Subgroups — #7119011

Order 512.

1385 conjugacy classes of subgroups.

The subgroup lattice has 1237 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#59436	C₂	1	1	yes	maximal, characteristic, complemented
2	#39024	C₂	1	1	yes	maximal, characteristic
3	#32638	C₂	1	1	yes	maximal, characteristic, complemented
4	#32568	C₂	1	1	yes	maximal, characteristic, complemented
5	#32293	C₂	1	1	yes	maximal, characteristic, complemented
6	#31430	C₂	1	1	yes	maximal, characteristic, complemented
7	#31329	C₂	1	1	yes	maximal, characteristic, complemented
8	#31298	C₂	1	1	yes	maximal, characteristic, complemented
9	#31270	C₂	1	1	yes	maximal, characteristic
10	#30639	C₂	1	1	yes	maximal, characteristic, complemented
11	#29523	C₂	1	1	yes	maximal, characteristic, complemented
12	#29513	C₂	1	1	yes	maximal, characteristic, complemented
13	#29069	C₂	1	1	yes	maximal, characteristic, complemented
14	#29067	C₂	1	1	yes	maximal, characteristic, complemented
15	#28855	C₂	1	1	yes	maximal, characteristic, complemented
16	#27836	C₂	1	1	yes	maximal, characteristic, complemented
17	#27726	C₂	1	1	yes	maximal, characteristic, complemented
18	#27534	C₂	1	1	yes	maximal, characteristic, complemented
19	#27408	C₂	1	1	yes	maximal, characteristic, complemented
20	#27256	C₂	1	1	yes	maximal, characteristic, complemented
21	#27181	C₂	1	1	yes	maximal, characteristic, complemented
22	#27055	C₂	1	1	yes	maximal, characteristic, complemented
23	#26327	C₂	1	1	yes	maximal, characteristic, complemented
24	#26216	C₂	1	1	yes	maximal, characteristic, complemented
25	#25007	C₂	1	1	yes	maximal, characteristic, complemented
26	#24865	C₂	1	1	yes	maximal, characteristic
27	#23821	C₂	1	1	yes	maximal, characteristic, complemented
28	#23270	C₂	1	1	yes	maximal, characteristic, complemented
29	#22943	C₂	1	1	yes	maximal, characteristic, complemented
30	#22562	C₂	1	1	yes	maximal, characteristic, complemented
31	#22222	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×#488	C₂²	1	1	yes	characteristic
33	C₂×#481	C₂²	1	1	yes	characteristic
34	C₂²×#102	C₂²	1	1	yes	characteristic
35	#2860	C₂²	1	1	yes	characteristic
36	#2756	—	2	1	no	—
37	#2745	—	2	1	no	—
38	#2745	—	2	1	no	—
39	#2735	—	2	1	no	—
40	#2702	—	2	1	no	—
41	#2685	—	2	1	no	—
42	#2648	—	2	1	no	—
43	#2599	—	2	1	no	—
44	#2599	—	2	1	no	—
45	#2592	C₂²	1	1	yes	characteristic
46	#2570	—	2	1	no	—
47	#2567	C₂²	1	1	yes	characteristic, complemented
48	#2563	C₂²	1	1	yes	characteristic
49	#2538	C₂²	1	1	yes	characteristic
50	#2518	—	2	1	no	—
51	#2514	—	2	1	no	—
52	#2500	C₂²	1	1	yes	characteristic
53	#2495	C₂²	1	1	yes	characteristic
54	#2495	C₂²	1	1	yes	characteristic
55	#2495	C₂²	1	1	yes	characteristic, complemented
56	#2494	C₂²	1	1	yes	characteristic
57	#2494	C₂²	1	1	yes	characteristic, complemented
58	#2472	—	2	1	no	—
59	#2447	—	2	1	no	—
60	#2442	C₂²	1	1	yes	characteristic
61	#2442	C₂²	1	1	yes	characteristic, complemented
62	#2435	C₂²	1	1	yes	characteristic
63	#2427	C₂²	1	1	yes	characteristic
64	#2426	C₂²	1	1	yes	characteristic
65	#2423	C₂²	1	1	yes	characteristic
66	#2415	C₂²	1	1	yes	characteristic
67	#2408	C₂²	1	1	yes	characteristic
68	#2363	C₂²	1	1	yes	characteristic
69	#2355	C₂²	1	1	yes	characteristic, complemented
70	#2354	—	2	1	no	—
71	D₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
72	#2344	C₂²	1	1	yes	characteristic
73	#2344	C₂²	1	1	yes	characteristic, complemented
74	D₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
75	#2312	—	2	1	no	—
76	C₄×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
77	C₄×#125	C₂²	1	1	yes	characteristic, complemented
78	C₄×#124	C₂²	1	1	yes	characteristic
79	C₄×#124	C₂²	1	1	yes	characteristic
80	#2101	C₂²	1	1	yes	characteristic, complemented
81	#2101	C₂²	1	1	yes	characteristic, complemented
82	#2101	C₂²	1	1	yes	characteristic, complemented
83	#2101	C₂²	1	1	yes	characteristic, complemented
84	#2100	C₂²	1	1	yes	characteristic, complemented
85	#2099	C₂²	1	1	yes	characteristic, complemented
86	#2097	C₂²	1	1	yes	characteristic, complemented
87	#2094	C₂²	1	1	yes	characteristic
88	#2092	C₂²	1	1	yes	characteristic
89	#2088	C₂²	1	1	yes	characteristic, complemented
90	#2084	C₂²	1	1	yes	characteristic, complemented
91	#2077	C₂²	1	1	yes	characteristic
92	#2076	C₂²	1	1	yes	characteristic
93	#2076	C₂²	1	1	yes	characteristic
94	#2075	C₂²	1	1	yes	characteristic
