1	yes	characteristic
109	#2033	C₂²	1	1	yes	characteristic
110	#1989	C₂²	1	1	yes	characteristic, complemented
111	#1949	C₂²	1	1	yes	characteristic, complemented
112	#1947	C₂²	1	1	yes	characteristic, complemented
113	#1947	C₂²	1	1	yes	characteristic, complemented
114	#1943	C₂²	1	1	yes	characteristic, complemented
115	#1942	C₂²	1	1	yes	characteristic, complemented
116	#1936	C₂²	1	1	yes	characteristic
117	#1934	C₂²	1	1	yes	characteristic
118	#1934	C₂²	1	1	yes	characteristic
119	#1934	C₂²	1	1	yes	characteristic
120	#1933	C₂²	1	1	yes	characteristic, complemented
121	#1933	C₂²	1	1	yes	characteristic, complemented
122	#1928	C₂²	1	1	yes	characteristic, complemented
123	#1927	C₂²	1	1	yes	characteristic, complemented
124	#1926	C₂²	1	1	yes	characteristic
125	#1925	C₂²	1	1	yes	characteristic
126	#1925	C₂²	1	1	yes	characteristic
127	#1925	C₂²	1	1	yes	characteristic
128	#1923	C₂²	1	1	yes	characteristic, complemented
129	#1923	C₂²	1	1	yes	characteristic, complemented
130	#1921	C₂²	1	1	yes	characteristic, complemented
131	#1921	C₂²	1	1	yes	characteristic, complemented
132	#1919	C₂²	1	1	yes	characteristic, complemented
133	#1919	C₂²	1	1	yes	characteristic, complemented
134	#1918	C₂²	1	1	yes	characteristic, complemented
135	#1918	C₂²	1	1	yes	characteristic, complemented
136	#1918	C₂²	1	1	yes	characteristic, complemented
137	#1918	C₂²	1	1	yes	characteristic, complemented
138	#1917	C₂²	1	1	yes	characteristic, complemented
139	#1916	C₂²	1	1	yes	characteristic, complemented
140	#1894	C₂²	1	1	yes	characteristic
141	#1892	C₂²	1	1	yes	characteristic
142	#1870	C₂²	1	1	yes	characteristic
143	#1869	C₂²	1	1	yes	characteristic
144	#1865	C₂²	1	1	yes	characteristic, complemented
145	#1864	C₂²	1	1	yes	characteristic
146	#1864	C₂²	1	1	yes	characteristic
147	#1864	C₂²	1	1	yes	characteristic
148	#1864	C₂²	1	1	yes	characteristic
149	#1863	C₂²	1	1	yes	characteristic, complemented
150	#1862	C₂²	1	1	yes	characteristic
151	#1862	C₂²	1	1	yes	characteristic
152	#1862	C₂²	1	1	yes	characteristic
153	#1862	C₂²	1	1	yes	characteristic
154	#1862	C₂²	1	1	yes	characteristic
155	#1862	C₂²	1	1	yes	characteristic
156	#1862	C₂²	1	1	yes	characteristic
157	#1862	C₂²	1	1	yes	characteristic
158	#1854	C₂²	1	1	yes	characteristic
159	#1854	C₂²	1	1	yes	characteristic
160	#1853	C₂²	1	1	yes	characteristic, complemented
161	#1852	C₂²	1	1	yes	characteristic, complemented
162	#1831	C₂²	1	1	yes	characteristic, complemented
163	#1825	C₂²	1	1	yes	characteristic
164	#1824	C₂²	1	1	yes	characteristic, complemented
165	#1823	C₂²	1	1	yes	characteristic
166	#1823	C₂²	1	1	yes	characteristic, complemented
167	#1809	C₂²	1	1	yes	characteristic
168	#1808	C₂²	1	1	yes	characteristic
169	#1805	C₂²	1	1	yes	characteristic, complemented
170	#1804	C₂²	1	1	yes	characteristic
171	#1804	C₂²	1	1	yes	characteristic
172	#1804	C₂²	1	1	yes	characteristic
173	#1804	C₂²	1	1	yes	characteristic
174	#1803	C₂²	1	1	yes	characteristic, complemented
175	#1803	C₂²	1	1	yes	characteristic, complemented
176	#1802	C₂²	1	1	yes	characteristic
177	#1802	C₂²	1	1	yes	characteristic
178	#1802	C₂²	1	1	yes	characteristic
179	#1802	C₂²	1	1	yes	characteristic
180	#1802	C₂²	1	1	yes	characteristic
181	#1802	C₂²	1	1	yes	characteristic
182	#1798	C₂²	1	1	yes	characteristic
183	#1798	C₂²	1	1	yes	characteristic, complemented
184	#1788	C₂²	1	1	yes	characteristic
185	#1788	C₂²	1	1	yes	characteristic
186	#1788	C₂²	1	1	yes	characteristic
187	#1788	C₂²	1	1	yes	characteristic
188	#1786	C₂²	1	1	yes	characteristic
189	#1786	C₂²	1	1	yes	characteristic
190	C₄×#107	C₂²	1	1	yes	characteristic, complemented
191	C₄×#106	C₂²	1	1	yes	characteristic, complemented
192	C₄×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
193	#1763	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	C₄×#102	C₂²	1	1	yes	characteristic
199	#1753	C₂²	1	1	yes	characteristic
200	C₈×C₂²⋊C₄	C₂²	1	1	yes	characteristic
201	#1736	C₂²	1	1	yes	characteristic
202	#1735	C₂²	1	1	yes	characteristic
