Subgroups — #7040799

Order 512.

1357 conjugacy classes of subgroups.

The subgroup lattice has 1215 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#59203	C₂	1	1	yes	maximal, characteristic
2	#59202	C₂	1	1	yes	maximal, characteristic
3	#32470	C₂	1	1	yes	maximal, characteristic, complemented
4	#32468	C₂	1	1	yes	maximal, characteristic, complemented
5	#32277	C₂	1	1	yes	maximal, characteristic, complemented
6	#32271	C₂	1	1	yes	maximal, characteristic, complemented
7	#31717	C₂	1	1	yes	maximal, characteristic, complemented
8	#31708	C₂	1	1	yes	maximal, characteristic, complemented
9	#31453	C₂	1	1	yes	maximal, characteristic, complemented
10	#31448	C₂	1	1	yes	maximal, characteristic, complemented
11	#28777	C₂	1	1	yes	maximal, characteristic, complemented
12	#27664	C₂	1	1	yes	maximal, characteristic, complemented
13	#27605	C₂	1	1	yes	maximal, characteristic, complemented
14	#27604	C₂	1	1	yes	maximal, characteristic, complemented
15	#27483	C₂	1	1	yes	maximal, characteristic, complemented
16	#27480	C₂	1	1	yes	maximal, characteristic, complemented
17	#27472	C₂	1	1	yes	maximal, characteristic, complemented
18	#27472	C₂	1	1	yes	maximal, characteristic, complemented
19	#26313	C₂	1	1	yes	maximal, characteristic, complemented
20	#26312	C₂	1	1	yes	maximal, characteristic, complemented
21	#25995	C₂	1	1	yes	maximal, characteristic, complemented
22	#25993	C₂	1	1	yes	maximal, characteristic, complemented
23	#24961	C₂	1	1	yes	maximal, characteristic, complemented
24	#24952	C₂	1	1	yes	maximal, characteristic, complemented
25	#24942	C₂	1	1	yes	maximal, characteristic, complemented
26	#24938	C₂	1	1	yes	maximal, characteristic, complemented
27	#23638	C₂	1	1	yes	maximal, characteristic, complemented
28	#22710	C₂	1	1	yes	maximal, characteristic, complemented
29	#22619	C₂	1	1	yes	maximal, characteristic, complemented
30	#22034	C₂	1	1	yes	maximal, characteristic
31	#21941	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×#435	C₂²	1	1	yes	characteristic
33	C₂×#427	C₂²	1	1	yes	characteristic
34	C₂²×C₂²⋊C₈	C₂²	1	1	yes	characteristic
35	#2744	—	2	1	no	—
36	#2737	—	2	1	no	—
37	#2735	—	2	1	no	—
38	#2684	—	2	1	no	—
39	#2576	—	2	1	no	—
40	#2576	—	2	1	no	—
41	#2574	—	2	1	no	—
42	#2563	C₂²	1	1	yes	characteristic
43	#2561	—	2	1	no	—
44	#2547	C₂²	1	1	yes	characteristic
45	#2531	—	2	1	no	—
46	#2527	—	2	1	no	—
47	#2527	—	2	1	no	—
48	#2517	—	2	1	no	—
49	#2497	C₂²	1	1	yes	characteristic
50	#2495	C₂²	1	1	yes	characteristic
51	#2494	C₂²	1	1	yes	characteristic
52	#2494	C₂²	1	1	yes	characteristic
53	#2488	—	2	1	no	—
54	#2487	C₂²	1	1	yes	characteristic
55	#2486	C₂²	1	1	yes	characteristic
56	#2485	C₂²	1	1	yes	characteristic
57	#2485	C₂²	1	1	yes	characteristic
58	#2485	C₂²	1	1	yes	characteristic
59	#2485	C₂²	1	1	yes	characteristic
60	#2440	C₂²	1	1	yes	characteristic
61	#2439	C₂²	1	1	yes	characteristic
62	#2439	C₂²	1	1	yes	characteristic
63	#2439	C₂²	1	1	yes	characteristic
64	#2411	—	2	1	no	—
65	#2372	—	2	1	no	—
66	#2354	C₂²	1	1	yes	characteristic
67	#2352	C₂²	1	1	yes	characteristic
68	#2352	C₂²	1	1	yes	characteristic
69	#2352	C₂²	1	1	yes	characteristic
70	#2346	C₂²	1	1	yes	characteristic
71	#2346	C₂²	1	1	yes	characteristic
72	#2346	C₂²	1	1	yes	characteristic
73	#2344	C₂²	1	1	yes	characteristic
74	#2343	—	2	1	no	—
75	C₄×#120	C₂²	1	1	yes	characteristic
76	#2280	C₂²	1	1	yes	characteristic
77	#2280	C₂²	1	1	yes	characteristic
78	#2280	C₂²	1	1	yes	characteristic
79	C₂×#380	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	#2099	C₂²	1	1	yes	characteristic, complemented
84	#2088	C₂²	1	1	yes	characteristic, complemented
85	#2088	C₂²	1	1	yes	characteristic, complemented
86	#2087	C₂²	1	1	yes	characteristic, complemented
87	#2087	C₂²	1	1	yes	characteristic, complemented
88	#2086	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
95	#2077	C₂²	1	1	yes	characteristic
96	#2077	C₂²	1	1	yes	characteristic
97	#2077	C₂²	1	1	yes	characteristic
98	#2077	C₂²	1	1	yes	characteristic
99	#2077	C₂²	1	1	yes	characteristic
100	#2077	C₂²	1	1	yes	characteristic
101	#2077	C₂²	1	1	yes	characteristic
102	#2077	C₂²	1	1	yes	characteristic, complemented
103	#2076	C₂²	1	1	yes	characteristic
104	#2076	C₂²	1	1	yes	characteristic
105	#2076	C₂²	1	1	yes	characteristic