95	#2073	C₂²	1	1	yes	characteristic
96	#2073	C₂²	1	1	yes	characteristic
97	#2072	C₂²	1	1	yes	characteristic, complemented
98	#2071	C₂²	1	1	yes	characteristic
99	#2067	C₂²	1	1	yes	characteristic
100	#2066	C₂²	1	1	yes	characteristic, complemented
101	#2065	C₂²	1	1	yes	characteristic
102	#2059	C₂²	1	1	yes	characteristic, complemented
103	#2058	C₂²	1	1	yes	characteristic, complemented
104	#2042	C₂²	1	1	yes	characteristic
105	#2042	C₂²	1	1	yes	characteristic
106	#2042	C₂²	1	1	yes	characteristic
107	#2042	C₂²	1	1	yes	characteristic
108	#2036	C₂²	1	1	yes	characteristic
109	#2035	C₂²	1	1	yes	characteristic
110	#2035	C₂²	1	1	yes	characteristic, complemented
111	#2035	C₂²	1	1	yes	characteristic, complemented
112	#2034	C₂²	1	1	yes	characteristic
113	#2034	C₂²	1	1	yes	characteristic
114	#2033	C₂²	1	1	yes	characteristic
115	#2033	C₂²	1	1	yes	characteristic
116	#2025	C₂²	1	1	yes	characteristic
117	#2024	C₂²	1	1	yes	characteristic, complemented
118	#2023	C₂²	1	1	yes	characteristic
119	#2023	C₂²	1	1	yes	characteristic
120	#1991	C₂²	1	1	yes	characteristic, complemented
121	#1985	C₂²	1	1	yes	characteristic, complemented
122	#1984	C₂²	1	1	yes	characteristic, complemented
123	#1983	C₂²	1	1	yes	characteristic
124	#1958	C₂²	1	1	yes	characteristic
125	#1958	C₂²	1	1	yes	characteristic
126	#1949	C₂²	1	1	yes	characteristic, complemented
127	#1947	C₂²	1	1	yes	characteristic, complemented
128	#1944	C₂²	1	1	yes	characteristic, complemented
129	#1943	C₂²	1	1	yes	characteristic, complemented
130	#1941	C₂²	1	1	yes	characteristic, complemented
131	#1941	C₂²	1	1	yes	characteristic, complemented
132	#1941	C₂²	1	1	yes	characteristic, complemented
133	#1936	C₂²	1	1	yes	characteristic
134	#1936	C₂²	1	1	yes	characteristic
135	#1936	C₂²	1	1	yes	characteristic
136	#1935	C₂²	1	1	yes	characteristic, complemented
137	#1934	C₂²	1	1	yes	characteristic
138	#1934	C₂²	1	1	yes	characteristic
139	#1934	C₂²	1	1	yes	characteristic
140	#1928	C₂²	1	1	yes	characteristic, complemented
141	#1927	C₂²	1	1	yes	characteristic, complemented
142	#1927	C₂²	1	1	yes	characteristic, complemented
143	#1926	C₂²	1	1	yes	characteristic
144	#1926	C₂²	1	1	yes	characteristic
145	#1926	C₂²	1	1	yes	characteristic
146	#1926	C₂²	1	1	yes	characteristic
147	#1926	C₂²	1	1	yes	characteristic
148	#1925	C₂²	1	1	yes	characteristic
149	#1925	C₂²	1	1	yes	characteristic
150	#1925	C₂²	1	1	yes	characteristic
151	#1924	C₂²	1	1	yes	characteristic
152	#1924	C₂²	1	1	yes	characteristic, complemented
153	#1923	C₂²	1	1	yes	characteristic
154	#1923	C₂²	1	1	yes	characteristic, complemented
155	#1921	C₂²	1	1	yes	characteristic, complemented
156	#1919	C₂²	1	1	yes	characteristic, complemented
157	#1919	C₂²	1	1	yes	characteristic, complemented
158	#1919	C₂²	1	1	yes	characteristic, complemented
159	#1919	C₂²	1	1	yes	characteristic, complemented
160	#1918	C₂²	1	1	yes	characteristic, complemented
161	#1918	C₂²	1	1	yes	characteristic, complemented
162	#1895	C₂²	1	1	yes	characteristic
163	#1895	C₂²	1	1	yes	characteristic
164	#1894	C₂²	1	1	yes	characteristic, complemented
165	#1892	C₂²	1	1	yes	characteristic
166	#1874	C₂²	1	1	yes	characteristic
167	#1872	C₂²	1	1	yes	characteristic
168	#1872	C₂²	1	1	yes	characteristic, complemented
169	#1870	C₂²	1	1	yes	characteristic
170	#1869	C₂²	1	1	yes	characteristic
171	#1865	C₂²	1	1	yes	characteristic, complemented
172	#1864	C₂²	1	1	yes	characteristic
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, complemented
178	#1854	C₂²	1	1	yes	characteristic, complemented
179	#1853	C₂²	1	1	yes	characteristic
180	#1846	C₂²	1	1	yes	characteristic, complemented
181	#1836	C₂²	1	1	yes	characteristic, complemented
182	#1825	C₂²	1	1	yes	characteristic, complemented
183	#1823	C₂²	1	1	yes	characteristic
184	#1807	C₂²	1	1	yes	characteristic
185	#1807	C₂²	1	1	yes	characteristic
186	#1804	C₂²	1	1	yes	characteristic
187	#1786	C₂²	1	1	yes	characteristic
188	#1786	C₂²	1	1	yes	characteristic
189	#1786	C₂²	1	1	yes	characteristic
190	C₄×#106	C₂²	1	1	yes	characteristic, complemented
191	#1763	C₂²	1	1	yes	characteristic, complemented
192	#1763	C₂²	1	1	yes	characteristic, complemented
193	#1762	C₂²	1	1	yes	characteristic
194	#1762	C₂²	1	1	yes	characteristic
195	#1762	C₂²	1	1	yes	characteristic
196	#1753	C₂²	1	1	yes	characteristic, complemented