203	C₂²×#41	C₂³	1	1	yes	characteristic
204	C₂³×D₄	C₂³	1	1	yes	characteristic
205	C₂²×M₁₆	C₂³	1	1	yes	characteristic
206	C₂³×C₈	C₂³	1	1	yes	characteristic
207	#546	—	2	4	no	—
208	#546	—	2	4	no	—
209	C₂×#126	—	2	1	no	—
210	C₂×#125	—	2	1	no	—
211	C₂×#125	C₂³	1	1	yes	characteristic
212	C₂×#124	C₂³	1	1	yes	characteristic
213	C₂×#123	—	2	1	no	—
214	C₂×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
215	C₂×#121	—	2	1	no	—
216	C₂×#121	C₂³	1	1	yes	characteristic
217	C₂×#120	—	2	1	no	—
218	#520	—	2	4	no	—
219	#520	—	4	2	no	—
220	#518	—	2	4	no	—
221	#518	—	4	2	no	—
222	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
223	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
224	C₂×C₄×D₄	—	2	1	no	—
225	C₂×C₄×D₄	—	2	1	no	—
226	C₂×C₄×D₄	—	2	1	no	—
227	C₂×C₄×D₄	—	2	1	no	—
228	C₂×C₄×D₄	—	2	1	no	—
229	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
230	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
231	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
232	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
233	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
234	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
235	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
236	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
237	C₂×#117	—	2	1	no	—
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	—	2	1	no	—
244	C₂²×C₄⋊C₄	C₂³	1	1	yes	characteristic
245	C₂²×C₄⋊C₄	C₂³	1	1	yes	characteristic
246	C₂²×C₂²⋊C₄	—	2	1	no	—
247	C₂²×C₂²⋊C₄	—	2	1	no	—
248	C₂²×C₂²⋊C₄	—	2	1	no	—
249	C₂²×C₂²⋊C₄	—	2	1	no	—
250	C₂²×C₄²	—	2	1	no	—
251	#485	—	2	4	no	—
252	#484	—	2	4	no	—
253	#479	—	4	2	no	—
254	#478	—	2	4	no	—
255	#478	—	4	2	no	—
256	#433	—	4	2	no	—
257	C₂×#107	C₂³	1	1	yes	characteristic
258	C₂×#107	C₂³	1	1	yes	characteristic
259	C₂×#107	C₂³	1	1	yes	characteristic
260	C₂×#107	C₂³	1	1	yes	characteristic
261	C₂×#107	C₂³	1	1	yes	characteristic
262	C₂×#107	C₂³	1	1	yes	characteristic
263	C₂×#107	C₂³	1	1	yes	characteristic
264	C₂×#107	C₂³	1	1	yes	characteristic
265	C₂×#106	C₂³	1	1	yes	characteristic
266	C₂×#106	C₂³	1	1	yes	characteristic
267	C₂×#106	C₂³	1	1	yes	characteristic
268	C₂×#106	C₂³	1	1	yes	characteristic
269	#424	—	4	2	no	—
270	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
271	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
272	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
273	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
274	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
275	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
276	#418	—	2	4	no	—
277	C₂×#103	C₂³	1	1	yes	characteristic
278	C₂×#103	C₂³	1	1	yes	characteristic
279	C₂×#103	C₂³	1	1	yes	characteristic
280	C₂×#103	C₂³	1	1	yes	characteristic
281	C₂×#103	C₂³	1	1	yes	characteristic
282	C₂×#103	C₂³	1	1	yes	characteristic
283	C₂×#103	C₂³	1	1	yes	characteristic
284	C₂×#103	C₂³	1	1	yes	characteristic
285	C₂×#102	—	2	4	no	—
286	C₂×#102	C₂³	1	1	yes	characteristic
287	C₂×#102	C₂³	1	1	yes	characteristic
288	C₂×#102	C₂³	1	1	yes	characteristic
289	C₂×#102	C₂³	1	1	yes	characteristic
290	C₂×#102	C₂³	1	1	yes	characteristic
291	C₂×#102	C₂³	1	1	yes	characteristic
292	C₂×#102	C₂³	1	1	yes	characteristic
293	C₂×#102	C₂³	1	1	yes	characteristic
294	C₂×#102	C₂³	1	1	yes	characteristic
295	C₂×#102	C₂³	1	1	yes	characteristic
296	C₂×#102	C₂³	1	1	yes	characteristic
297	C₂×#102	C₂³	1	1	yes	characteristic
298	C₂×#102	C₂³	1	1	yes	characteristic
299	C₂×#102	C₂³	1	1	yes	characteristic
300	C₂×#102	C₂³	1	1	yes	characteristic
301	C₂×#102	C₂³	1	1	yes	characteristic
302	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
303	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
304	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
305	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
306	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
307	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
308	C₂×#97	C₂³	1	1	yes	characteristic
309	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