106	#2076	C₂²	1	1	yes	characteristic, complemented
107	#2076	C₂²	1	1	yes	characteristic, complemented
108	#2076	C₂²	1	1	yes	characteristic, complemented
109	#2075	C₂²	1	1	yes	characteristic
110	#2075	C₂²	1	1	yes	characteristic
111	#2075	C₂²	1	1	yes	characteristic
112	#2075	C₂²	1	1	yes	characteristic
113	#2075	C₂²	1	1	yes	characteristic
114	#2075	C₂²	1	1	yes	characteristic, complemented
115	#2075	C₂²	1	1	yes	characteristic, complemented
116	#2058	C₂²	1	1	yes	characteristic, complemented
117	#2057	C₂²	1	1	yes	characteristic, complemented
118	#2057	C₂²	1	1	yes	characteristic, complemented
119	#2057	C₂²	1	1	yes	characteristic, complemented
120	#1993	C₂²	1	1	yes	characteristic, complemented
121	#1993	C₂²	1	1	yes	characteristic, complemented
122	#1988	C₂²	1	1	yes	characteristic, complemented
123	#1987	C₂²	1	1	yes	characteristic, complemented
124	#1955	C₂²	1	1	yes	characteristic
125	#1955	C₂²	1	1	yes	characteristic
126	#1949	C₂²	1	1	yes	characteristic, complemented
127	#1949	C₂²	1	1	yes	characteristic, complemented
128	#1949	C₂²	1	1	yes	characteristic, complemented
129	#1948	C₂²	1	1	yes	characteristic, complemented
130	#1943	C₂²	1	1	yes	characteristic, complemented
131	#1943	C₂²	1	1	yes	characteristic, complemented
132	#1943	C₂²	1	1	yes	characteristic, complemented
133	#1943	C₂²	1	1	yes	characteristic, complemented
134	#1943	C₂²	1	1	yes	characteristic, complemented
135	#1943	C₂²	1	1	yes	characteristic, complemented
136	#1924	C₂²	1	1	yes	characteristic
137	#1924	C₂²	1	1	yes	characteristic
138	#1924	C₂²	1	1	yes	characteristic
139	#1924	C₂²	1	1	yes	characteristic
140	#1921	C₂²	1	1	yes	characteristic, complemented
141	#1921	C₂²	1	1	yes	characteristic, complemented
142	#1920	C₂²	1	1	yes	characteristic, complemented
143	#1920	C₂²	1	1	yes	characteristic, complemented
144	#1919	C₂²	1	1	yes	characteristic, complemented
145	#1919	C₂²	1	1	yes	characteristic, complemented
146	#1919	C₂²	1	1	yes	characteristic, complemented
147	#1919	C₂²	1	1	yes	characteristic, complemented
148	#1919	C₂²	1	1	yes	characteristic, complemented
149	#1919	C₂²	1	1	yes	characteristic, complemented
150	#1919	C₂²	1	1	yes	characteristic, complemented
151	#1918	C₂²	1	1	yes	characteristic, complemented
152	#1870	C₂²	1	1	yes	characteristic
153	#1870	C₂²	1	1	yes	characteristic
154	#1869	C₂²	1	1	yes	characteristic
155	#1854	C₂²	1	1	yes	characteristic
156	#1854	C₂²	1	1	yes	characteristic
157	#1854	C₂²	1	1	yes	characteristic
158	#1854	C₂²	1	1	yes	characteristic
159	#1854	C₂²	1	1	yes	characteristic
160	#1854	C₂²	1	1	yes	characteristic
161	#1854	C₂²	1	1	yes	characteristic
162	#1854	C₂²	1	1	yes	characteristic
163	#1854	C₂²	1	1	yes	characteristic
164	#1854	C₂²	1	1	yes	characteristic
165	#1854	C₂²	1	1	yes	characteristic, complemented
166	#1854	C₂²	1	1	yes	characteristic, complemented
167	#1853	C₂²	1	1	yes	characteristic
168	#1853	C₂²	1	1	yes	characteristic
169	#1853	C₂²	1	1	yes	characteristic
170	#1853	C₂²	1	1	yes	characteristic, complemented
171	#1853	C₂²	1	1	yes	characteristic, complemented
172	#1852	C₂²	1	1	yes	characteristic
173	#1852	C₂²	1	1	yes	characteristic
174	#1852	C₂²	1	1	yes	characteristic
175	#1850	C₂²	1	1	yes	characteristic
176	#1836	C₂²	1	1	yes	characteristic, complemented
177	#1825	C₂²	1	1	yes	characteristic
178	#1825	C₂²	1	1	yes	characteristic
179	#1825	C₂²	1	1	yes	characteristic
180	#1825	C₂²	1	1	yes	characteristic
181	#1825	C₂²	1	1	yes	characteristic
182	#1825	C₂²	1	1	yes	characteristic
183	#1825	C₂²	1	1	yes	characteristic, complemented
184	#1824	C₂²	1	1	yes	characteristic
185	#1824	C₂²	1	1	yes	characteristic
186	#1823	C₂²	1	1	yes	characteristic, complemented
187	#1809	C₂²	1	1	yes	characteristic, complemented
188	#1809	C₂²	1	1	yes	characteristic, complemented
189	#1809	C₂²	1	1	yes	characteristic, complemented
190	#1808	C₂²	1	1	yes	characteristic
191	#1808	C₂²	1	1	yes	characteristic
192	#1807	C₂²	1	1	yes	characteristic
193	#1807	C₂²	1	1	yes	characteristic
194	#1779	C₂²	1	1	yes	characteristic
195	#1776	C₂²	1	1	yes	characteristic, complemented
196	#1776	C₂²	1	1	yes	characteristic, complemented
197	#1776	C₂²	1	1	yes	characteristic, complemented
198	#1752	C₂²	1	1	yes	characteristic
199	#1736	C₂²	1	1	yes	characteristic, complemented
200	#1735	C₂²	1	1	yes	characteristic