197	#1753	C₂²	1	1	yes	characteristic, complemented
198	#1752	C₂²	1	1	yes	characteristic
199	C₈×C₂²⋊C₄	C₂²	1	1	yes	characteristic
200	#1745	C₂²	1	1	yes	characteristic, complemented
201	#1744	C₂²	1	1	yes	characteristic, complemented
202	#1736	C₂²	1	1	yes	characteristic, complemented
203	C₂³×D₄	C₂³	1	1	yes	characteristic
204	C₂²×M₁₆	C₂³	1	1	yes	characteristic
205	C₂³×C₈	C₂³	1	1	yes	characteristic
206	C₂×C₄⋊Q₈	C₂³	1	1	yes	characteristic
207	C₂×#126	—	2	1	no	—
208	C₂×#125	C₂³	1	1	yes	characteristic
209	C₂×#124	D₄	1	1	yes	characteristic
210	C₂×#124	C₂³	1	1	yes	characteristic
211	C₂×#124	C₂³	1	1	yes	characteristic
212	C₂×C₂²⋊Q₈	—	2	1	no	—
213	C₂×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
214	C₂×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
215	C₂×#121	C₂³	1	1	yes	characteristic
216	C₂×#121	C₂³	1	1	yes	characteristic
217	C₂×#120	—	2	1	no	—
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	—	2	1	no	—
222	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
223	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
224	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
225	C₂×#117	—	2	1	no	—
226	C₂×#117	—	2	1	no	—
227	C₂×#117	C₂³	1	1	yes	characteristic
228	C₂²×C₄⋊C₄	C₂³	1	1	yes	characteristic
229	C₂²×C₄⋊C₄	C₂³	1	1	yes	characteristic
230	C₂²×C₂²⋊C₄	—	2	1	no	—
231	#488	—	2	4	no	—
232	#481	—	2	4	no	—
233	C₂×#107	C₂³	1	1	yes	characteristic
234	C₂×#107	C₂³	1	1	yes	characteristic
235	C₂×#107	C₂³	1	1	yes	characteristic
236	C₂×#107	C₂³	1	1	yes	characteristic
237	C₂×#106	C₂³	1	1	yes	characteristic
238	C₂×#106	C₂³	1	1	yes	characteristic
239	C₂×#106	C₂³	1	1	yes	characteristic
240	C₂×#106	C₂³	1	1	yes	characteristic
241	C₂×#106	C₂³	1	1	yes	characteristic
242	C₂×#106	C₂³	1	1	yes	characteristic
243	C₂×#106	C₂³	1	1	yes	characteristic
244	C₂×#106	C₂³	1	1	yes	characteristic
245	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
246	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
247	C₂×#103	C₂³	1	1	yes	characteristic
248	C₂×#103	C₂³	1	1	yes	characteristic
249	C₂×#103	C₂³	1	1	yes	characteristic
250	C₂×#103	C₂³	1	1	yes	characteristic
251	C₂×#103	C₂³	1	1	yes	characteristic
252	C₂×#103	C₂³	1	1	yes	characteristic
253	C₂×#103	C₂³	1	1	yes	characteristic
254	C₂×#103	C₂³	1	1	yes	characteristic
255	C₂×#102	—	2	4	no	—
256	C₂×#102	C₂³	1	1	yes	characteristic
257	C₂×#102	C₂³	1	1	yes	characteristic
258	C₂×#102	C₂³	1	1	yes	characteristic
259	C₂×#102	C₂³	1	1	yes	characteristic
260	C₂×#102	C₂³	1	1	yes	characteristic
261	C₂×#102	C₂³	1	1	yes	characteristic
262	C₂×#102	C₂³	1	1	yes	characteristic
263	C₂×#102	C₂³	1	1	yes	characteristic
264	C₂×#102	C₂³	1	1	yes	characteristic
265	C₂×#102	C₂³	1	1	yes	characteristic
266	C₂×#102	C₂³	1	1	yes	characteristic
267	C₂×#102	C₂³	1	1	yes	characteristic
268	C₂×#102	C₂³	1	1	yes	characteristic
269	C₂×#102	C₂³	1	1	yes	characteristic
270	C₂×#102	C₂³	1	1	yes	characteristic
271	C₂×#102	C₂³	1	1	yes	characteristic
272	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
273	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
274	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
275	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
276	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
277	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
278	C₂×#97	C₂³	1	1	yes	characteristic
279	C₂×#97	C₂³	1	1	yes	characteristic
280	C₂×#97	C₂³	1	1	yes	characteristic
281	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
282	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
283	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
284	#401	—	2	1	no	—
285	#401	—	2	1	no	—
286	#400	—	2	1	no	—
287	#400	—	2	1	no	—
288	#400	—	2	1	no	—
289	#400	—	2	1	no	—
290	#400	—	2	1	no	—
291	#399	—	2	1	no	—
292	#398	—	2	1	no	—
293	#398	—	2	1	no	—
294	#398	—	2	1	no	—
295	#397	—	2	1	no	—
296	#397	—	2	1	no	—
297	#397	—	2	1	no	—
298	#397	—	2	1	no	—
299	#397	—	2	1	no	—
300	#397	—	2	1	no	—
301	#397	—	2	1	no	—
302	#397	—	2	1	no	—
303	#396	—	2	1	no	—
304	#396	—	2	1	no	—
305	#396	—	2	1	no	—
306	#395	—	2	1	no	—
307	#395	—	2	1	no	—
308	#394	—	2	1	no	—
309	#394	—	2	1	no	—
310	#394	—	2	1	no	—
311	#394	—	2	1	no	—
312	#394	—	2	1	no	—
313	#394	—	2	1	no	—
314	#394	—	2	1	no	—
315	#394	—	2	1	no	—
316	#393	—	2	1	no	—
317	#393	—	2	1	no	—
318	#393	—	2	1	no	—
319	#392	—	2	1	no	—