310	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
311	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
312	#401	—	2	1	no	—
313	#400	—	2	1	no	—
314	#400	—	2	1	no	—
315	#400	—	2	1	no	—
316	#399	—	2	1	no	—
317	#398	—	2	1	no	—
318	#398	—	2	1	no	—
319	#398	—	2	1	no	—
320	#398	—	2	1	no	—
321	#398	—	2	1	no	—
322	#398	—	2	1	no	—
323	#398	—	2	1	no	—
324	#397	—	2	1	no	—
325	#397	—	2	1	no	—
326	#397	—	2	1	no	—
327	#396	—	2	1	no	—
328	#396	—	2	1	no	—
329	#396	—	2	1	no	—
330	#396	—	2	1	no	—
331	#394	—	2	1	no	—
332	#391	C₂³	1	1	yes	characteristic
333	#391	C₂³	1	1	yes	characteristic
334	#390	—	2	1	no	—
335	#390	D₄	1	1	yes	characteristic
336	#390	D₄	1	1	yes	characteristic
337	#390	C₂³	1	1	yes	characteristic
338	#390	C₂³	1	1	yes	characteristic
339	#389	—	2	1	no	—
340	#389	—	2	1	no	—
341	#389	—	2	1	no	—
342	#389	—	2	1	no	—
343	#389	—	2	1	no	—
344	#389	—	2	1	no	—
345	#389	D₄	1	1	yes	characteristic
346	#389	D₄	1	1	yes	characteristic
347	#389	C₂³	1	1	yes	characteristic
348	#389	C₂³	1	1	yes	characteristic
349	#389	C₂³	1	1	yes	characteristic
350	#389	C₂³	1	1	yes	characteristic
351	#389	C₂³	1	1	yes	characteristic
352	#389	C₂³	1	1	yes	characteristic
353	#389	C₂³	1	1	yes	characteristic
354	#389	C₂³	1	1	yes	characteristic
355	#389	C₂³	1	1	yes	characteristic
356	#389	C₂³	1	1	yes	characteristic
357	#389	C₂³	1	1	yes	characteristic
358	#389	C₂³	1	1	yes	characteristic
359	#388	—	2	1	no	—
360	#388	—	2	1	no	—
361	#388	—	2	1	no	—
362	#388	—	2	1	no	—
363	#388	—	2	1	no	—
364	#388	—	2	1	no	—
365	#388	—	2	1	no	—
366	#388	—	2	1	no	—
367	#388	—	2	1	no	—
368	#388	—	2	1	no	—
369	#388	—	2	1	no	—
370	#388	—	2	1	no	—
371	#388	—	2	1	no	—
372	#388	—	2	1	no	—
373	#388	—	2	1	no	—
374	#388	—	2	1	no	—
375	#388	—	2	1	no	—
376	#388	D₄	1	1	yes	characteristic
377	#388	D₄	1	1	yes	characteristic
378	#388	D₄	1	1	yes	characteristic
379	#388	D₄	1	1	yes	characteristic
380	#387	—	2	1	no	—
381	#387	—	2	1	no	—
382	#387	—	2	1	no	—
383	#387	—	2	1	no	—
384	#387	—	2	1	no	—
385	#387	—	2	1	no	—
386	#387	—	2	1	no	—
387	#387	—	2	1	no	—
388	#387	—	2	1	no	—
389	#387	—	2	1	no	—
390	#387	—	2	1	no	—
391	#387	—	2	1	no	—
392	#387	—	2	1	no	—
393	#387	—	2	1	no	—
394	#386	—	2	1	no	—
395	#386	—	2	1	no	—
396	#386	—	2	1	no	—
397	#386	—	2	1	no	—
398	#386	—	2	1	no	—
399	#386	—	2	1	no	—
400	#386	—	2	1	no	—
401	#386	—	2	1	no	—
402	#385	—	2	1	no	—
403	#385	—	2	1	no	—
404	#385	—	2	1	no	—
405	#385	—	2	1	no	—
406	#385	—	2	1	no	—
407	#385	—	2	1	no	—
408	#385	—	2	1	no	—
409	#385	—	2	1	no	—
410	#384	C₂³	1	1	yes	characteristic
411	#384	C₂³	1	1	yes	characteristic
412	#384	C₂³	1	1	yes	characteristic
413	#383	—	2	1	no	—
414	#382	—	2	1	no	—
415	#382	—	2	1	no	—
416	#382	C₂³	1	1	yes	characteristic
417	#382	C₂³	1	1	yes	characteristic
418	#382	C₂³	1	1	yes	characteristic
419	#381	—	2	1	no	—
420	#381	—	2	1	no	—
421	#380	—	2	1	no	—
422	#380	C₂³	1	1	yes	characteristic
423	#380	C₂³	1	1	yes	characteristic
424	#380	C₂³	1	1	yes	characteristic
425	#380	C₂³	1	1	yes	characteristic
426	#380	C₂³	1	1	yes	characteristic
427	#380	C₂³	1	1	yes	characteristic
428	#380	C₂³	1	1	yes	characteristic
429	#380	C₂³	1	1	yes	characteristic
430	#379	—	2	1	no	—
431	C₄×C₄⋊C₄	—	2	1	no	—
432	C₄×C₄⋊C₄	—	2	1	no	—
433	C₄×C₄⋊C₄	—	2	1	no	—
434	C₄×C₄⋊C₄	—	2	1	no	—
435	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
436	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
437	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
438	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
439	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
440	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
441	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
442	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
443	C₄×C₂²⋊C₄	—	2	1	no	—
444	C₄×C₂²⋊C₄	—	2	1	no	—
445	C₄×C₂²⋊C₄	—	2	1	no	—
446	C₄×C₂²⋊C₄	—	2	1	no	—
447	C₄×C₂²⋊C₄	—	2	1	no	—
448	C₄×C₂²⋊C₄	—	2	1	no	—
449	C₄×C₂²⋊C₄	—	2	1	no	—
450	C₄×C₂²⋊C₄	C₂³	1	1	yes	characteristic