201	#1735	C₂²	1	1	yes	characteristic
202	#1735	C₂²	1	1	yes	characteristic
203	C₂⁴×C₄	C₂³	1	1	yes	characteristic
204	C₂²×M₁₆	C₂³	1	1	yes	characteristic
205	C₂³×C₈	C₂³	1	1	yes	characteristic
206	C₂³×C₈	C₂³	1	1	yes	characteristic
207	C₂×C₄⋊Q₈	C₂³	1	1	yes	characteristic
208	C₂×C₄⋊Q₈	C₂³	1	1	yes	characteristic
209	C₂×#124	—	2	1	no	—
210	C₂×#123	—	2	1	no	—
211	C₂×C₂²⋊Q₈	—	2	1	no	—
212	C₂×#120	D₄	1	1	yes	characteristic
213	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
214	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
215	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
216	C₂×#117	—	2	1	no	—
217	C₂×#117	C₂³	1	1	yes	characteristic
218	C₂×#117	C₂³	1	1	yes	characteristic
219	C₂×#117	C₂³	1	1	yes	characteristic
220	C₂×#117	C₂³	1	1	yes	characteristic
221	C₂×#117	C₂³	1	1	yes	characteristic
222	C₂×#117	C₂³	1	1	yes	characteristic
223	C₂×#117	C₂³	1	1	yes	characteristic
224	C₂²×C₄⋊C₄	C₂³	1	1	yes	characteristic
225	C₂²×C₄⋊C₄	C₂³	1	1	yes	characteristic
226	C₂²×C₄⋊C₄	C₂³	1	1	yes	characteristic
227	C₂²×C₂²⋊C₄	—	2	1	no	—
228	#435	—	2	4	no	—
229	#427	—	2	4	no	—
230	C₂×#107	C₂³	1	1	yes	characteristic
231	C₂×#107	C₂³	1	1	yes	characteristic
232	C₂×#107	C₂³	1	1	yes	characteristic
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×#107	C₂³	1	1	yes	characteristic
238	C₂×#107	C₂³	1	1	yes	characteristic
239	C₂×#107	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×#106	C₂³	1	1	yes	characteristic
246	C₂×#106	C₂³	1	1	yes	characteristic
247	C₂×#106	C₂³	1	1	yes	characteristic
248	C₂×#106	C₂³	1	1	yes	characteristic
249	C₂×#106	C₂³	1	1	yes	characteristic
250	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
251	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
252	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
253	C₂×C₂²⋊C₈	—	2	4	no	—
254	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
255	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
256	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
257	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
258	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
259	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
260	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
261	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
262	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
263	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
264	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
265	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
266	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
267	C₂×#97	C₂³	1	1	yes	characteristic
268	C₂×#97	C₂³	1	1	yes	characteristic
269	C₂×#97	C₂³	1	1	yes	characteristic
270	#401	—	2	1	no	—
271	#401	—	2	1	no	—
272	#400	—	2	1	no	—
273	#400	—	2	1	no	—
274	#400	—	2	1	no	—
275	#399	—	2	1	no	—
276	#398	—	2	1	no	—
277	#398	—	2	1	no	—
278	#397	—	2	1	no	—
279	#397	—	2	1	no	—
280	#397	—	2	1	no	—
281	#397	—	2	1	no	—
282	#397	—	2	1	no	—
283	#397	—	2	1	no	—
284	#397	—	2	1	no	—
285	#397	—	2	1	no	—
286	#397	—	2	1	no	—
287	#397	—	2	1	no	—
288	#396	—	2	1	no	—
289	#396	—	2	1	no	—
290	#396	—	2	1	no	—
291	#396	—	2	1	no	—
292	#395	—	2	1	no	—
293	#394	—	2	1	no	—
294	#394	—	2	1	no	—
295	#394	—	2	1	no	—
296	#394	—	2	1	no	—
297	#393	—	2	1	no	—
298	#393	—	2	1	no	—
299	#393	—	2	1	no	—
300	#393	—	2	1	no	—
301	#393	—	2	1	no	—
302	#391	—	2	1	no	—
303	#391	—	2	1	no	—
304	#391	—	2	1	no	—
305	#391	—	2	1	no	—
306	#390	—	2	1	no	—
307	#390	—	2	1	no	—
308	#389	C₂³	1	1	yes	characteristic
309	#389	C₂³	1	1	yes	characteristic
310	#389	C₂³	1	1	yes	characteristic
311	#389	C₂³	1	1	yes	characteristic
312	#389	C₂³	1	1	yes	characteristic
313	#389	C₂³	1	1	yes	characteristic
314	#389	C₂³	1	1	yes	characteristic
315	#389	C₂³	1	1	yes	characteristic
316	#389	C₂³	1	1	yes	characteristic
317	#389	C₂³	1	1	yes	characteristic
318	#389	C₂³	1	1	yes	characteristic
319	#389	C₂³	1	1	yes	characteristic
320	#388	—	2	1	no	—
321	#388	—	2	1	no	—
322	#388	—	2	1	no	—
323	#388	—	2	1	no	—
324	#388	—	2	1	no	—
325	#388	—	2	1	no	—
326	#388	—	2	1	no	—
327	#388	—	2	1	no	—
328	#388	—	2	1	no	—
329	#388	—	2	1	no	—
330	#388	—	2	1	no	—
331	#388	—	2	1	no	—
332	#388	—	2	1	no	—
333	#388	—	2	1	no	—
334	#388	—	2	1	no	—
335	#388	—	2	1	no	—
336	#388	—	2	1	no	—
337	#388	—	2	1	no	—