320	#391	—	2	1	no	—
321	#391	—	2	1	no	—
322	#391	—	2	1	no	—
323	#391	D₄	1	1	yes	characteristic
324	#391	C₂³	1	1	yes	characteristic
325	#391	C₂³	1	1	yes	characteristic
326	#390	—	2	1	no	—
327	#390	—	2	1	no	—
328	#390	—	2	1	no	—
329	#390	D₄	1	1	yes	characteristic
330	#390	C₂³	1	1	yes	characteristic
331	#390	C₂³	1	1	yes	characteristic
332	#390	C₂³	1	1	yes	characteristic
333	#390	C₂³	1	1	yes	characteristic
334	#390	C₂³	1	1	yes	characteristic
335	#390	C₂³	1	1	yes	characteristic
336	#389	—	2	1	no	—
337	#389	—	2	1	no	—
338	#389	—	2	1	no	—
339	#389	C₂³	1	1	yes	characteristic
340	#389	C₂³	1	1	yes	characteristic
341	#389	C₂³	1	1	yes	characteristic
342	#389	C₂³	1	1	yes	characteristic
343	#389	C₂³	1	1	yes	characteristic
344	#389	C₂³	1	1	yes	characteristic
345	#389	C₂³	1	1	yes	characteristic
346	#389	C₂³	1	1	yes	characteristic
347	#389	C₂³	1	1	yes	characteristic
348	#389	C₂³	1	1	yes	characteristic
349	#389	C₂³	1	1	yes	characteristic
350	#389	C₂³	1	1	yes	characteristic
351	#388	—	2	1	no	—
352	#388	—	2	1	no	—
353	#388	—	2	1	no	—
354	#388	—	2	1	no	—
355	#388	—	2	1	no	—
356	#388	—	2	1	no	—
357	#388	—	2	1	no	—
358	#388	—	2	1	no	—
359	#388	—	2	1	no	—
360	#388	—	2	1	no	—
361	#388	—	2	1	no	—
362	#388	—	2	1	no	—
363	#388	—	2	1	no	—
364	#388	—	2	1	no	—
365	#388	—	2	1	no	—
366	#388	—	2	1	no	—
367	#388	—	2	1	no	—
368	#388	—	2	1	no	—
369	#388	D₄	1	1	yes	characteristic
370	#388	D₄	1	1	yes	characteristic
371	#388	D₄	1	1	yes	characteristic
372	#388	D₄	1	1	yes	characteristic
373	#387	—	2	1	no	—
374	#387	—	2	1	no	—
375	#387	—	2	1	no	—
376	#387	—	2	1	no	—
377	#387	—	2	1	no	—
378	#387	—	2	1	no	—
379	#387	—	2	1	no	—
380	#387	—	2	1	no	—
381	#387	—	2	1	no	—
382	#387	—	2	1	no	—
383	#387	—	2	1	no	—
384	#386	—	2	1	no	—
385	#386	—	2	1	no	—
386	#386	—	2	1	no	—
387	#386	—	2	1	no	—
388	#385	—	2	1	no	—
389	#385	—	2	1	no	—
390	#385	—	2	1	no	—
391	#385	—	2	1	no	—
392	#384	—	2	1	no	—
393	#384	C₂³	1	1	yes	characteristic
394	#384	C₂³	1	1	yes	characteristic
395	#383	—	2	1	no	—
396	#383	—	2	1	no	—
397	#383	—	2	1	no	—
398	#382	—	2	1	no	—
399	#382	D₄	1	1	yes	characteristic
400	#382	C₂³	1	1	yes	characteristic
401	#382	C₂³	1	1	yes	characteristic
402	#382	C₂³	1	1	yes	characteristic
403	#382	C₂³	1	1	yes	characteristic
404	#381	—	2	1	no	—
405	#381	—	2	1	no	—
406	#380	—	2	1	no	—
407	#380	—	2	1	no	—
408	#380	—	2	1	no	—
409	#380	—	2	1	no	—
410	#380	C₂³	1	1	yes	characteristic
411	#380	C₂³	1	1	yes	characteristic
412	#380	C₂³	1	1	yes	characteristic
413	#380	C₂³	1	1	yes	characteristic
414	#380	C₂³	1	1	yes	characteristic
415	#380	C₂³	1	1	yes	characteristic
416	#380	C₂³	1	1	yes	characteristic
417	#380	C₂³	1	1	yes	characteristic
418	#379	—	2	1	no	—
419	#379	—	2	1	no	—
420	#379	—	2	1	no	—
421	#379	—	2	1	no	—
422	C₄×C₄⋊C₄	—	2	1	no	—
423	C₄×C₄⋊C₄	—	2	1	no	—
424	C₄×C₄⋊C₄	—	2	1	no	—
425	C₄×C₄⋊C₄	—	2	1	no	—
426	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
427	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
428	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
429	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
430	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
431	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
432	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
433	C₄×C₂²⋊C₄	—	2	1	no	—
434	C₄×C₂²⋊C₄	—	2	1	no	—
435	C₄×C₂²⋊C₄	—	2	1	no	—
436	C₄×C₂²⋊C₄	C₂³	1	1	yes	characteristic
437	C₄×C₂²⋊C₄	C₂³	1	1	yes	characteristic
438	C₄×C₂²⋊C₄	C₂³	1	1	yes	characteristic
439	C₄×C₂²⋊C₄	C₂³	1	1	yes	characteristic
440	C₄³	C₂³	1	1	yes	characteristic
441	#340	C₂³	1	1	yes	characteristic
442	#340	C₂³	1	1	yes	characteristic
443	#340	C₂³	1	1	yes	characteristic
444	#340	C₂³	1	1	yes	characteristic
445	#340	C₂³	1	1	yes	characteristic
446	#340	C₂³	1	1	yes	characteristic
447	#340	C₂³	1	1	yes	characteristic
448	#340	C₂³	1	1	yes	characteristic
449	#340	C₂³	1	1	yes	characteristic
450	#340	C₂³	1	1	yes	characteristic
451	#340	C₂³	1	1	yes	characteristic
452	#340	C₂³	1	1	yes	characteristic
453	#340	C₂³	1	1	yes	characteristic
454	#340	C₂³	1	1	yes	characteristic
455	#340	C₂³	1	1	yes	characteristic
456	#340	C₂³	1	1	yes	characteristic
457	#340	C₂³	1	1	yes	characteristic
458	#340	C₂³	1	1	yes	characteristic
459	#340	C₂³	1	1	yes	characteristic
460	#340	C₂³	1	1	yes	characteristic
461	#340	C₂³	1	1	yes	characteristic
462	#340	C₂³	1	1	yes	characteristic