451	C₄×C₂²⋊C₄	C₂³	1	1	yes	characteristic
452	C₂×#95	—	2	1	no	—
453	C₂×#95	—	2	1	no	—
454	C₄³	C₂³	1	1	yes	characteristic
455	#340	C₂³	1	1	yes	characteristic
456	#340	C₂³	1	1	yes	characteristic
457	#340	C₂³	1	1	yes	characteristic
458	#340	C₂³	1	1	yes	characteristic
459	#340	C₂³	1	1	yes	characteristic
460	#340	C₂³	1	1	yes	characteristic
461	#340	C₂³	1	1	yes	characteristic
462	#340	C₂³	1	1	yes	characteristic
463	#340	C₂³	1	1	yes	characteristic
464	#340	C₂³	1	1	yes	characteristic
465	#340	C₂³	1	1	yes	characteristic
466	#340	C₂³	1	1	yes	characteristic
467	#340	C₂³	1	1	yes	characteristic
468	#340	C₂³	1	1	yes	characteristic
469	#340	C₂³	1	1	yes	characteristic
470	#340	C₂³	1	1	yes	characteristic
471	#340	C₂³	1	1	yes	characteristic
472	#340	C₂³	1	1	yes	characteristic
473	#340	C₂³	1	1	yes	characteristic
474	#340	C₂³	1	1	yes	characteristic
475	#340	C₂³	1	1	yes	characteristic
476	#340	C₂³	1	1	yes	characteristic
477	#340	C₂³	1	1	yes	characteristic
478	#340	C₂³	1	1	yes	characteristic
479	#340	C₂³	1	1	yes	characteristic
480	#340	C₂³	1	1	yes	characteristic
481	#340	C₂³	1	1	yes	characteristic
482	#340	C₂³	1	1	yes	characteristic
483	#336	C₂³	1	1	yes	characteristic
484	#336	C₂³	1	1	yes	characteristic
485	#336	C₂³	1	1	yes	characteristic
486	#336	C₂³	1	1	yes	characteristic
487	#336	C₂³	1	1	yes	characteristic
488	#336	C₂³	1	1	yes	characteristic
489	#336	C₂³	1	1	yes	characteristic
490	#336	C₂³	1	1	yes	characteristic
491	#336	C₂³	1	1	yes	characteristic
492	#336	C₂³	1	1	yes	characteristic
493	C₂⁵	—	2	1	no	—
494	C₂×#41	—	2	2	no	—
495	C₂×#41	—	2	2	no	—
496	C₂×#41	—	2	2	no	—
497	C₂×#41	—	2	2	no	—
498	C₂×#41	—	4	1	no	—
499	C₂×#41	—	4	1	no	—
500	C₂²×Q₈	C₂⁴	1	1	yes	characteristic
501	C₂²×D₄	—	2	2	no	—
502	C₂²×D₄	—	2	2	no	—
503	C₂²×D₄	—	2	1	no	—
504	C₂²×D₄	—	2	1	no	—
505	C₂²×D₄	—	2	1	no	—
506	C₂²×D₄	—	2	2	no	—
507	C₂²×D₄	—	4	1	no	—
508	C₂²×D₄	—	4	1	no	—
509	C₂²×D₄	C₂×D₄	1	1	yes	characteristic
510	C₂²×D₄	#41	1	4	yes	—
511	C₂²×D₄	C₂⁴	1	1	yes	characteristic
512	C₂²×D₄	C₂⁴	1	1	yes	characteristic
513	C₂³×C₄	—	2	1	no	—
514	C₂³×C₄	—	2	1	no	—
515	C₂³×C₄	—	2	1	no	—
516	C₂³×C₄	—	2	1	no	—
517	C₂³×C₄	—	2	1	no	—
518	C₂³×C₄	—	2	1	no	—
519	C₂³×C₄	—	2	1	no	—
520	C₂³×C₄	—	2	1	no	—
521	C₂³×C₄	—	2	1	no	—
522	C₂³×C₄	—	2	1	no	—
523	C₂³×C₄	C₂⁴	1	1	yes	characteristic
524	C₂³×C₄	C₂⁴	1	1	yes	characteristic
525	C₂×M₁₆	—	2	2	no	—
526	C₂×M₁₆	—	4	1	no	—
527	C₂×M₁₆	—	4	1	no	—
528	C₂²×C₈	—	2	2	no	—
529	C₂²×C₈	—	4	1	no	—
530	C₂²×C₈	—	4	1	no	—
531	C₂²×C₈	C₂⁴	1	1	yes	characteristic
532	C₂²×C₈	C₂⁴	1	1	yes	characteristic
533	C₂²×C₈	C₂⁴	1	1	yes	characteristic
534	C₂²×C₈	C₂⁴	1	1	yes	characteristic
535	C₂²×C₈	C₂⁴	1	1	yes	characteristic
536	C₂²×C₈	C₂⁴	1	1	yes	characteristic
537	C₂²×C₈	C₂⁴	1	1	yes	characteristic
538	C₂²×C₈	C₂⁴	1	1	yes	characteristic
539	#126	—	8	2	no	—
540	#125	—	2	2	no	—
541	#125	—	2	2	no	—
542	#125	—	8	2	no	—
543	#124	—	2	2	no	—
544	#124	—	2	2	no	—
545	#123	—	2	8	no	—
546	C₂²⋊Q₈	—	2	2	no	—
547	C₂²⋊Q₈	#41	1	4	yes	—
548	#121	—	2	8	no	—
549	#121	—	2	2	no	—
550	#121	—	2	2	no	—
551	#120	—	2	8	no	—
552	C₄×Q₈	—	2	2	no	—
553	C₄×Q₈	—	2	2	no	—
554	C₄×Q₈	—	2	2	no	—
555	C₄×Q₈	—	4	1	no	—
556	C₄×D₄	—	2	2	no	—
557	C₄×D₄	—	2	2	no	—
558	C₄×D₄	—	2	2	no	—
559	C₄×D₄	—	2	2	no	—
560	C₄×D₄	—	2	2	no	—
561	C₄×D₄	—	2	2	no	—
562	C₄×D₄	—	2	2	no	—
563	C₄×D₄	—	2	2	no	—
564	C₄×D₄	—	2	2	no	—
565	C₄×D₄	—	2	2	no	—
566	C₄×D₄	—	2	2	no	—
567	C₄×D₄	—	4	1	no	—
568	C₄×D₄	—	4	1	no	—
569	C₄×D₄	—	4	1	no	—
570	C₄×D₄	—	4	1	no	—
571	C₄×D₄	—	4	4	no	—
572	C₄×D₄	—	4	4	no	—
573	C₄×D₄	—	4	4	no	—
574	C₄×D₄	—	4	4	no	—
575	C₄×D₄	—	8	2	no	—
576	C₄×D₄	#41	1	4	yes	—
577	#117	—	2	2	no	—
578	#117	—	2	2	no	—
579	#117	—	2	2	no	—
580	#117	—	2	2	no	—
581	#117	—	2	2	no	—
582	#117	—	2	2	no	—
583	#117	—	2	2	no	—
584	#117	—	4	4	no	—
585	#117	—	4	1	no	—
586	#117	—	8	2	no	—
587	C₂×C₄⋊C₄	—	2	1	no	—
588	C₂×C₄⋊C₄	—	2	2	no	—
589	C₂×C₄⋊C₄	—	2	2	no	—
590	C₂×C₄⋊C₄	—	2	2	no	—
591	C₂×C₄⋊C₄	—	2	1	no	—
592	C₂×C₄⋊C₄	—	2	1	no	—
593	C₂×C₄⋊C₄	—	2	1	no	—
594	C₂×C₄⋊C₄	—	2	1	no	—
595	C₂×C₄⋊C₄	—	2	1	no	—
