Subgroups — #6532039

Order 512.

1511 conjugacy classes of subgroups.

The subgroup lattice has 1220 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#35515	C₂	1	1	yes	maximal, characteristic
2	#34373	C₂	1	1	yes	maximal, characteristic, complemented
3	#27623	C₂	1	1	yes	maximal, characteristic, complemented
4	#27620	C₂	1	1	yes	maximal, characteristic, complemented
5	#27618	C₂	1	1	yes	maximal, characteristic, complemented
6	#27615	C₂	1	1	yes	maximal, characteristic, complemented
7	#27594	C₂	1	1	yes	maximal, characteristic
8	#27591	C₂	1	1	yes	maximal, characteristic
9	#27588	C₂	1	1	yes	maximal, characteristic
10	#27582	C₂	1	1	yes	maximal, characteristic
11	#25072	C₂	1	1	yes	maximal, characteristic, complemented
12	#25072	C₂	1	1	yes	maximal, characteristic, complemented
13	#25069	C₂	1	1	yes	maximal, characteristic, complemented
14	#25068	C₂	1	1	yes	maximal, characteristic, complemented
15	#25065	C₂	1	1	yes	maximal, characteristic, complemented
16	#25064	C₂	1	1	yes	maximal, characteristic, complemented
17	#25057	C₂	1	1	yes	maximal, characteristic, complemented
18	#25056	C₂	1	1	yes	maximal, characteristic, complemented
19	#25007	C₂	1	1	yes	maximal, characteristic, complemented
20	#25006	C₂	1	1	yes	maximal, characteristic, complemented
21	#25003	C₂	1	1	yes	maximal, characteristic, complemented
22	#25002	C₂	1	1	yes	maximal, characteristic, complemented
23	#24998	C₂	1	1	yes	maximal, characteristic, complemented
24	#24998	C₂	1	1	yes	maximal, characteristic, complemented
25	#24993	C₂	1	1	yes	maximal, characteristic, complemented
26	#24990	C₂	1	1	yes	maximal, characteristic, complemented
27	#21992	C₂	1	1	yes	maximal, characteristic, complemented
28	#21991	C₂	1	1	yes	maximal, characteristic, complemented
29	#21824	C₂	1	1	yes	maximal, characteristic, complemented
30	#20744	C₂	1	1	yes	maximal, characteristic
31	#20744	C₂	1	1	yes	maximal, characteristic
32	C₂×#533	C₂²	1	1	yes	characteristic
33	C₂×#518	C₂²	1	1	yes	characteristic
34	C₂×#433	C₂²	1	1	yes	characteristic
35	C₂×#433	C₂²	1	1	yes	characteristic
36	#2580	C₂²	1	1	yes	characteristic
37	#2580	C₂²	1	1	yes	characteristic
38	#2580	C₂²	1	1	yes	characteristic
39	#2580	C₂²	1	1	yes	characteristic
40	#2538	C₂²	1	1	yes	characteristic
41	#2538	C₂²	1	1	yes	characteristic
42	#2538	C₂²	1	1	yes	characteristic
43	#2538	C₂²	1	1	yes	characteristic
44	#2454	—	2	1	no	—
45	#2454	—	2	1	no	—
46	#2452	—	2	1	no	—
47	#2452	—	2	1	no	—
48	#2437	—	2	1	no	—
49	#2437	—	2	1	no	—
50	#2437	—	2	1	no	—
51	#2437	—	2	1	no	—
52	#2378	—	2	1	no	—
53	#2378	—	2	1	no	—
54	#2362	—	2	1	no	—
55	#2362	—	2	1	no	—
56	#2355	C₂²	1	1	yes	characteristic, complemented
57	#2355	C₂²	1	1	yes	characteristic, complemented
58	#2355	C₂²	1	1	yes	characteristic, complemented
59	#2355	C₂²	1	1	yes	characteristic, complemented
60	#2355	C₂²	1	1	yes	characteristic, complemented
61	#2355	C₂²	1	1	yes	characteristic, complemented
62	Q₈×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