338	#388	—	2	1	no	—
339	#387	—	2	1	no	—
340	#387	—	2	1	no	—
341	#387	—	2	1	no	—
342	#387	—	2	1	no	—
343	#387	—	2	1	no	—
344	#387	—	2	1	no	—
345	#387	—	2	1	no	—
346	#387	—	2	1	no	—
347	#387	—	2	1	no	—
348	#387	—	2	1	no	—
349	#387	—	2	1	no	—
350	#387	—	2	1	no	—
351	#387	—	2	1	no	—
352	#387	—	2	1	no	—
353	#387	—	2	1	no	—
354	#386	—	2	1	no	—
355	#386	—	2	1	no	—
356	#386	—	2	1	no	—
357	#386	—	2	1	no	—
358	#386	D₄	1	1	yes	characteristic
359	#386	D₄	1	1	yes	characteristic
360	#386	D₄	1	1	yes	characteristic
361	#385	—	2	1	no	—
362	#385	—	2	1	no	—
363	#385	D₄	1	1	yes	characteristic
364	#385	D₄	1	1	yes	characteristic
365	#385	D₄	1	1	yes	characteristic
366	#384	C₂³	1	1	yes	characteristic
367	#383	—	2	1	no	—
368	#382	—	2	1	no	—
369	#382	—	2	1	no	—
370	#382	—	2	1	no	—
371	#382	—	2	1	no	—
372	#382	C₂³	1	1	yes	characteristic
373	#382	C₂³	1	1	yes	characteristic
374	#382	C₂³	1	1	yes	characteristic
375	#381	—	2	1	no	—
376	#381	—	2	1	no	—
377	#381	—	2	1	no	—
378	#381	—	2	1	no	—
379	#381	—	2	1	no	—
380	#380	—	2	1	no	—
381	#380	—	2	1	no	—
382	#380	C₂³	1	1	yes	characteristic
383	#380	C₂³	1	1	yes	characteristic
384	#380	C₂³	1	1	yes	characteristic
385	#380	C₂³	1	1	yes	characteristic
386	#380	C₂³	1	1	yes	characteristic
387	#380	C₂³	1	1	yes	characteristic
388	#380	C₂³	1	1	yes	characteristic
389	#380	C₂³	1	1	yes	characteristic
390	#380	C₂³	1	1	yes	characteristic
391	#380	C₂³	1	1	yes	characteristic
392	#380	C₂³	1	1	yes	characteristic
393	#380	C₂³	1	1	yes	characteristic
394	#380	C₂³	1	1	yes	characteristic
395	#380	C₂³	1	1	yes	characteristic
396	#380	C₂³	1	1	yes	characteristic
397	#380	C₂³	1	1	yes	characteristic
398	#380	C₂³	1	1	yes	characteristic
399	#380	C₂³	1	1	yes	characteristic
400	#380	C₂³	1	1	yes	characteristic
401	#380	C₂³	1	1	yes	characteristic
402	#380	C₂³	1	1	yes	characteristic
403	#380	C₂³	1	1	yes	characteristic
404	#379	—	2	1	no	—
405	#379	—	2	1	no	—
406	#379	—	2	1	no	—
407	#379	D₄	1	1	yes	characteristic
408	C₄×C₄⋊C₄	—	2	1	no	—
409	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
410	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
411	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
412	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
413	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
414	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
415	C₄×C₂²⋊C₄	—	2	1	no	—
416	C₄×C₂²⋊C₄	—	2	1	no	—
417	C₄×C₂²⋊C₄	—	2	1	no	—
418	C₄×C₂²⋊C₄	—	2	1	no	—
419	C₄×C₂²⋊C₄	—	2	1	no	—
420	C₄×C₂²⋊C₄	—	2	1	no	—
421	C₄×C₂²⋊C₄	—	2	1	no	—
422	C₄×C₂²⋊C₄	—	2	1	no	—
423	C₄×C₂²⋊C₄	—	2	1	no	—
424	C₄×C₂²⋊C₄	C₂³	1	1	yes	characteristic
425	C₄×C₂²⋊C₄	C₂³	1	1	yes	characteristic
426	C₄×C₂²⋊C₄	C₂³	1	1	yes	characteristic
427	#376	—	2	1	no	—
428	#376	—	2	1	no	—
429	#376	—	2	1	no	—
430	C₂×#95	—	2	1	no	—
431	#340	C₂³	1	1	yes	characteristic
432	#340	C₂³	1	1	yes	characteristic
433	#340	C₂³	1	1	yes	characteristic
434	#340	C₂³	1	1	yes	characteristic
435	#340	C₂³	1	1	yes	characteristic
436	#340	C₂³	1	1	yes	characteristic
437	#340	C₂³	1	1	yes	characteristic
438	#340	C₂³	1	1	yes	characteristic
439	#340	C₂³	1	1	yes	characteristic
440	#340	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	#340	C₂³	1	1	yes	characteristic
470	#340	C₂³	1	1	yes	characteristic
471	#340	C₂³	1	1	yes	characteristic
472	#340	C₂³	1	1	yes	characteristic
473	#340	C₂³	1	1	yes	characteristic
474	#340	C₂³	1	1	yes	characteristic
475	#336	C₂³	1	1	yes	characteristic
476	#336	C₂³	1	1	yes	characteristic
477	#336	C₂³	1	1	yes	characteristic
478	#336	C₂³	1	1	yes	characteristic
479	#336	C₂³	1	1	yes	characteristic
480	#336	C₂³	1	1	yes	characteristic
481	C₂⁵	C₂×D₄	1	1	yes	characteristic
482	C₂²×Q₈	—	2	1	no	—
483	C₂²×Q₈	—	2	1	no	—
484	C₂²×D₄	C₂×D₄	1	1	yes	characteristic
485	C₂²×D₄	C₂×D₄	1	1	yes	characteristic
486	C₂²×D₄	C₂×D₄	1	1	yes	characteristic
487	C₂³×C₄	—	2	2	no	—
488	C₂³×C₄	—	2	2	no	—
489	C₂³×C₄	—	2	1	no	—
490	C₂³×C₄	—	2	1	no	—
491	C₂³×C₄	—	2	1	no	—
492	C₂³×C₄	—	4	1	no	—
493	C₂³×C₄	—	4	1	no	—
494	C₂³×C₄	—	4	1	no	—
495	C₂³×C₄	—	4	1	no	—
496	C₂³×C₄	C₂×D₄	1	1	yes	characteristic
497	C₂³×C₄	C₂×D₄	1	1	yes	characteristic
498	C₂³×C₄	C₂×D₄	1	1	yes	characteristic
499	C₂³×C₄	C₂⁴	1	1	yes	characteristic
500	C₂³×C₄	C₂⁴	1	1	yes	characteristic
501	C₂³×C₄	C₂⁴	1	1	yes	characteristic
502	C₂³×C₄	C₂⁴	1	1	yes	characteristic