596	C₂×C₄⋊C₄	—	2	1	no	—
597	C₂×C₄⋊C₄	—	2	1	no	—
598	C₂×C₄⋊C₄	—	2	1	no	—
599	C₂×C₄⋊C₄	—	2	1	no	—
600	C₂×C₄⋊C₄	—	2	1	no	—
601	C₂×C₄⋊C₄	—	2	1	no	—
602	C₂×C₄⋊C₄	—	2	1	no	—
603	C₂×C₄⋊C₄	—	2	1	no	—
604	C₂×C₄⋊C₄	—	2	1	no	—
605	C₂×C₄⋊C₄	—	2	1	no	—
606	C₂×C₄⋊C₄	—	2	1	no	—
607	C₂×C₄⋊C₄	—	2	1	no	—
608	C₂×C₄⋊C₄	—	2	1	no	—
609	C₂×C₄⋊C₄	—	2	1	no	—
610	C₂×C₄⋊C₄	—	2	1	no	—
611	C₂×C₄⋊C₄	—	2	1	no	—
612	C₂×C₄⋊C₄	—	2	1	no	—
613	C₂×C₄⋊C₄	—	2	1	no	—
614	C₂×C₄⋊C₄	—	2	1	no	—
615	C₂×C₄⋊C₄	—	4	1	no	—
616	C₂×C₄⋊C₄	—	4	4	no	—
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	C₂×D₄	1	1	yes	characteristic
621	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
622	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
623	C₂×C₄⋊C₄	C₂×D₄	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×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
632	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
633	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
634	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
635	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
636	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
637	C₂×C₂²⋊C₄	—	2	8	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	—	4	4	no	—
664	C₂×C₂²⋊C₄	—	4	4	no	—
665	C₂×C₂²⋊C₄	—	8	2	no	—
666	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
667	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
668	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
669	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
670	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
671	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
672	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
673	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
674	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
675	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
676	C₂×C₄²	—	2	1	no	—
677	C₂×C₄²	—	2	1	no	—
678	C₂×C₄²	—	2	1	no	—
679	C₂×C₄²	—	2	1	no	—
680	C₂×C₄²	—	2	1	no	—
681	C₂×C₄²	—	2	1	no	—
682	C₂×C₄²	—	2	1	no	—
683	C₂×C₄²	—	2	1	no	—
684	C₂×C₄²	—	2	1	no	—
685	C₂×C₄²	—	2	1	no	—
686	C₂×C₄²	—	2	1	no	—
687	C₂×C₄²	—	8	2	no	—
688	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
689	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
690	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
691	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
692	C₂×C₄²	C₂⁴	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	#107	—	2	2	no	—
698	#107	—	2	2	no	—
699	#107	—	2	2	no	—
700	#107	—	2	2	no	—
701	#107	—	4	1	no	—
702	#107	—	4	1	no	—
703	#107	—	4	1	no	—
704	#107	—	4	1	no	—
705	#106	—	2	2	no	—
706	#106	—	2	2	no	—
707	#106	—	4	1	no	—
708	#106	—	4	1	no	—
709	C₄⋊C₈	—	2	2	no	—
710	C₄⋊C₈	—	2	2	no	—
711	C₄⋊C₈	—	2	2	no	—
712	C₄⋊C₈	—	2	2	no	—
713	C₄⋊C₈	—	4	1	no	—
714	C₄⋊C₈	—	4	1	no	—
715	#103	—	2	2	no	—
716	#103	—	2	2	no	—
717	#103	—	2	2	no	—
718	#103	—	2	2	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	—	2	2	no	—
726	#102	—	2	2	no	—
727	#102	—	2	2	no	—
728	#102	—	2	2	no	—
729	#102	—	2	2	no	—
730	#102	—	2	2	no	—
731	#102	—	2	2	no	—
732	#102	—	2	2	no	—
733	#102	—	2	2	no	—
734	#102	—	2	2	no	—
735	#102	—	4	1	no	—
736	#102	—	4	1	no	—
737	#102	—	4	1	no	—
738	#102	—	4	1	no	—
739	C₂²⋊C₈	—	2	2	no	—
740	C₂²⋊C₈	—	2	2	no	—
741	C₂²⋊C₈	—	4	1	no	—
742	C₂²⋊C₈	—	4	1	no	—
743	C₂²⋊C₈	—	4	1	no	—
744	C₂²⋊C₈	—	4	1	no	—
745	#97	—	4	1	no	—
746	C₄×C₈	—	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	—	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	C₂×D₄	1	1	yes	characteristic
787	#95	C₂×D₄	1	1	yes	characteristic
788	#95	C₂×D₄	1	1	yes	characteristic
789	#95	C₂×D₄	1	1	yes	characteristic
790	#95	C₂×D₄	1	1	yes	characteristic
791	#95	C₂×D₄	1	1	yes	characteristic
792	C₂⁴	—	2	1	no	—
793	C₂⁴	—	2	1	no	—
794	C₂⁴	—	2	4	no	—
795	C₂⁴	—	4	2	no	—
796	C₂⁴	—	4	2	no	—
797	C₂⁴	—	8	1	no	—
798	C₂⁴	—	8	1	no	—
799	C₂⁴	—	8	1	no	—
800	C₂⁴	—	8	1	no	—
801	C₂⁴	C₂²×D₄	1	1	yes	characteristic
802	C₂⁴	C₂²×D₄	1	1	yes	characteristic