463	#340	C₂³	1	1	yes	characteristic
464	#340	C₂³	1	1	yes	characteristic
465	#340	C₂³	1	1	yes	characteristic
466	#340	C₂³	1	1	yes	characteristic
467	#340	C₂³	1	1	yes	characteristic
468	#340	C₂³	1	1	yes	characteristic
469	#336	C₂³	1	1	yes	characteristic
470	#336	C₂³	1	1	yes	characteristic
471	#336	C₂³	1	1	yes	characteristic
472	#336	C₂³	1	1	yes	characteristic
473	#336	C₂³	1	1	yes	characteristic
474	#336	C₂³	1	1	yes	characteristic
475	#336	C₂³	1	1	yes	characteristic
476	#336	C₂³	1	1	yes	characteristic
477	#336	C₂³	1	1	yes	characteristic
478	#336	C₂³	1	1	yes	characteristic
479	#336	C₂³	1	1	yes	characteristic
480	#336	C₂³	1	1	yes	characteristic
481	C₂⁵	—	2	1	no	—
482	C₂²×Q₈	—	2	1	no	—
483	C₂²×Q₈	C₂×D₄	1	1	yes	characteristic
484	C₂²×Q₈	C₂⁴	1	1	yes	characteristic
485	C₂²×D₄	—	2	2	no	—
486	C₂²×D₄	—	2	1	no	—
487	C₂²×D₄	—	2	1	no	—
488	C₂²×D₄	—	2	1	no	—
489	C₂²×D₄	—	4	1	no	—
490	C₂²×D₄	—	4	1	no	—
491	C₂²×D₄	—	4	1	no	—
492	C₂²×D₄	—	4	1	no	—
493	C₂²×D₄	—	4	1	no	—
494	C₂²×D₄	C₂×D₄	1	1	yes	characteristic
495	C₂²×D₄	C₂⁴	1	1	yes	characteristic
496	C₂²×D₄	C₂⁴	1	1	yes	characteristic
497	C₂³×C₄	—	2	1	no	—
498	C₂³×C₄	—	2	1	no	—
499	C₂³×C₄	—	2	1	no	—
500	C₂³×C₄	—	2	1	no	—
501	C₂³×C₄	C₂⁴	1	1	yes	characteristic
502	C₂³×C₄	C₂⁴	1	1	yes	characteristic
503	C₂×M₁₆	—	4	1	no	—
504	C₂×M₁₆	—	4	1	no	—
505	C₂×M₁₆	—	4	1	no	—
506	C₂²×C₈	—	2	2	no	—
507	C₂²×C₈	—	4	1	no	—
508	C₂²×C₈	—	4	1	no	—
509	C₂²×C₈	C₂⁴	1	1	yes	characteristic
510	C₂²×C₈	C₂⁴	1	1	yes	characteristic
511	C₂²×C₈	C₂⁴	1	1	yes	characteristic
512	C₂²×C₈	C₂⁴	1	1	yes	characteristic
513	C₂²×C₈	C₂⁴	1	1	yes	characteristic
514	C₂²×C₈	C₂⁴	1	1	yes	characteristic
515	C₂²×C₈	C₂⁴	1	1	yes	characteristic
516	C₂²×C₈	C₂⁴	1	1	yes	characteristic
517	C₄⋊Q₈	—	4	1	no	—
518	C₄⋊Q₈	—	4	1	no	—
519	#126	—	8	2	no	—
520	#125	—	2	2	no	—
521	#125	—	4	1	no	—
522	#124	—	2	2	no	—
523	#124	—	4	1	no	—
524	#124	—	4	1	no	—
525	#124	—	4	1	no	—
526	#124	—	4	2	no	—
527	C₂²⋊Q₈	—	4	1	no	—
528	C₂²⋊Q₈	—	4	1	no	—
529	C₂²⋊Q₈	—	4	1	no	—
530	C₂²⋊Q₈	—	4	1	no	—
531	C₂²⋊Q₈	—	8	2	no	—
532	#121	—	2	2	no	—
533	#121	—	4	1	no	—
534	#121	—	4	1	no	—
535	#121	—	4	1	no	—
536	#120	—	8	2	no	—
537	C₄×Q₈	—	4	1	no	—
538	C₄×Q₈	—	4	1	no	—
539	C₄×Q₈	—	4	1	no	—
540	C₄×Q₈	—	4	1	no	—
541	C₄×Q₈	—	8	2	no	—
542	C₄×D₄	—	4	1	no	—
543	C₄×D₄	—	4	1	no	—
544	C₄×D₄	—	4	1	no	—
545	C₄×D₄	—	4	1	no	—
546	C₄×D₄	—	4	1	no	—
547	C₄×D₄	—	4	1	no	—
548	C₄×D₄	—	4	4	no	—
549	#117	—	4	1	no	—
550	#117	—	4	1	no	—
551	#117	—	8	2	no	—
552	#117	—	8	2	no	—
553	C₂×C₄⋊C₄	—	2	2	no	—
554	C₂×C₄⋊C₄	—	2	2	no	—
555	C₂×C₄⋊C₄	—	2	1	no	—
556	C₂×C₄⋊C₄	—	2	1	no	—
557	C₂×C₄⋊C₄	—	2	1	no	—
558	C₂×C₄⋊C₄	—	2	1	no	—
559	C₂×C₄⋊C₄	—	2	1	no	—
560	C₂×C₄⋊C₄	—	2	1	no	—
561	C₂×C₄⋊C₄	—	2	1	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	—	4	1	no	—
580	C₂×C₄⋊C₄	—	4	1	no	—
581	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
582	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
583	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
584	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
585	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
586	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
587	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
588	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
589	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
590	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
591	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
592	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
593	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
594	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
595	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
596	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
597	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
598	C₂×C₂²⋊C₄	—	2	1	no	—
599	C₂×C₂²⋊C₄	—	2	1	no	—
600	C₂×C₂²⋊C₄	—	2	1	no	—
601	C₂×C₂²⋊C₄	—	2	1	no	—
602	C₂×C₂²⋊C₄	—	2	1	no	—
603	C₂×C₂²⋊C₄	—	2	1	no	—
604	C₂×C₂²⋊C₄	—	2	1	no	—
605	C₂×C₂²⋊C₄	—	2	1	no	—
606	C₂×C₂²⋊C₄	—	2	1	no	—
607	C₂×C₂²⋊C₄	—	2	1	no	—
608	C₂×C₂²⋊C₄	—	2	1	no	—
609	C₂×C₂²⋊C₄	—	2	1	no	—
610	C₂×C₂²⋊C₄	—	2	1	no	—
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	—	4	4	no	—
630	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
631	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