503	C₂×M₁₆	—	2	2	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	—	4	1	no	—
510	C₂²×C₈	—	4	1	no	—
511	C₂²×C₈	#41	1	4	yes	—
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	C₂²×C₈	C₂⁴	1	1	yes	characteristic
518	C₂²×C₈	C₂⁴	1	1	yes	characteristic
519	C₂²×C₈	C₂⁴	1	1	yes	characteristic
520	C₄⋊Q₈	—	4	1	no	—
521	C₄⋊Q₈	—	4	1	no	—
522	C₄⋊Q₈	—	4	1	no	—
523	C₄⋊Q₈	—	4	1	no	—
524	#124	—	4	4	no	—
525	#123	—	8	2	no	—
526	C₂²⋊Q₈	—	8	2	no	—
527	#120	—	4	2	no	—
528	C₄×D₄	—	2	2	no	—
529	C₄×D₄	—	2	2	no	—
530	C₄×D₄	—	4	1	no	—
531	C₄×D₄	—	4	1	no	—
532	C₄×D₄	—	4	1	no	—
533	C₄×D₄	—	4	1	no	—
534	#117	—	2	2	no	—
535	#117	—	2	2	no	—
536	#117	—	2	2	no	—
537	#117	—	2	2	no	—
538	#117	—	4	4	no	—
539	#117	—	4	1	no	—
540	#117	—	4	1	no	—
541	#117	—	4	1	no	—
542	#117	—	4	1	no	—
543	#117	—	4	1	no	—
544	#117	—	4	1	no	—
545	#117	—	4	1	no	—
546	#117	—	4	1	no	—
547	#117	—	4	1	no	—
548	#117	—	4	1	no	—
549	C₂×C₄⋊C₄	—	2	1	no	—
550	C₂×C₄⋊C₄	—	2	1	no	—
551	C₂×C₄⋊C₄	—	2	1	no	—
552	C₂×C₄⋊C₄	—	2	1	no	—
553	C₂×C₄⋊C₄	—	2	1	no	—
554	C₂×C₄⋊C₄	—	2	1	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	—	4	1	no	—
569	C₂×C₄⋊C₄	—	4	1	no	—
570	C₂×C₄⋊C₄	—	4	1	no	—
571	C₂×C₄⋊C₄	—	4	1	no	—
572	C₂×C₄⋊C₄	—	4	1	no	—
573	C₂×C₄⋊C₄	—	4	1	no	—
574	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
575	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
576	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
577	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
578	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
579	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
580	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
581	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
582	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
583	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
584	C₂×C₄⋊C₄	C₂⁴	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×C₂²⋊C₄	—	2	1	no	—
594	C₂×C₂²⋊C₄	—	2	1	no	—
595	C₂×C₂²⋊C₄	—	2	1	no	—
596	C₂×C₂²⋊C₄	—	2	1	no	—
597	C₂×C₂²⋊C₄	—	2	1	no	—
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	—	8	2	no	—
623	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
624	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
625	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
626	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
627	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
628	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
629	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
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×C₄²	—	2	1	no	—
636	C₂×C₄²	—	2	1	no	—
637	C₂×C₄²	—	2	1	no	—
638	C₂×C₄²	—	2	1	no	—
639	C₂×C₄²	—	2	1	no	—
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	C₂⁴	1	1	yes	characteristic
649	C₂×C₄²	C₂⁴	1	1	yes	characteristic
650	C₂×C₄²	C₂⁴	1	1	yes	characteristic
651	#107	—	2	2	no	—
652	#107	—	2	2	no	—
653	#107	—	4	1	no	—
654	#107	—	4	1	no	—
655	#107	—	4	1	no	—
656	#107	—	4	1	no	—
657	#107	—	4	1	no	—
658	#107	—	4	1	no	—
659	#107	—	4	1	no	—
660	#107	—	4	1	no	—
661	#106	—	2	2	no	—
662	#106	—	2	2	no	—
663	#106	—	4	1	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	#106	—	4	1	no	—
671	C₄⋊C₈	—	2	2	no	—
672	C₄⋊C₈	—	4	1	no	—
673	C₄⋊C₈	—	4	1	no	—
674	C₂²⋊C₈	—	2	2	no	—
675	C₂²⋊C₈	—	2	2	no	—
676	C₂²⋊C₈	—	2	2	no	—
677	C₂²⋊C₈	—	2	2	no	—
678	C₂²⋊C₈	—	2	2	no	—
679	C₂²⋊C₈	—	2	2	no	—
680	C₂²⋊C₈	—	2	2	no	—
681	C₂²⋊C₈	—	4	1	no	—
682	C₂²⋊C₈	—	4	1	no	—
683	C₂²⋊C₈	—	4	1	no	—
684	C₂²⋊C₈	—	4	1	no	—
685	C₂²⋊C₈	—	4	1	no	—
686	C₂²⋊C₈	—	4	1	no	—
687	#97	—	2	2	no	—
688	#97	—	4	1	no	—
689	#97	—	4	1	no	—
690	#95	—	2	1	no	—
691	#95	—	2	1	no	—
692	#95	—	2	1	no	—
693	#95	—	2	1	no	—
694	#95	—	2	1	no	—
695	#95	—	2	1	no	—
696	#95	—	2	1	no	—
697	#95	—	2	1	no	—
698	#95	—	2	1	no	—
699	#95	—	2	1	no	—
700	#95	—	2	1	no	—
701	#95	—	2	1	no	—
702	#95	—	2	1	no	—
703	#95	—	2	1	no	—
704	#95	—	2	1	no	—
705	#95	—	2	1	no	—
706	#95	—	2	1	no	—
707	#95	—	2	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	C₂×D₄	1	1	yes	characteristic
737	#95	C₂×D₄	1	1	yes	characteristic
738	#95	C₂×D₄	1	1	yes	characteristic
739	#95	C₂×D₄	1	1	yes	characteristic
740	#95	C₂×D₄	1	1	yes	characteristic
741	#95	C₂×D₄	1	1	yes	characteristic
742	C₂⁴	—	2	2	no	—
743	C₂⁴	—	2	2	no	—
744	C₂⁴	—	4	1	no	—
745	C₂⁴	—	4	1	no	—