803	#41	—	4	4	no	—
804	#41	—	4	4	no	—
805	#41	—	4	4	no	—
806	#41	—	4	4	no	—
807	C₂×Q₈	—	2	1	no	—
808	C₂×Q₈	—	2	1	no	—
809	C₂×Q₈	—	2	1	no	—
810	C₂×Q₈	—	2	1	no	—
811	C₂×Q₈	—	2	1	no	—
812	C₂×Q₈	C₂×#41	1	2	yes	—
813	C₂×D₄	—	2	8	no	—
814	C₂×D₄	—	2	4	no	—
815	C₂×D₄	—	2	4	no	—
816	C₂×D₄	—	2	2	no	—
817	C₂×D₄	—	2	4	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	—	2	1	no	—
826	C₂×D₄	—	4	4	no	—
827	C₂×D₄	—	4	4	no	—
828	C₂×D₄	—	4	4	no	—
829	C₂×D₄	—	4	2	no	—
830	C₂×D₄	—	4	2	no	—
831	C₂×D₄	—	4	1	no	—
832	C₂×D₄	—	4	1	no	—
833	C₂×D₄	—	4	2	no	—
834	C₂×D₄	—	4	2	no	—
835	C₂×D₄	—	8	1	no	—
836	C₂×D₄	—	8	1	no	—
837	C₂×D₄	C₂×#41	1	2	yes	—
838	C₂×D₄	C₂×#41	1	2	yes	—
839	C₂×D₄	C₂×#41	1	2	yes	—
840	C₂×D₄	2₋¹⁺⁴	1	2	yes	—
841	C₂²×C₄	—	2	1	no	—
842	C₂²×C₄	—	2	1	no	—
843	C₂²×C₄	—	2	1	no	—
844	C₂²×C₄	—	2	1	no	—
845	C₂²×C₄	—	2	4	no	—
846	C₂²×C₄	—	2	1	no	—
847	C₂²×C₄	—	2	1	no	—
848	C₂²×C₄	—	2	1	no	—
849	C₂²×C₄	—	2	4	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	—	2	1	no	—
855	C₂²×C₄	—	2	1	no	—
856	C₂²×C₄	—	2	4	no	—
857	C₂²×C₄	—	2	1	no	—
858	C₂²×C₄	—	2	1	no	—
859	C₂²×C₄	—	2	1	no	—
860	C₂²×C₄	—	2	1	no	—
861	C₂²×C₄	—	2	1	no	—
862	C₂²×C₄	—	2	1	no	—
863	C₂²×C₄	—	2	1	no	—
864	C₂²×C₄	—	2	1	no	—
865	C₂²×C₄	—	2	1	no	—
866	C₂²×C₄	—	2	1	no	—
867	C₂²×C₄	—	2	1	no	—
868	C₂²×C₄	—	4	2	no	—
869	C₂²×C₄	—	4	2	no	—
870	C₂²×C₄	—	4	2	no	—
871	C₂²×C₄	—	4	2	no	—
872	C₂²×C₄	—	4	2	no	—
873	C₂²×C₄	—	4	2	no	—
874	C₂²×C₄	—	4	2	no	—
875	C₂²×C₄	—	4	2	no	—
876	C₂²×C₄	—	4	2	no	—
877	C₂²×C₄	—	4	2	no	—
878	C₂²×C₄	—	8	1	no	—
879	C₂²×C₄	—	8	1	no	—
880	C₂²×C₄	—	8	1	no	—
881	C₂²×C₄	—	8	1	no	—
882	C₂²×C₄	—	8	1	no	—
883	C₂²×C₄	—	8	1	no	—
884	C₂²×C₄	—	8	1	no	—
885	C₂²×C₄	—	8	1	no	—
886	C₂²×C₄	—	8	1	no	—
887	C₂²×C₄	—	8	1	no	—
888	C₂²×C₄	—	8	1	no	—
889	C₂²×C₄	—	8	1	no	—
890	C₂²×C₄	—	8	1	no	—
891	C₂²×C₄	—	8	1	no	—
892	C₂²×C₄	—	8	1	no	—
893	C₂²×C₄	—	8	1	no	—
894	C₂²×C₄	—	8	1	no	—
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	C₂²×D₄	1	1	yes	characteristic
904	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
905	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
906	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
907	C₂²×C₄	C₂×#41	1	2	yes	—
908	C₂²×C₄	C₂×#41	1	2	yes	—
909	C₂²×C₄	C₂⁵	1	1	yes	characteristic
910	M₁₆	—	8	2	no	—
911	C₂×C₈	—	2	1	no	—
912	C₂×C₈	—	2	1	no	—
913	C₂×C₈	—	2	1	no	—
914	C₂×C₈	—	2	1	no	—
915	C₂×C₈	—	2	1	no	—
916	C₂×C₈	—	2	1	no	—
917	C₂×C₈	—	2	1	no	—
918	C₂×C₈	—	2	1	no	—
919	C₂×C₈	—	2	1	no	—
920	C₂×C₈	—	2	1	no	—
921	C₂×C₈	—	2	1	no	—
922	C₂×C₈	—	2	1	no	—
923	C₂×C₈	—	2	1	no	—
924	C₂×C₈	—	2	1	no	—
925	C₂×C₈	—	2	1	no	—
926	C₂×C₈	—	2	1	no	—
927	C₂×C₈	—	2	1	no	—
928	C₂×C₈	—	2	1	no	—
929	C₂×C₈	—	2	1	no	—
930	C₂×C₈	—	2	1	no	—
931	C₂×C₈	—	2	1	no	—
932	C₂×C₈	—	2	1	no	—
933	C₂×C₈	—	2	1	no	—
934	C₂×C₈	—	2	1	no	—
935	C₂×C₈	—	8	2	no	—
936	C₄⋊C₄	—	2	4	no	—
937	C₄⋊C₄	—	2	2	no	—
938	C₄⋊C₄	—	2	2	no	—
939	C₄⋊C₄	—	2	2	no	—
940	C₄⋊C₄	—	2	2	no	—
941	C₄⋊C₄	—	2	2	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	—	2	1	no	—
959	C₄⋊C₄	—	2	1	no	—
960	C₄⋊C₄	—	2	1	no	—
961	C₄⋊C₄	—	2	1	no	—
962	C₄⋊C₄	—	2	1	no	—
963	C₄⋊C₄	—	2	1	no	—
964	C₄⋊C₄	—	2	1	no	—
965	C₄⋊C₄	—	2	1	no	—
966	C₄⋊C₄	—	4	1	no	—
967	C₄⋊C₄	—	4	1	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	—	8	1	no	—
978	C₄⋊C₄	—	8	1	no	—
979	C₄⋊C₄	—	8	1	no	—
980	C₄⋊C₄	—	8	1	no	—
981	C₄⋊C₄	—	8	1	no	—
982	C₄⋊C₄	—	8	1	no	—
983	C₄⋊C₄	—	8	1	no	—
984	C₄⋊C₄	—	8	1	no	—
985	C₄⋊C₄	—	8	1	no	—
986	C₄⋊C₄	—	8	1	no	—
987	C₄⋊C₄	—	8	1	no	—
988	C₄⋊C₄	—	8	1	no	—
989	C₄⋊C₄	—	8	1	no	—
990	C₄⋊C₄	—	8	1	no	—
991	C₄⋊C₄	—	8	1	no	—
992	C₄⋊C₄	C₂×#41	1	2	yes	—
993	C₄⋊C₄	C₂×#41	1	2	yes	—
994	C₂²⋊C₄	—	2	4	no	—
995	C₂²⋊C₄	—	2	4	no	—
996	C₂²⋊C₄	—	2	4	no	—
997	C₂²⋊C₄	—	2	4	no	—
998	C₂²⋊C₄	—	2	2	no	—
999	C₂²⋊C₄	—	2	4	no	—
1000	C₂²⋊C₄	—	2	2	no	—
1001	C₂²⋊C₄	—	2	4	no	—
1002	C₂²⋊C₄	—	2	2	no	—
1003	C₂²⋊C₄	—	2	2	no	—
1004	C₂²⋊C₄	—	2	2	no	—
1005	C₂²⋊C₄	—	2	2	no	—
1006	C₂²⋊C₄	—	2	2	no	—
1007	C₂²⋊C₄	—	2	2	no	—
1008	C₂²⋊C₄	—	4	1	no	—
1009	C₂²⋊C₄	—	4	1	no	—
1010	C₂²⋊C₄	—	4	2	no	—