63	Q₈×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
64	#2336	—	2	1	no	—
65	#2336	—	2	1	no	—
66	#2331	—	2	1	no	—
67	#2327	—	2	1	no	—
68	#2317	C₂²	1	1	yes	characteristic
69	#2316	C₂²	1	1	yes	characteristic
70	#2314	C₂²	1	1	yes	characteristic
71	#2314	C₂²	1	1	yes	characteristic
72	#2314	C₂²	1	1	yes	characteristic
73	#2314	C₂²	1	1	yes	characteristic
74	#2309	C₂²	1	1	yes	characteristic
75	#2296	C₂²	1	1	yes	characteristic
76	C₂×#390	C₂²	1	1	yes	characteristic
77	#2285	C₂²	1	1	yes	characteristic
78	#2283	C₂²	1	1	yes	characteristic
79	#2101	C₂²	1	1	yes	characteristic, complemented
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	#2100	C₂²	1	1	yes	characteristic, complemented
84	#2099	C₂²	1	1	yes	characteristic, complemented
85	#2099	C₂²	1	1	yes	characteristic, complemented
86	#2099	C₂²	1	1	yes	characteristic, complemented
87	#2094	C₂²	1	1	yes	characteristic
88	#2093	C₂²	1	1	yes	characteristic
89	#2093	C₂²	1	1	yes	characteristic
90	#2093	C₂²	1	1	yes	characteristic
91	#2092	C₂²	1	1	yes	characteristic
92	#2092	C₂²	1	1	yes	characteristic
93	#2092	C₂²	1	1	yes	characteristic
94	#2092	C₂²	1	1	yes	characteristic
95	#2085	C₂²	1	1	yes	characteristic, complemented
96	#2085	C₂²	1	1	yes	characteristic, complemented
97	#2085	C₂²	1	1	yes	characteristic, complemented
98	#2085	C₂²	1	1	yes	characteristic, complemented
99	#2084	C₂²	1	1	yes	characteristic, complemented
100	#2083	C₂²	1	1	yes	characteristic, complemented
101	#2083	C₂²	1	1	yes	characteristic, complemented
102	#2083	C₂²	1	1	yes	characteristic, complemented
103	#2073	C₂²	1	1	yes	characteristic
104	#2073	C₂²	1	1	yes	characteristic
105	#2073	C₂²	1	1	yes	characteristic
106	#2073	C₂²	1	1	yes	characteristic
107	#2071	C₂²	1	1	yes	characteristic
108	#2071	C₂²	1	1	yes	characteristic
109	#2071	C₂²	1	1	yes	characteristic
110	#2071	C₂²	1	1	yes	characteristic
111	#1985	C₂²	1	1	yes	characteristic, complemented
112	#1985	C₂²	1	1	yes	characteristic, complemented
113	#1985	C₂²	1	1	yes	characteristic, complemented
114	#1985	C₂²	1	1	yes	characteristic, complemented
115	#1984	C₂²	1	1	yes	characteristic, complemented
116	#1984	C₂²	1	1	yes	characteristic, complemented
117	#1984	C₂²	1	1	yes	characteristic, complemented
118	#1984	C₂²	1	1	yes	characteristic, complemented
119	#1949	C₂²	1	1	yes	characteristic, complemented
120	#1949	C₂²	1	1	yes	characteristic, complemented
121	#1949	C₂²	1	1	yes	characteristic, complemented
122	#1949	C₂²	1	1	yes	characteristic, complemented
123	#1948	C₂²	1	1	yes	characteristic, complemented
124	#1947	C₂²	1	1	yes	characteristic, complemented
125	#1947	C₂²	1	1	yes	characteristic, complemented
126	#1947	C₂²	1	1	yes	characteristic, complemented
127	#1926	C₂²	1	1	yes	characteristic
128	#1926	C₂²	1	1	yes	characteristic
129	#1926	C₂²	1	1	yes	characteristic
130	#1926	C₂²	1	1	yes	characteristic
131	#1926	C₂²	1	1	yes	characteristic
132	#1926	C₂²	1	1	yes	characteristic
133	#1925	C₂²	1	1	yes	characteristic