746	C₂⁴	—	4	1	no	—
747	C₂⁴	—	4	1	no	—
748	C₂⁴	—	4	1	no	—
749	C₂⁴	C₂²×D₄	1	1	yes	characteristic
750	C₂⁴	C₂²×D₄	1	1	yes	characteristic
751	C₂⁴	C₂²×D₄	1	1	yes	characteristic
752	C₂⁴	C₂²×D₄	1	1	yes	characteristic
753	C₂×Q₈	—	4	2	no	—
754	C₂×Q₈	—	8	1	no	—
755	C₂×Q₈	—	8	1	no	—
756	C₂×Q₈	—	8	1	no	—
757	C₂×Q₈	—	8	1	no	—
758	C₂×Q₈	—	8	1	no	—
759	C₂×D₄	—	2	2	no	—
760	C₂×D₄	—	2	2	no	—
761	C₂×D₄	—	4	1	no	—
762	C₂×D₄	—	4	1	no	—
763	C₂×D₄	—	4	1	no	—
764	C₂×D₄	—	4	1	no	—
765	C₂×D₄	—	4	1	no	—
766	C₂×D₄	—	4	1	no	—
767	C₂×D₄	—	4	1	no	—
768	C₂²×C₄	—	2	1	no	—
769	C₂²×C₄	—	2	1	no	—
770	C₂²×C₄	—	2	1	no	—
771	C₂²×C₄	—	2	1	no	—
772	C₂²×C₄	—	2	2	no	—
773	C₂²×C₄	—	2	1	no	—
774	C₂²×C₄	—	2	1	no	—
775	C₂²×C₄	—	2	1	no	—
776	C₂²×C₄	—	2	1	no	—
777	C₂²×C₄	—	2	1	no	—
778	C₂²×C₄	—	2	1	no	—
779	C₂²×C₄	—	2	1	no	—
780	C₂²×C₄	—	2	1	no	—
781	C₂²×C₄	—	2	1	no	—
782	C₂²×C₄	—	2	1	no	—
783	C₂²×C₄	—	2	1	no	—
784	C₂²×C₄	—	2	1	no	—
785	C₂²×C₄	—	2	1	no	—
786	C₂²×C₄	—	2	1	no	—
787	C₂²×C₄	—	2	1	no	—
788	C₂²×C₄	—	2	1	no	—
789	C₂²×C₄	—	2	1	no	—
790	C₂²×C₄	—	2	1	no	—
791	C₂²×C₄	—	2	2	no	—
792	C₂²×C₄	—	2	2	no	—
793	C₂²×C₄	—	2	1	no	—
794	C₂²×C₄	—	2	1	no	—
795	C₂²×C₄	—	2	1	no	—
796	C₂²×C₄	—	2	1	no	—
797	C₂²×C₄	—	2	1	no	—
798	C₂²×C₄	—	2	1	no	—
799	C₂²×C₄	—	2	1	no	—
800	C₂²×C₄	—	2	1	no	—
801	C₂²×C₄	—	2	1	no	—
802	C₂²×C₄	—	2	1	no	—
803	C₂²×C₄	—	2	1	no	—
804	C₂²×C₄	—	2	1	no	—
805	C₂²×C₄	—	2	1	no	—
806	C₂²×C₄	—	2	1	no	—
807	C₂²×C₄	—	2	1	no	—
808	C₂²×C₄	—	2	1	no	—
809	C₂²×C₄	—	4	1	no	—
810	C₂²×C₄	—	4	1	no	—
811	C₂²×C₄	—	4	1	no	—
812	C₂²×C₄	—	4	1	no	—
813	C₂²×C₄	—	4	1	no	—
814	C₂²×C₄	—	4	1	no	—
815	C₂²×C₄	—	4	2	no	—
816	C₂²×C₄	—	4	2	no	—
817	C₂²×C₄	—	4	2	no	—
818	C₂²×C₄	—	4	2	no	—
819	C₂²×C₄	—	8	2	no	—
820	C₂²×C₄	—	8	2	no	—
821	C₂²×C₄	—	8	2	no	—
822	C₂²×C₄	—	8	2	no	—
823	C₂²×C₄	—	8	1	no	—
824	C₂²×C₄	—	8	1	no	—
825	C₂²×C₄	—	8	1	no	—
826	C₂²×C₄	—	8	1	no	—
827	C₂²×C₄	—	8	1	no	—
828	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
829	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
830	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
831	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
832	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
833	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
834	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
835	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
836	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
837	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
838	C₂²×C₄	C₂×#41	1	2	yes	—
839	C₂²×C₄	2₋¹⁺⁴	1	2	yes	—
840	C₂²×C₄	C₂⁵	1	1	yes	characteristic
841	M₁₆	—	8	2	no	—
842	C₂×C₈	—	2	1	no	—
843	C₂×C₈	—	2	1	no	—
844	C₂×C₈	—	2	1	no	—
845	C₂×C₈	—	2	1	no	—
846	C₂×C₈	—	2	1	no	—
847	C₂×C₈	—	2	1	no	—
848	C₂×C₈	—	2	1	no	—
849	C₂×C₈	—	2	1	no	—
850	C₂×C₈	—	2	1	no	—
851	C₂×C₈	—	2	1	no	—
852	C₂×C₈	—	2	1	no	—
853	C₂×C₈	—	2	1	no	—
854	C₂×C₈	—	2	1	no	—
855	C₂×C₈	—	2	1	no	—
856	C₂×C₈	—	2	1	no	—
857	C₂×C₈	—	2	1	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	—	4	4	no	—
865	C₂×C₈	—	8	2	no	—
866	C₂×C₈	C₂×#41	1	2	yes	—
867	C₂×C₈	C₂×#41	1	2	yes	—
868	C₄⋊C₄	—	2	2	no	—
869	C₄⋊C₄	—	2	1	no	—
870	C₄⋊C₄	—	2	1	no	—
871	C₄⋊C₄	—	2	1	no	—
872	C₄⋊C₄	—	2	1	no	—
873	C₄⋊C₄	—	2	1	no	—
874	C₄⋊C₄	—	2	1	no	—
875	C₄⋊C₄	—	2	1	no	—
876	C₄⋊C₄	—	2	1	no	—
877	C₄⋊C₄	—	2	1	no	—
878	C₄⋊C₄	—	2	1	no	—
879	C₄⋊C₄	—	2	1	no	—
880	C₄⋊C₄	—	2	1	no	—
881	C₄⋊C₄	—	2	1	no	—
882	C₄⋊C₄	—	2	1	no	—
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	—	4	1	no	—
902	C₄⋊C₄	—	4	1	no	—
903	C₄⋊C₄	—	4	2	no	—
904	C₄⋊C₄	—	4	2	no	—
905	C₄⋊C₄	—	4	2	no	—
906	C₄⋊C₄	—	8	1	no	—
907	C₄⋊C₄	—	8	1	no	—
908	C₄⋊C₄	—	8	1	no	—
909	C₄⋊C₄	—	8	1	no	—
910	C₄⋊C₄	—	8	1	no	—
911	C₄⋊C₄	—	8	1	no	—
912	C₄⋊C₄	—	8	1	no	—
913	C₄⋊C₄	—	8	1	no	—
914	C₄⋊C₄	—	8	1	no	—
915	C₄⋊C₄	—	8	1	no	—
916	C₄⋊C₄	—	8	1	no	—
917	C₄⋊C₄	—	8	1	no	—
918	C₄⋊C₄	—	8	1	no	—
919	C₄⋊C₄	—	8	1	no	—
920	C₄⋊C₄	—	8	1	no	—
921	C₄⋊C₄	—	8	1	no	—
922	C₂²⋊C₄	—	2	2	no	—
923	C₂²⋊C₄	—	2	2	no	—
924	C₂²⋊C₄	—	2	2	no	—
925	C₂²⋊C₄	—	4	1	no	—
926	C₂²⋊C₄	—	4	1	no	—
927	C₂²⋊C₄	—	4	1	no	—
928	C₂²⋊C₄	—	4	1	no	—
929	C₂²⋊C₄	—	4	1	no	—
930	C₂²⋊C₄	—	4	1	no	—
931	C₂²⋊C₄	—	4	1	no	—
932	C₂²⋊C₄	—	4	1	no	—
933	C₂²⋊C₄	—	4	1	no	—
934	C₂²⋊C₄	—	4	2	no	—
935	C₂²⋊C₄	—	4	2	no	—
936	C₂²⋊C₄	—	4	2	no	—
937	C₂²⋊C₄	—	4	2	no	—
938	C₂²⋊C₄	—	4	2	no	—
939	C₂²⋊C₄	—	4	2	no	—