1011	C₂²⋊C₄	—	4	2	no	—
1012	C₂²⋊C₄	—	4	2	no	—
1013	C₂²⋊C₄	—	4	2	no	—
1014	C₂²⋊C₄	—	4	2	no	—
1015	C₂²⋊C₄	—	4	2	no	—
1016	C₂²⋊C₄	—	4	2	no	—
1017	C₂²⋊C₄	—	4	2	no	—
1018	C₂²⋊C₄	—	8	1	no	—
1019	C₂²⋊C₄	—	8	1	no	—
1020	C₂²⋊C₄	—	8	1	no	—
1021	C₂²⋊C₄	—	8	1	no	—
1022	C₂²⋊C₄	—	8	1	no	—
1023	C₂²⋊C₄	—	8	1	no	—
1024	C₂²⋊C₄	—	8	1	no	—
1025	C₂²⋊C₄	—	8	1	no	—
1026	C₂²⋊C₄	—	8	1	no	—
1027	C₂²⋊C₄	—	8	1	no	—
1028	C₂²⋊C₄	—	8	1	no	—
1029	C₄²	—	2	2	no	—
1030	C₄²	—	2	1	no	—
1031	C₄²	—	2	1	no	—
1032	C₄²	—	2	1	no	—
1033	C₄²	—	2	1	no	—
1034	C₄²	—	2	1	no	—
1035	C₄²	—	2	1	no	—
1036	C₄²	—	2	1	no	—
1037	C₄²	—	2	1	no	—
1038	C₄²	—	4	1	no	—
1039	C₄²	—	4	1	no	—
1040	C₄²	—	4	1	no	—
1041	C₄²	—	4	2	no	—
1042	C₄²	—	4	2	no	—
1043	C₄²	—	4	2	no	—
1044	C₄²	—	4	2	no	—
1045	C₄²	—	4	2	no	—
1046	C₄²	—	4	2	no	—
1047	C₄²	—	8	1	no	—
1048	C₄²	—	8	1	no	—
1049	C₄²	—	8	1	no	—
1050	C₄²	—	8	1	no	—
1051	C₄²	—	8	1	no	—
1052	C₄²	C₂×#41	1	2	yes	—
1053	C₄²	H(5,𝔽₂)	1	2	yes	—
1054	C₂³	—	2	1	no	—
1055	C₂³	—	2	1	no	—
1056	C₂³	—	2	1	no	—
1057	C₂³	—	2	2	no	—
1058	C₂³	—	2	1	no	—
1059	C₂³	—	2	2	no	—
1060	C₂³	—	2	2	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	2	no	—
1067	C₂³	—	2	1	no	—
1068	C₂³	—	2	1	no	—
1069	C₂³	—	2	1	no	—
1070	C₂³	—	2	1	no	—
1071	C₂³	—	4	8	no	—
1072	C₂³	—	4	1	no	—
1073	C₂³	—	4	1	no	—
1074	C₂³	—	4	1	no	—
1075	C₂³	—	4	1	no	—
1076	C₂³	—	4	1	no	—
1077	C₂³	—	4	1	no	—
1078	C₂³	—	4	1	no	—
1079	C₂³	—	4	1	no	—
1080	C₂³	—	4	1	no	—
1081	C₂³	—	4	1	no	—
1082	C₂³	—	8	4	no	—
1083	C₂³	—	8	4	no	—
1084	C₂³	—	16	2	no	—
1085	C₂³	—	16	2	no	—
1086	C₂³	—	16	2	no	—
1087	C₂³	—	16	2	no	—
1088	C₂³	#525	1	2	yes	—
1089	C₂³	C₂³×D₄	1	1	yes	characteristic
1090	Q₈	—	2	2	no	—
1091	Q₈	—	2	2	no	—
1092	Q₈	—	4	1	no	—
1093	Q₈	—	4	1	no	—
1094	D₄	—	2	2	no	—
1095	D₄	—	2	2	no	—
1096	D₄	—	2	2	no	—
1097	D₄	—	2	2	no	—
1098	D₄	—	2	2	no	—
1099	D₄	—	4	8	no	—
1100	D₄	—	4	8	no	—
1101	D₄	—	4	1	no	—
1102	D₄	—	4	1	no	—
1103	D₄	—	8	2	no	—
1104	D₄	—	8	4	no	—
1105	D₄	#552	1	4	yes	—
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	2	no	—
1115	C₂×C₄	—	2	2	no	—
1116	C₂×C₄	—	2	2	no	—
1117	C₂×C₄	—	2	2	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	2	no	—
1132	C₂×C₄	—	2	1	no	—
1133	C₂×C₄	—	2	2	no	—
1134	C₂×C₄	—	2	1	no	—
1135	C₂×C₄	—	2	1	no	—
1136	C₂×C₄	—	2	1	no	—
1137	C₂×C₄	—	2	1	no	—
1138	C₂×C₄	—	2	2	no	—
1139	C₂×C₄	—	2	1	no	—
1140	C₂×C₄	—	2	1	no	—
1141	C₂×C₄	—	2	1	no	—
1142	C₂×C₄	—	2	1	no	—
1143	C₂×C₄	—	2	1	no	—
1144	C₂×C₄	—	2	1	no	—
1145	C₂×C₄	—	4	8	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	—	8	4	no	—
1190	C₂×C₄	—	8	4	no	—
1191	C₂×C₄	—	8	4	no	—
1192	C₂×C₄	—	8	4	no	—
1193	C₂×C₄	—	16	2	no	—
1194	C₂×C₄	—	16	2	no	—
1195	C₂×C₄	—	16	2	no	—
1196	C₂×C₄	—	16	2	no	—
1197	C₂×C₄	—	16	2	no	—
1198	C₂×C₄	#525	1	2	yes	—
1199	C₂×C₄	#546	1	2	yes	—
1200	C₂×C₄	#546	1	2	yes	—
1201	C₂×C₄	#576	1	2	yes	—
1202	C₂×C₄	C₂²×#41	1	1	yes	characteristic
1203	C₂×C₄	C₂²×#41	1	1	yes	characteristic
1204	C₂×C₄	C₂²×#41	1	1	yes	characteristic
1205	C₂×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
1206	C₂×C₄	C₂×2₋¹⁺⁴	1	1	yes	characteristic
1207	C₂×C₄	#585	1	1	yes	characteristic
1208	C₈	—	4	1	no	—
1209	C₈	—	4	1	no	—
1210	C₈	—	4	1	no	—
1211	C₈	—	4	1	no	—
1212	C₈	—	4	1	no	—
1213	C₈	—	4	1	no	—
1214	C₈	—	4	1	no	—
1215	C₈	—	4	1	no	—
1216	C₂²	—	2	2	no	—
1217	C₂²	—	2	4	no	—
1218	C₂²	—	2	2	no	—
1219	C₂²	—	2	2	no	—
1220	C₂²	—	4	2	no	—
1221	C₂²	—	4	1	no	—
1222	C₂²	—	4	2	no	—
1223	C₂²	—	4	1	no	—
1224	C₂²	—	4	2	no	—
1225	C₂²	—	4	1	no	—
1226	C₂²	—	4	2	no	—
1227	C₂²	—	4	2	no	—
1228	C₂²	—	4	1	no	—
1229	C₂²	—	4	2	no	—
1230	C₂²	—	4	1	no	—
1231	C₂²	—	4	1	no	—
1232	C₂²	—	4	1	no	—
1233	C₂²	—	4	1	no	—
1234	C₂²	—	4	2	no	—
1235	C₂²	—	4	1	no	—
1236	C₂²	—	4	2	no	—
1237	C₂²	—	4	1	no	—
1238	C₂²	—	4	2	no	—
1239	C₂²	—	4	1	no	—
1240	C₂²	—	8	1	no	—
1241	C₂²	—	8	1	no	—
1242	C₂²	—	8	1	no	—
1243	C₂²	—	8	1	no	—
1244	C₂²	—	16	8	no	—
1245	C₂²	C₂×#525	1	1	yes	characteristic
1246	C₂²	C₂×#546	1	1	yes	characteristic
1247	C₂²	#3489	1	1	yes	characteristic
1248	C₂²	C₂×#576	1	1	yes	characteristic