134	#1925	C₂²	1	1	yes	characteristic
135	#1925	C₂²	1	1	yes	characteristic
136	#1925	C₂²	1	1	yes	characteristic
137	#1925	C₂²	1	1	yes	characteristic
138	#1925	C₂²	1	1	yes	characteristic
139	#1925	C₂²	1	1	yes	characteristic
140	#1925	C₂²	1	1	yes	characteristic
141	#1925	C₂²	1	1	yes	characteristic
142	#1925	C₂²	1	1	yes	characteristic
143	#1921	C₂²	1	1	yes	characteristic, complemented
144	#1921	C₂²	1	1	yes	characteristic, complemented
145	#1921	C₂²	1	1	yes	characteristic, complemented
146	#1921	C₂²	1	1	yes	characteristic, complemented
147	#1921	C₂²	1	1	yes	characteristic, complemented
148	#1921	C₂²	1	1	yes	characteristic, complemented
149	#1920	C₂²	1	1	yes	characteristic, complemented
150	#1920	C₂²	1	1	yes	characteristic, complemented
151	#1919	C₂²	1	1	yes	characteristic, complemented
152	#1919	C₂²	1	1	yes	characteristic, complemented
153	#1919	C₂²	1	1	yes	characteristic, complemented
154	#1919	C₂²	1	1	yes	characteristic, complemented
155	#1918	C₂²	1	1	yes	characteristic, complemented
156	#1918	C₂²	1	1	yes	characteristic, complemented
157	#1918	C₂²	1	1	yes	characteristic, complemented
158	#1918	C₂²	1	1	yes	characteristic, complemented
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	#1853	C₂²	1	1	yes	characteristic
164	#1852	C₂²	1	1	yes	characteristic
165	#1852	C₂²	1	1	yes	characteristic
166	#1852	C₂²	1	1	yes	characteristic
167	#1847	C₂²	1	1	yes	characteristic, complemented
168	#1847	C₂²	1	1	yes	characteristic, complemented
169	#1846	C₂²	1	1	yes	characteristic, complemented
170	#1845	C₂²	1	1	yes	characteristic, complemented
171	#1836	C₂²	1	1	yes	characteristic, complemented
172	#1836	C₂²	1	1	yes	characteristic, complemented
173	#1835	C₂²	1	1	yes	characteristic, complemented
174	#1834	C₂²	1	1	yes	characteristic, complemented
175	#1825	C₂²	1	1	yes	characteristic
176	#1825	C₂²	1	1	yes	characteristic
177	#1825	C₂²	1	1	yes	characteristic
178	#1825	C₂²	1	1	yes	characteristic
179	#1818	C₂²	1	1	yes	characteristic
180	#1818	C₂²	1	1	yes	characteristic
181	#1817	C₂²	1	1	yes	characteristic
182	#1817	C₂²	1	1	yes	characteristic
183	#1804	C₂²	1	1	yes	characteristic
184	#1804	C₂²	1	1	yes	characteristic
185	#1804	C₂²	1	1	yes	characteristic
186	#1804	C₂²	1	1	yes	characteristic
187	#1802	C₂²	1	1	yes	characteristic
188	#1802	C₂²	1	1	yes	characteristic
189	#1802	C₂²	1	1	yes	characteristic
190	#1802	C₂²	1	1	yes	characteristic
191	#1786	C₂²	1	1	yes	characteristic
192	#1786	C₂²	1	1	yes	characteristic
193	#1786	C₂²	1	1	yes	characteristic
194	#1786	C₂²	1	1	yes	characteristic
195	#1762	C₂²	1	1	yes	characteristic
196	#1762	C₂²	1	1	yes	characteristic
197	#1762	C₂²	1	1	yes	characteristic
198	#1762	C₂²	1	1	yes	characteristic
199	C₄×#102	C₂²	1	1	yes	characteristic
200	C₄×#102	C₂²	1	1	yes	characteristic
201	C₄×#102	C₂²	1	1	yes	characteristic
202	C₄×#102	C₂²	1	1	yes	characteristic
203	C₂³×D₄	C₂³	1	1	yes	characteristic
204	#533	—	2	4	no	—
205	#533	—	2	4	no	—
206	C₂×C₄⋊Q₈	D₄	1	1	yes	characteristic