940	C₂²⋊C₄	—	4	2	no	—
941	C₂²⋊C₄	—	4	2	no	—
942	C₂²⋊C₄	—	4	2	no	—
943	C₂²⋊C₄	—	4	2	no	—
944	C₂²⋊C₄	—	8	1	no	—
945	C₂²⋊C₄	—	8	1	no	—
946	C₂²⋊C₄	—	8	1	no	—
947	C₂²⋊C₄	—	8	1	no	—
948	C₂²⋊C₄	—	8	1	no	—
949	C₂²⋊C₄	—	8	1	no	—
950	C₂²⋊C₄	—	8	1	no	—
951	C₂²⋊C₄	—	8	1	no	—
952	C₂²⋊C₄	—	8	1	no	—
953	C₂²⋊C₄	—	8	1	no	—
954	C₂²⋊C₄	—	8	1	no	—
955	C₂²⋊C₄	—	8	1	no	—
956	C₂²⋊C₄	—	8	1	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	C₄²	—	2	1	no	—
964	C₄²	—	2	1	no	—
965	C₄²	—	2	1	no	—
966	C₄²	—	2	1	no	—
967	C₄²	—	2	1	no	—
968	C₄²	—	2	1	no	—
969	C₄²	—	4	2	no	—
970	C₄²	—	4	2	no	—
971	C₄²	—	4	2	no	—
972	C₄²	—	4	2	no	—
973	C₄²	—	4	2	no	—
974	C₄²	—	4	2	no	—
975	C₄²	—	8	1	no	—
976	C₄²	—	8	1	no	—
977	C₄²	—	8	1	no	—
978	C₄²	—	8	1	no	—
979	C₄²	—	8	1	no	—
980	C₄²	—	8	1	no	—
981	C₄²	—	8	1	no	—
982	C₂³	—	2	1	no	—
983	C₂³	—	2	1	no	—
984	C₂³	—	2	1	no	—
985	C₂³	—	2	1	no	—
986	C₂³	—	2	1	no	—
987	C₂³	—	2	1	no	—
988	C₂³	—	2	1	no	—
989	C₂³	—	2	1	no	—
990	C₂³	—	2	1	no	—
991	C₂³	—	2	1	no	—
992	C₂³	—	2	1	no	—
993	C₂³	—	2	1	no	—
994	C₂³	—	2	1	no	—
995	C₂³	—	2	1	no	—
996	C₂³	—	2	1	no	—
997	C₂³	—	2	1	no	—
998	C₂³	—	2	1	no	—
999	C₂³	—	2	1	no	—
1000	C₂³	—	2	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	—	4	4	no	—
1009	C₂³	—	4	4	no	—
1010	C₂³	—	8	2	no	—
1011	C₂³	—	8	2	no	—
1012	C₂³	—	8	2	no	—
1013	C₂³	—	8	2	no	—
1014	C₂³	—	8	2	no	—
1015	C₂³	#547	1	2	yes	—
1016	C₂³	#575	1	2	yes	—
1017	C₂³	C₂³×D₄	1	1	yes	characteristic
1018	Q₈	—	16	2	no	—
1019	Q₈	—	16	2	no	—
1020	D₄	—	8	2	no	—
1021	D₄	—	8	2	no	—
1022	D₄	—	8	2	no	—
1023	C₂×C₄	—	2	1	no	—
1024	C₂×C₄	—	2	1	no	—
1025	C₂×C₄	—	2	2	no	—
1026	C₂×C₄	—	2	2	no	—
1027	C₂×C₄	—	2	2	no	—
1028	C₂×C₄	—	2	2	no	—
1029	C₂×C₄	—	2	1	no	—
1030	C₂×C₄	—	2	1	no	—
1031	C₂×C₄	—	2	1	no	—
1032	C₂×C₄	—	2	1	no	—
1033	C₂×C₄	—	2	1	no	—
1034	C₂×C₄	—	2	1	no	—
1035	C₂×C₄	—	2	1	no	—
1036	C₂×C₄	—	2	1	no	—
1037	C₂×C₄	—	2	1	no	—
1038	C₂×C₄	—	2	1	no	—
1039	C₂×C₄	—	2	1	no	—
1040	C₂×C₄	—	2	1	no	—
1041	C₂×C₄	—	2	1	no	—
1042	C₂×C₄	—	2	1	no	—
1043	C₂×C₄	—	2	1	no	—
1044	C₂×C₄	—	2	1	no	—
1045	C₂×C₄	—	2	1	no	—
1046	C₂×C₄	—	2	1	no	—
1047	C₂×C₄	—	2	1	no	—
1048	C₂×C₄	—	2	1	no	—
1049	C₂×C₄	—	2	1	no	—
1050	C₂×C₄	—	2	1	no	—
1051	C₂×C₄	—	2	1	no	—
1052	C₂×C₄	—	2	1	no	—
1053	C₂×C₄	—	2	1	no	—
1054	C₂×C₄	—	2	1	no	—
1055	C₂×C₄	—	2	1	no	—
1056	C₂×C₄	—	4	1	no	—
1057	C₂×C₄	—	4	1	no	—
1058	C₂×C₄	—	4	1	no	—
1059	C₂×C₄	—	4	1	no	—
1060	C₂×C₄	—	4	1	no	—
1061	C₂×C₄	—	4	1	no	—
1062	C₂×C₄	—	4	1	no	—
1063	C₂×C₄	—	4	1	no	—
1064	C₂×C₄	—	4	1	no	—
1065	C₂×C₄	—	4	1	no	—
1066	C₂×C₄	—	4	1	no	—
1067	C₂×C₄	—	4	1	no	—
1068	C₂×C₄	—	4	1	no	—
1069	C₂×C₄	—	4	1	no	—
1070	C₂×C₄	—	4	1	no	—
1071	C₂×C₄	—	4	1	no	—
1072	C₂×C₄	—	4	1	no	—
1073	C₂×C₄	—	4	1	no	—
1074	C₂×C₄	—	4	1	no	—
1075	C₂×C₄	—	4	1	no	—
1076	C₂×C₄	—	4	1	no	—
1077	C₂×C₄	—	4	1	no	—
1078	C₂×C₄	—	4	1	no	—
1079	C₂×C₄	—	4	1	no	—
1080	C₂×C₄	—	4	1	no	—
1081	C₂×C₄	—	4	1	no	—
1082	C₂×C₄	—	4	1	no	—
1083	C₂×C₄	—	4	1	no	—
1084	C₂×C₄	—	4	1	no	—
1085	C₂×C₄	—	4	1	no	—
1086	C₂×C₄	—	4	1	no	—
1087	C₂×C₄	—	4	1	no	—
1088	C₂×C₄	—	4	1	no	—
1089	C₂×C₄	—	4	1	no	—
1090	C₂×C₄	—	4	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	—	8	2	no	—
1117	C₂×C₄	—	8	2	no	—
1118	C₂×C₄	—	8	2	no	—
1119	C₂×C₄	—	8	4	no	—
1120	C₂×C₄	—	16	2	no	—
1121	C₂×C₄	—	16	2	no	—
1122	C₂×C₄	#547	1	2	yes	—
1123	C₂×C₄	C₂²×#41	1	1	yes	characteristic
1124	C₂×C₄	C₂×2₋¹⁺⁴	1	1	yes	characteristic
1125	C₂×C₄	#585	1	1	yes	characteristic
1126	C₂×C₄	#585	1	1	yes	characteristic
1127	C₂×C₄	#585	1	1	yes	characteristic
1128	C₂×C₄	#585	1	1	yes	characteristic
1129	C₈	—	2	2	no	—
1130	C₈	—	2	2	no	—
1131	C₈	—	4	1	no	—
1132	C₈	—	4	1	no	—
1133	C₈	—	4	1	no	—
1134	C₈	—	4	1	no	—
1135	C₈	—	4	1	no	—
1136	C₈	—	4	1	no	—
1137	C₂²	—	2	2	no	—
1138	C₂²	—	2	2	no	—
1139	C₂²	—	2	2	no	—
1140	C₂²	—	2	2	no	—
1141	C₂²	—	2	2	no	—
1142	C₂²	—	2	2	no	—
1143	C₂²	—	4	1	no	—
1144	C₂²	—	4	1	no	—
1145	C₂²	—	4	1	no	—
1146	C₂²	—	4	1	no	—
1147	C₂²	—	4	1	no	—
1148	C₂²	—	4	1	no	—
1149	C₂²	—	4	1	no	—
1150	C₂²	—	4	1	no	—
1151	C₂²	—	4	1	no	—
1152	C₂²	—	4	1	no	—
1153	C₂²	—	4	1	no	—
1154	C₂²	—	4	1	no	—
1155	C₂²	—	4	1	no	—
1156	C₂²	—	4	1	no	—
1157	C₂²	—	4	1	no	—
1158	C₂²	—	4	1	no	—
1159	C₂²	—	4	1	no	—
1160	C₂²	—	4	1	no	—
1161	C₂²	—	4	1	no	—
1162	C₂²	—	4	1	no	—
1163	C₂²	—	4	1	no	—
1164	C₂²	—	4	1	no	—
1165	C₂²	—	8	8	no	—