632	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
633	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
634	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
635	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
636	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
637	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
638	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
639	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
640	C₂×C₄²	—	2	1	no	—
641	C₂×C₄²	—	2	1	no	—
642	C₂×C₄²	—	2	1	no	—
643	C₂×C₄²	—	2	1	no	—
644	C₂×C₄²	—	2	1	no	—
645	C₂×C₄²	—	2	1	no	—
646	C₂×C₄²	—	2	1	no	—
647	C₂×C₄²	—	2	1	no	—
648	C₂×C₄²	—	2	1	no	—
649	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
650	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
651	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
652	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
653	C₂×C₄²	C₂⁴	1	1	yes	characteristic
654	C₂×C₄²	C₂⁴	1	1	yes	characteristic
655	C₂×C₄²	C₂⁴	1	1	yes	characteristic
656	C₂×C₄²	C₂⁴	1	1	yes	characteristic
657	C₂×C₄²	C₂⁴	1	1	yes	characteristic
658	#107	—	4	1	no	—
659	#107	—	4	1	no	—
660	#107	—	4	1	no	—
661	#107	—	4	1	no	—
662	#106	—	2	2	no	—
663	#106	—	2	2	no	—
664	#106	—	4	1	no	—
665	#106	—	4	1	no	—
666	#106	—	4	1	no	—
667	#106	—	4	1	no	—
668	#106	—	4	1	no	—
669	#106	—	4	1	no	—
670	C₄⋊C₈	—	4	1	no	—
671	C₄⋊C₈	—	4	1	no	—
672	#103	—	2	2	no	—
673	#103	—	2	2	no	—
674	#103	—	4	1	no	—
675	#103	—	4	1	no	—
676	#103	—	4	1	no	—
677	#103	—	4	1	no	—
678	#103	—	4	1	no	—
679	#103	—	4	1	no	—
680	#102	—	2	2	no	—
681	#102	—	2	2	no	—
682	#102	—	2	2	no	—
683	#102	—	2	2	no	—
684	#102	—	2	2	no	—
685	#102	—	4	1	no	—
686	#102	—	4	1	no	—
687	#102	—	4	1	no	—
688	#102	—	4	1	no	—
689	#102	—	4	1	no	—
690	#102	—	4	1	no	—
691	#102	—	4	1	no	—
692	#102	—	4	1	no	—
693	#102	—	4	1	no	—
694	#102	—	4	1	no	—
695	#102	#41	1	4	yes	—
696	C₂²⋊C₈	—	2	2	no	—
697	C₂²⋊C₈	—	4	1	no	—
698	C₂²⋊C₈	—	4	1	no	—
699	C₂²⋊C₈	—	4	1	no	—
700	C₂²⋊C₈	—	4	1	no	—
701	C₂²⋊C₈	—	4	1	no	—
702	#97	—	4	1	no	—
703	#97	—	4	1	no	—
704	#97	—	4	1	no	—
705	C₄×C₈	—	2	2	no	—
706	C₄×C₈	—	4	1	no	—
707	C₄×C₈	—	4	1	no	—
708	#95	—	2	1	no	—
709	#95	—	2	1	no	—
710	#95	—	2	1	no	—
711	#95	—	2	1	no	—
712	#95	—	2	1	no	—
713	#95	—	2	1	no	—
714	#95	—	2	1	no	—
715	#95	—	2	1	no	—
716	#95	—	2	1	no	—
717	#95	—	2	1	no	—
718	#95	—	2	1	no	—
719	#95	—	2	1	no	—
720	#95	—	2	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	C₂×D₄	1	1	yes	characteristic
748	#95	C₂×D₄	1	1	yes	characteristic
749	#95	C₂×D₄	1	1	yes	characteristic
750	#95	C₂×D₄	1	1	yes	characteristic
751	#95	C₂×D₄	1	1	yes	characteristic
752	#95	C₂×D₄	1	1	yes	characteristic
753	#95	C₂×D₄	1	1	yes	characteristic
754	#95	C₂×D₄	1	1	yes	characteristic
755	C₂⁴	—	2	1	no	—
756	C₂⁴	—	2	1	no	—
757	C₂⁴	—	4	2	no	—
758	C₂⁴	—	4	2	no	—
759	C₂⁴	—	8	1	no	—
760	C₂⁴	—	8	1	no	—
761	C₂⁴	—	8	1	no	—
762	C₂⁴	—	8	1	no	—
763	C₂⁴	—	8	1	no	—
764	C₂⁴	C₂²×D₄	1	1	yes	characteristic
765	C₂⁴	C₂²×D₄	1	1	yes	characteristic
766	C₂×Q₈	—	2	2	no	—
767	C₂×Q₈	—	2	1	no	—
768	C₂×Q₈	—	2	1	no	—
769	C₂×Q₈	—	2	1	no	—
770	C₂×Q₈	—	2	1	no	—
771	C₂×Q₈	—	2	1	no	—
772	C₂×Q₈	—	2	1	no	—
773	C₂×Q₈	—	4	1	no	—
774	C₂×Q₈	—	4	1	no	—
775	C₂×Q₈	—	4	2	no	—
776	C₂×Q₈	—	8	1	no	—
777	C₂×Q₈	—	8	1	no	—
778	C₂×D₄	—	2	2	no	—
779	C₂×D₄	—	2	2	no	—
780	C₂×D₄	—	2	1	no	—
781	C₂×D₄	—	2	1	no	—
782	C₂×D₄	—	2	1	no	—
783	C₂×D₄	—	2	1	no	—
784	C₂×D₄	—	2	1	no	—
785	C₂×D₄	—	2	1	no	—
786	C₂×D₄	—	2	1	no	—
787	C₂×D₄	—	2	1	no	—
788	C₂×D₄	—	2	1	no	—
789	C₂×D₄	—	2	1	no	—
790	C₂×D₄	—	2	1	no	—
791	C₂×D₄	—	4	1	no	—
792	C₂×D₄	—	4	2	no	—
793	C₂×D₄	—	4	4	no	—
794	C₂×D₄	—	4	2	no	—
795	C₂×D₄	—	8	1	no	—
796	C₂×D₄	—	8	1	no	—
797	C₂×D₄	—	8	2	no	—
798	C₂×D₄	—	8	2	no	—
799	C₂×D₄	—	8	2	no	—
800	C₂×D₄	—	8	1	no	—
801	C₂×D₄	—	8	1	no	—
802	C₂×D₄	—	8	1	no	—
803	C₂×D₄	—	8	1	no	—
804	C₂×D₄	—	8	1	no	—
805	C₂×D₄	C₂×#41	1	2	yes	—
806	C₂²×C₄	—	2	1	no	—
807	C₂²×C₄	—	2	1	no	—
808	C₂²×C₄	—	2	1	no	—
809	C₂²×C₄	—	2	1	no	—
810	C₂²×C₄	—	2	1	no	—
811	C₂²×C₄	—	2	1	no	—
812	C₂²×C₄	—	2	1	no	—
813	C₂²×C₄	—	2	1	no	—
814	C₂²×C₄	—	2	1	no	—
815	C₂²×C₄	—	2	1	no	—
816	C₂²×C₄	—	2	1	no	—
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	—	4	2	no	—
833	C₂²×C₄	—	4	2	no	—
834	C₂²×C₄	—	4	2	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	C₂⁵	1	1	yes	characteristic
857	M₁₆	—	8	2	no	—
858	C₂×C₈	—	2	1	no	—