1249	C₂²	#3584	1	1	yes	characteristic
1250	C₂²	#3584	1	1	yes	characteristic
1251	C₂²	#3586	1	1	yes	characteristic
1252	C₄	—	2	2	no	—
1253	C₄	—	2	2	no	—
1254	C₄	—	2	2	no	—
1255	C₄	—	2	2	no	—
1256	C₄	—	4	1	no	—
1257	C₄	—	4	1	no	—
1258	C₄	—	4	2	no	—
1259	C₄	—	4	1	no	—
1260	C₄	—	4	1	no	—
1261	C₄	—	4	1	no	—
1262	C₄	—	4	2	no	—
1263	C₄	—	4	1	no	—
1264	C₄	—	4	2	no	—
1265	C₄	—	4	1	no	—
1266	C₄	—	4	1	no	—
1267	C₄	—	8	1	no	—
1268	C₄	—	8	1	no	—
1269	C₄	—	8	1	no	—
1270	C₄	—	8	1	no	—
1271	C₄	—	8	1	no	—
1272	C₄	—	8	1	no	—
1273	C₄	—	8	1	no	—
1274	C₄	—	8	1	no	—
1275	C₄	—	8	1	no	—
1276	C₄	—	8	1	no	—
1277	C₄	—	8	1	no	—
1278	C₄	C₂×#552	1	1	yes	characteristic
1279	C₄	#3475	1	1	yes	characteristic
1280	C₄	#3505	1	1	yes	characteristic
1281	C₄	#3520	1	1	yes	characteristic
1282	C₂	—	4	2	no	—
1283	C₂	—	4	4	no	—
1284	C₂	—	8	1	no	—
1285	C₂	—	8	2	no	—
1286	C₂	#36156	1	1	yes	characteristic
1287	C₂	#60570	1	1	yes	characteristic
1288	C₂	#60581	1	1	yes	characteristic
1289	C₂	#61199	1	1	yes	characteristic
1290	C₂	#61216	1	1	yes	characteristic
1291	C₂	#62172	1	1	yes	characteristic
1292	C₂	#62211	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³	C₂³×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁵
prime radical	C₂×#546	C₂²
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
1. #39546	C₂	semidirect
3. #33066	C₂	semidirect
4. #32968	C₂	semidirect
5. #32966	C₂	semidirect
6. #29122	C₂	semidirect
7. #28208	C₂	semidirect
8. #27656	C₂	semidirect
9. #27640	C₂	semidirect
10. #27531	C₂	semidirect
11. #27528	C₂	semidirect
12. #27323	C₂	semidirect
13. #27309	C₂	semidirect
14. #27097	C₂	semidirect
15. #27094	C₂	semidirect
16. #26782	C₂	semidirect
17. #26764	C₂	semidirect
18. #24956	C₂	semidirect
19. #24934	C₂	semidirect
20. #24850	C₂	semidirect
21. #24713	C₂	semidirect
24. #22947	C₂	semidirect
25. #22919	C₂	semidirect
26. #22756	C₂	semidirect
27. #22580	C₂	semidirect
28. #22570	C₂	semidirect
29. C₄×#478	C₂	semidirect
30. #20746	C₂	semidirect
31. #20650	C₂	semidirect
37. C₂×#479	C₂²	semidirect
40. C₂×#433	C₂²	semidirect
44. #2859	C₂²	semidirect
50. #2629	C₂²	semidirect
54. #2508	C₂²	semidirect
55. #2507	C₂²	semidirect
56. #2496	C₂²	semidirect
57. #2494	C₂²	semidirect
79. #2314	C₂²	semidirect
80. C₄×#125	C₂²	semidirect
86. #2101	C₂²	semidirect
87. #2101	C₂²	semidirect
88. #2088	C₂²	semidirect
89. #2086	C₂²	semidirect
90. #2085	C₂²	semidirect
91. #2085	C₂²	semidirect
92. #2085	C₂²	semidirect
93. #2083	C₂²	semidirect
94. #2077	C₂²	semidirect
95. #2076	C₂²	semidirect
96. #2076	C₂²	semidirect
97. #2075	C₂²	semidirect
98. #2074	C₂²	semidirect
99. #2072	C₂²	semidirect
100. #2068	C₂²	semidirect
101. #2068	C₂²	semidirect
110. #1989	C₂²	semidirect
111. #1949	C₂²	semidirect
112. #1947	C₂²	semidirect
113. #1947	C₂²	semidirect
114. #1943	C₂²	semidirect
115. #1942	C₂²	semidirect
120. #1933	C₂²	semidirect
121. #1933	C₂²	semidirect
122. #1928	C₂²	semidirect
123. #1927	C₂²	semidirect
128. #1923	C₂²	semidirect
129. #1923	C₂²	semidirect
130. #1921	C₂²	semidirect
131. #1921	C₂²	semidirect
132. #1919	C₂²	semidirect
133. #1919	C₂²	semidirect
134. #1918	C₂²	semidirect
135. #1918	C₂²	semidirect
136. #1918	C₂²	semidirect
137. #1918	C₂²	semidirect
138. #1917	C₂²	semidirect
139. #1916	C₂²	semidirect
144. #1865	C₂²	semidirect
149. #1863	C₂²	semidirect
160. #1853	C₂²	semidirect
161. #1852	C₂²	semidirect
162. #1831	C₂²	semidirect
164. #1824	C₂²	semidirect
166. #1823	C₂²	semidirect
169. #1805	C₂²	semidirect
174. #1803	C₂²	semidirect
175. #1803	C₂²	semidirect
183. #1798	C₂²	semidirect
190. C₄×#107	C₂²	semidirect
191. C₄×#106	C₂²	semidirect
192. C₄×C₄⋊C₈	C₂²	semidirect
193. #1763	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
#39546	2
#34309	2
#33066	2
#32968	2
#32966	2
#29122	2
#28208	2
#27656	2
#27640	2
#27531	2
#27528	2
#27323	2
#27309	2
#27097	2
#27094	2
#26782	2
#26764	2
#24956	2
#24934	2
#24850	2
#24713	2
#24050	2
#24039	2
#22947	2
#22919	2
#22756	2
#22580	2
#22570	2
C₄×#478	2
#20746	2
#20650	2