1166	C₂²	C₂×#547	1	1	yes	characteristic
1167	C₂²	#3485	1	1	yes	characteristic
1168	C₂²	#3485	1	1	yes	characteristic
1169	C₂²	C₂×#575	1	1	yes	characteristic
1170	C₂²	#3584	1	1	yes	characteristic
1171	C₂²	#3585	1	1	yes	characteristic
1172	C₂²	#3586	1	1	yes	characteristic
1173	C₄	—	2	2	no	—
1174	C₄	—	4	1	no	—
1175	C₄	—	4	1	no	—
1176	C₄	—	4	1	no	—
1177	C₄	—	4	1	no	—
1178	C₄	—	4	1	no	—
1179	C₄	—	4	1	no	—
1180	C₄	—	4	1	no	—
1181	C₄	—	4	1	no	—
1182	C₄	—	4	1	no	—
1183	C₄	—	8	1	no	—
1184	C₄	—	8	1	no	—
1185	C₄	—	8	1	no	—
1186	C₄	—	8	1	no	—
1187	C₄	—	8	1	no	—
1188	C₄	—	8	1	no	—
1189	C₄	—	8	1	no	—
1190	C₄	—	8	1	no	—
1191	C₄	—	8	1	no	—
1192	C₄	—	8	1	no	—
1193	C₄	—	8	1	no	—
1194	C₄	—	8	1	no	—
1195	C₄	—	8	1	no	—
1196	C₄	—	8	1	no	—
1197	C₄	—	8	1	no	—
1198	C₄	—	8	1	no	—
1199	C₄	#3491	1	1	yes	characteristic
1200	C₄	#3510	1	1	yes	characteristic
1201	C₄	#3564	1	1	yes	characteristic
1202	C₄	#3564	1	1	yes	characteristic
1203	C₂	—	4	2	no	—
1204	C₂	—	4	2	no	—
1205	C₂	—	8	1	no	—
1206	C₂	—	8	1	no	—
1207	C₂	#43510	1	1	yes	characteristic
1208	C₂	#61243	1	1	yes	characteristic
1209	C₂	#61265	1	1	yes	characteristic
1210	C₂	#61710	1	1	yes	characteristic
1211	C₂	#61715	1	1	yes	characteristic
1212	C₂	#61749	1	1	yes	characteristic
1213	C₂	#61760	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³	C₂³×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁵
prime radical	C₂×#120	D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³ ◁ C₄×#120 ◁ G
LECS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
3. #32470	C₂	semidirect
4. #32468	C₂	semidirect
5. #32277	C₂	semidirect
6. #32271	C₂	semidirect
7. #31717	C₂	semidirect
8. #31708	C₂	semidirect
9. #31453	C₂	semidirect
10. #31448	C₂	semidirect
11. #28777	C₂	semidirect
12. #27664	C₂	semidirect
13. #27605	C₂	semidirect
14. #27604	C₂	semidirect
15. #27483	C₂	semidirect
16. #27480	C₂	semidirect
17. #27472	C₂	semidirect
18. #27472	C₂	semidirect
19. #26313	C₂	semidirect
20. #26312	C₂	semidirect
21. #25995	C₂	semidirect
22. #25993	C₂	semidirect
23. #24961	C₂	semidirect
24. #24952	C₂	semidirect
25. #24942	C₂	semidirect
26. #24938	C₂	semidirect
27. #23638	C₂	semidirect
28. #22710	C₂	semidirect
29. #22619	C₂	semidirect
31. #21941	C₂	semidirect
80. #2101	C₂²	semidirect
81. #2101	C₂²	semidirect
82. #2101	C₂²	semidirect
83. #2099	C₂²	semidirect
84. #2088	C₂²	semidirect
85. #2088	C₂²	semidirect
86. #2087	C₂²	semidirect
87. #2087	C₂²	semidirect
88. #2086	C₂²	semidirect
89. #2086	C₂²	semidirect
90. #2085	C₂²	semidirect
91. #2085	C₂²	semidirect
92. #2085	C₂²	semidirect
93. #2083	C₂²	semidirect
102. #2077	C₂²	semidirect
106. #2076	C₂²	semidirect
107. #2076	C₂²	semidirect
108. #2076	C₂²	semidirect
114. #2075	C₂²	semidirect
115. #2075	C₂²	semidirect
116. #2058	C₂²	semidirect
117. #2057	C₂²	semidirect
118. #2057	C₂²	semidirect
119. #2057	C₂²	semidirect
120. #1993	C₂²	semidirect
121. #1993	C₂²	semidirect
122. #1988	C₂²	semidirect
123. #1987	C₂²	semidirect
126. #1949	C₂²	semidirect
127. #1949	C₂²	semidirect
128. #1949	C₂²	semidirect
129. #1948	C₂²	semidirect
130. #1943	C₂²	semidirect
131. #1943	C₂²	semidirect
132. #1943	C₂²	semidirect
133. #1943	C₂²	semidirect
134. #1943	C₂²	semidirect
135. #1943	C₂²	semidirect
140. #1921	C₂²	semidirect
141. #1921	C₂²	semidirect
142. #1920	C₂²	semidirect
143. #1920	C₂²	semidirect
144. #1919	C₂²	semidirect
145. #1919	C₂²	semidirect
146. #1919	C₂²	semidirect
147. #1919	C₂²	semidirect
148. #1919	C₂²	semidirect
149. #1919	C₂²	semidirect
150. #1919	C₂²	semidirect
151. #1918	C₂²	semidirect
165. #1854	C₂²	semidirect
166. #1854	C₂²	semidirect
170. #1853	C₂²	semidirect
171. #1853	C₂²	semidirect
176. #1836	C₂²	semidirect
183. #1825	C₂²	semidirect
186. #1823	C₂²	semidirect
187. #1809	C₂²	semidirect
188. #1809	C₂²	semidirect
189. #1809	C₂²	semidirect
195. #1776	C₂²	semidirect
196. #1776	C₂²	semidirect
197. #1776	C₂²	semidirect
199. #1736	C₂²	semidirect

Maximal subgroups

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

subgroup	index
#59203	2
#59202	2
#32470	2
#32468	2
#32277	2
#32271	2
#31717	2
#31708	2
#31453	2
#31448	2
#28777	2
#27664	2
#27605	2
#27604	2
#27483	2
#27480	2
#27472	2
#26313	2
#26312	2
#25995	2
#25993	2
#24961	2
#24952	2
#24942	2
#24938	2
#23638	2
#22710	2
#22619	2
#22034	2
#21941	2