859	C₂×C₈	—	2	1	no	—
860	C₂×C₈	—	2	1	no	—
861	C₂×C₈	—	2	1	no	—
862	C₂×C₈	—	2	1	no	—
863	C₂×C₈	—	2	1	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	—	8	2	no	—
882	C₂×C₈	C₂×#41	1	2	yes	—
883	C₄⋊C₄	—	2	1	no	—
884	C₄⋊C₄	—	2	1	no	—
885	C₄⋊C₄	—	2	1	no	—
886	C₄⋊C₄	—	2	1	no	—
887	C₄⋊C₄	—	2	1	no	—
888	C₄⋊C₄	—	2	1	no	—
889	C₄⋊C₄	—	2	1	no	—
890	C₄⋊C₄	—	2	1	no	—
891	C₄⋊C₄	—	2	1	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	—	4	1	no	—
909	C₄⋊C₄	—	4	1	no	—
910	C₄⋊C₄	—	4	1	no	—
911	C₄⋊C₄	—	4	1	no	—
912	C₄⋊C₄	—	4	2	no	—
913	C₄⋊C₄	—	4	2	no	—
914	C₄⋊C₄	—	4	2	no	—
915	C₄⋊C₄	—	4	2	no	—
916	C₄⋊C₄	—	4	2	no	—
917	C₄⋊C₄	—	4	2	no	—
918	C₄⋊C₄	—	4	2	no	—
919	C₄⋊C₄	—	4	2	no	—
920	C₄⋊C₄	—	8	1	no	—
921	C₄⋊C₄	—	8	1	no	—
922	C₄⋊C₄	—	8	1	no	—
923	C₄⋊C₄	—	8	1	no	—
924	C₄⋊C₄	—	8	1	no	—
925	C₄⋊C₄	—	8	1	no	—
926	C₄⋊C₄	—	8	1	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	C₂×#41	1	2	yes	—
937	C₂²⋊C₄	—	2	2	no	—
938	C₂²⋊C₄	—	2	2	no	—
939	C₂²⋊C₄	—	4	1	no	—
940	C₂²⋊C₄	—	4	1	no	—
941	C₂²⋊C₄	—	4	1	no	—
942	C₂²⋊C₄	—	4	1	no	—
943	C₂²⋊C₄	—	4	1	no	—
944	C₂²⋊C₄	—	4	1	no	—
945	C₂²⋊C₄	—	4	1	no	—
946	C₂²⋊C₄	—	4	1	no	—
947	C₂²⋊C₄	—	4	2	no	—
948	C₂²⋊C₄	—	4	2	no	—
949	C₂²⋊C₄	—	4	2	no	—
950	C₂²⋊C₄	—	4	2	no	—
951	C₂²⋊C₄	—	4	2	no	—
952	C₂²⋊C₄	—	4	2	no	—
953	C₂²⋊C₄	—	4	2	no	—
954	C₂²⋊C₄	—	4	2	no	—
955	C₂²⋊C₄	—	4	2	no	—
956	C₂²⋊C₄	—	4	2	no	—
957	C₂²⋊C₄	—	8	1	no	—
958	C₂²⋊C₄	—	8	1	no	—
959	C₂²⋊C₄	—	8	1	no	—
960	C₂²⋊C₄	—	8	1	no	—
961	C₂²⋊C₄	—	8	1	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	C₄²	—	2	2	no	—
979	C₄²	—	2	1	no	—
980	C₄²	—	2	1	no	—
981	C₄²	—	2	1	no	—
982	C₄²	—	2	1	no	—
983	C₄²	—	2	1	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	—	4	1	no	—
990	C₄²	—	4	1	no	—
991	C₄²	—	4	1	no	—
992	C₄²	—	4	2	no	—
993	C₄²	—	4	2	no	—
994	C₄²	—	4	2	no	—
995	C₄²	—	4	2	no	—
996	C₄²	—	8	1	no	—
997	C₄²	—	8	1	no	—
998	C₄²	—	8	1	no	—
999	C₄²	—	8	1	no	—
1000	C₄²	—	8	1	no	—
1001	C₂³	—	2	1	no	—
1002	C₂³	—	2	1	no	—
1003	C₂³	—	2	1	no	—
1004	C₂³	—	2	1	no	—
1005	C₂³	—	2	1	no	—
1006	C₂³	—	2	1	no	—
1007	C₂³	—	2	1	no	—
1008	C₂³	—	2	1	no	—
1009	C₂³	—	2	2	no	—
1010	C₂³	—	2	1	no	—
1011	C₂³	—	2	1	no	—
1012	C₂³	—	2	1	no	—
1013	C₂³	—	2	1	no	—
1014	C₂³	—	2	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	—	4	1	no	—
1028	C₂³	—	8	4	no	—
1029	C₂³	—	8	4	no	—
1030	C₂³	—	16	2	no	—
1031	C₂³	—	16	2	no	—
1032	C₂³	—	16	2	no	—
1033	C₂³	—	16	2	no	—
1034	C₂³	—	16	2	no	—
1035	C₂³	#575	1	2	yes	—
1036	C₂³	C₂³×D₄	1	1	yes	characteristic
1037	Q₈	—	4	1	no	—
1038	Q₈	—	4	1	no	—
1039	Q₈	—	4	1	no	—
1040	Q₈	—	4	1	no	—
1041	Q₈	—	8	2	no	—
1042	Q₈	—	8	4	no	—
1043	D₄	—	2	2	no	—
1044	D₄	—	2	2	no	—
1045	D₄	—	4	4	no	—
1046	D₄	—	4	1	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	—	8	4	no	—
1053	D₄	—	16	2	no	—
1054	D₄	—	16	2	no	—
1055	C₂×C₄	—	2	1	no	—
1056	C₂×C₄	—	2	1	no	—
1057	C₂×C₄	—	2	1	no	—
1058	C₂×C₄	—	2	1	no	—
1059	C₂×C₄	—	2	1	no	—
1060	C₂×C₄	—	2	1	no	—
1061	C₂×C₄	—	2	1	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	2	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	1	no	—
1088	C₂×C₄	—	2	1	no	—
1089	C₂×C₄	—	2	1	no	—
1090	C₂×C₄	—	2	1	no	—
1091	C₂×C₄	—	4	1	no	—
1092	C₂×C₄	—	4	1	no	—
1093	C₂×C₄	—	4	1	no	—
1094	C₂×C₄	—	4	1	no	—
1095	C₂×C₄	—	4	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	—	4	1	no	—
1138	C₂×C₄	—	4	1	no	—
1139	C₂×C₄	—	4	1	no	—
1140	C₂×C₄	—	8	4	no	—
1141	C₂×C₄	—	8	4	no	—
1142	C₂×C₄	—	16	2	no	—
1143	C₂×C₄	—	16	2	no	—
1144	C₂×C₄	#577	1	2	yes	—
1145	C₂×C₄	C₂²×#41	1	1	yes	characteristic
1146	C₂×C₄	#585	1	1	yes	characteristic
1147	C₂×C₄	#585	1	1	yes	characteristic
1148	C₂×C₄	#585	1	1	yes	characteristic
1149	C₂×C₄	#585	1	1	yes	characteristic
1150	C₂×C₄	#585	1	1	yes	characteristic
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	C₈	—	4	1	no	—
1157	C₈	—	4	1	no	—
1158	C₈	—	4	1	no	—
1159	C₂²	—	2	2	no	—
1160	C₂²	—	2	2	no	—
1161	C₂²	—	2	2	no	—
1162	C₂²	—	4	1	no	—
1163	C₂²	—	4	1	no	—
1164	C₂²	—	4	1	no	—
1165	C₂²	—	4	1	no	—
1166	C₂²	—	4	1	no	—
1167	C₂²	—	4	2	no	—
1168	C₂²	—	4	1	no	—
1169	C₂²	—	4	1	no	—
1170	C₂²	—	4	2	no	—
1171	C₂²	—	4	1	no	—
1172	C₂²	—	4	1	no	—
1173	C₂²	—	4	1	no	—
1174	C₂²	—	4	2	no	—
1175	C₂²	—	4	1	no	—
1176	C₂²	—	8	1	no	—
1177	C₂²	—	8	1	no	—
1178	C₂²	—	8	1	no	—
1179	C₂²	—	8	1	no	—
1180	C₂²	—	8	1	no	—
1181	C₂²	—	8	1	no	—
1182	C₂²	—	8	1	no	—
1183	C₂²	—	8	1	no	—
1184	C₂²	—	8	1	no	—
1185	C₂²	—	8	1	no	—
1186	C₂²	—	8	1	no	—
1187	C₂²	—	16	8	no	—
1188	C₂²	D₄×#41	1	1	yes	characteristic
1189	C₂²	#3485	1	1	yes	characteristic
1190	C₂²	#3500	1	1	yes	characteristic
1191	C₂²	C₂×#575	1	1	yes	characteristic
1192	C₂²	C₂×#577	1	1	yes	characteristic
1193	C₂²	#3584	1	1	yes	characteristic
1194	C₂²	#3585	1	1	yes	characteristic
1195	C₄	—	2	2	no	—
1196	C₄	—	4	1	no	—
1197	C₄	—	4	2	no	—
1198	C₄	—	4	1	no	—
1199	C₄	—	4	1	no	—
1200	C₄	—	4	1	no	—
1201	C₄	—	4	1	no	—
1202	C₄	—	4	1	no	—
1203	C₄	—	4	1	no	—
1204	C₄	—	4	1	no	—
1205	C₄	—	4	1	no	—
1206	C₄	—	4	1	no	—
1207	C₄	—	4	1	no	—
1208	C₄	—	8	1	no	—
1209	C₄	—	8	1	no	—
1210	C₄	—	8	1	no	—
1211	C₄	—	8	1	no	—
1212	C₄	—	8	1	no	—
1213	C₄	—	8	1	no	—
1214	C₄	—	8	1	no	—
1215	C₄	—	8	1	no	—
1216	C₄	—	8	1	no	—
1217	C₄	—	8	1	no	—
1218	C₄	—	8	1	no	—
1219	C₄	—	8	1	no	—
1220	C₄	—	8	1	no	—
1221	C₄	#3493	1	1	yes	characteristic
1222	C₄	#3521	1	1	yes	characteristic
1223	C₄	#3566	1	1	yes	characteristic
1224	C₄	#3568	1	1	yes	characteristic
1225	C₂	—	4	2	no	—
1226	C₂	—	8	1	no	—
1227	C₂	—	8	2	no	—
1228	C₂	—	16	1	no	—
1229	C₂	#44677	1	1	yes	characteristic
1230	C₂	#61454	1	1	yes	characteristic
1231	C₂	#61474	1	1	yes	characteristic
1232	C₂	#61729	1	1	yes	characteristic
1233	C₂	#61804	1	1	yes	characteristic
1234	C₂	#62547	1	1	yes	characteristic
1235	C₂	#62617	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³	C₂³×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁵
prime radical	#2408	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³ ◁ C₄×#124 ◁ G
LECS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #59436	C₂	semidirect
3. #32638	C₂	semidirect
4. #32568	C₂	semidirect
5. #32293	C₂	semidirect
6. #31430	C₂	semidirect
7. #31329	C₂	semidirect
8. #31298	C₂	semidirect
10. #30639	C₂	semidirect
11. #29523	C₂	semidirect
12. #29513	C₂	semidirect
13. #29069	C₂	semidirect
14. #29067	C₂	semidirect
15. #28855	C₂	semidirect
16. #27836	C₂	semidirect
17. #27726	C₂	semidirect
18. #27534	C₂	semidirect
19. #27408	C₂	semidirect
20. #27256	C₂	semidirect
21. #27181	C₂	semidirect
22. #27055	C₂	semidirect
23. #26327	C₂	semidirect
24. #26216	C₂	semidirect
25. #25007	C₂	semidirect
27. #23821	C₂	semidirect
28. #23270	C₂	semidirect
29. #22943	C₂	semidirect
30. #22562	C₂	semidirect
31. #22222	C₂	semidirect
47. #2567	C₂²	semidirect
55. #2495	C₂²	semidirect
57. #2494	C₂²	semidirect
61. #2442	C₂²	semidirect
69. #2355	C₂²	semidirect
73. #2344	C₂²	semidirect
76. C₄×C₄⋊Q₈	C₂²	semidirect
77. C₄×#125	C₂²	semidirect
80. #2101	C₂²	semidirect
81. #2101	C₂²	semidirect
82. #2101	C₂²	semidirect
83. #2101	C₂²	semidirect
84. #2100	C₂²	semidirect
85. #2099	C₂²	semidirect
86. #2097	C₂²	semidirect
89. #2088	C₂²	semidirect
90. #2084	C₂²	semidirect
97. #2072	C₂²	semidirect
100. #2066	C₂²	semidirect
102. #2059	C₂²	semidirect
103. #2058	C₂²	semidirect
110. #2035	C₂²	semidirect
111. #2035	C₂²	semidirect
117. #2024	C₂²	semidirect
120. #1991	C₂²	semidirect
121. #1985	C₂²	semidirect
122. #1984	C₂²	semidirect
126. #1949	C₂²	semidirect
127. #1947	C₂²	semidirect
128. #1944	C₂²	semidirect
129. #1943	C₂²	semidirect
130. #1941	C₂²	semidirect
131. #1941	C₂²	semidirect
132. #1941	C₂²	semidirect
136. #1935	C₂²	semidirect
140. #1928	C₂²	semidirect
141. #1927	C₂²	semidirect
142. #1927	C₂²	semidirect
152. #1924	C₂²	semidirect
154. #1923	C₂²	semidirect
155. #1921	C₂²	semidirect
156. #1919	C₂²	semidirect
157. #1919	C₂²	semidirect
158. #1919	C₂²	semidirect
159. #1919	C₂²	semidirect
160. #1918	C₂²	semidirect
161. #1918	C₂²	semidirect
164. #1894	C₂²	semidirect
168. #1872	C₂²	semidirect
171. #1865	C₂²	semidirect
175. #1863	C₂²	semidirect
177. #1854	C₂²	semidirect
178. #1854	C₂²	semidirect
180. #1846	C₂²	semidirect
181. #1836	C₂²	semidirect
182. #1825	C₂²	semidirect
190. C₄×#106	C₂²	semidirect
191. #1763	C₂²	semidirect
192. #1763	C₂²	semidirect
196. #1753	C₂²	semidirect
197. #1753	C₂²	semidirect
200. #1745	C₂²	semidirect
201. #1744	C₂²	semidirect
202. #1736	C₂²	semidirect

Maximal subgroups

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

subgroup	index
#59436	2
#39024	2
#32638	2
#32568	2
#32293	2
#31430	2
#31329	2
#31298	2
#31270	2
#30639	2
#29523	2
#29513	2
#29069	2
#29067	2
#28855	2
#27836	2
#27726	2
#27534	2
#27408	2
#27256	2
#27181	2
#27055	2
#26327	2
#26216	2
#25007	2
#24865	2
#23821	2
#23270	2
#22943	2
#22562	2
#22222	2