207	C₂×C₄⋊Q₈	D₄	1	1	yes	characteristic
208	C₂×#125	D₄	1	1	yes	characteristic
209	C₂×#125	D₄	1	1	yes	characteristic
210	C₂×C₂²⋊Q₈	—	2	1	no	—
211	C₂×C₂²⋊Q₈	—	2	1	no	—
212	C₂×C₂²⋊Q₈	—	2	1	no	—
213	C₂×C₂²⋊Q₈	—	2	1	no	—
214	C₂×C₂²⋊Q₈	D₄	1	1	yes	characteristic
215	C₂×C₂²⋊Q₈	D₄	1	1	yes	characteristic
216	C₂×C₂²⋊Q₈	D₄	1	1	yes	characteristic
217	C₂×C₂²⋊Q₈	D₄	1	1	yes	characteristic
218	#518	—	2	4	no	—
219	#518	—	2	4	no	—
220	C₂×C₄×Q₈	—	2	1	no	—
221	C₂×C₄×Q₈	—	2	1	no	—
222	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
223	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
224	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
225	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
226	C₂×C₄×D₄	—	2	1	no	—
227	C₂×C₄×D₄	—	2	1	no	—
228	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
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×#117	—	2	1	no	—
233	C₂×#117	C₂³	1	1	yes	characteristic
234	C₂×#117	C₂³	1	1	yes	characteristic
235	C₂×#117	C₂³	1	1	yes	characteristic
236	C₂×#117	C₂³	1	1	yes	characteristic
237	C₂²×C₄⋊C₄	C₂³	1	1	yes	characteristic
238	C₂²×C₂²⋊C₄	—	2	1	no	—
239	C₂²×C₂²⋊C₄	—	2	1	no	—
240	C₂²×C₂²⋊C₄	—	2	1	no	—
241	C₂²×C₂²⋊C₄	—	2	1	no	—
242	C₂²×C₄²	C₂³	1	1	yes	characteristic
243	#433	—	2	4	no	—
244	#433	—	2	4	no	—
245	C₂×#107	C₂³	1	1	yes	characteristic
246	C₂×#107	C₂³	1	1	yes	characteristic
247	C₂×#107	C₂³	1	1	yes	characteristic
248	C₂×#107	C₂³	1	1	yes	characteristic
249	C₂×#107	C₂³	1	1	yes	characteristic
250	C₂×#107	C₂³	1	1	yes	characteristic
251	C₂×#107	C₂³	1	1	yes	characteristic
252	C₂×#107	C₂³	1	1	yes	characteristic
253	C₂×#107	C₂³	1	1	yes	characteristic
254	C₂×#107	C₂³	1	1	yes	characteristic
255	C₂×#106	C₂³	1	1	yes	characteristic
256	C₂×#106	C₂³	1	1	yes	characteristic
257	C₂×#106	C₂³	1	1	yes	characteristic
258	C₂×#106	C₂³	1	1	yes	characteristic
259	C₂×#106	C₂³	1	1	yes	characteristic
260	C₂×#106	C₂³	1	1	yes	characteristic
261	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
262	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
263	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
264	C₂×C₄⋊C₈	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×#102	C₂³	1	1	yes	characteristic
273	C₂×#102	C₂³	1	1	yes	characteristic
274	C₂×#102	C₂³	1	1	yes	characteristic
275	C₂×#102	C₂³	1	1	yes	characteristic
276	C₂×#102	C₂³	1	1	yes	characteristic
277	C₂×#102	C₂³	1	1	yes	characteristic
278	C₂×#102	C₂³	1	1	yes	characteristic
279	C₂×#102	C₂³	1	1	yes	characteristic
280	C₂×#102	C₂³	1	1	yes	characteristic
281	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
282	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
283	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
284	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
285	C₂×#97	C₂³	1	1	yes	characteristic
286	C₂×#97	C₂³	1	1	yes	characteristic
287	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
288	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
289	#399	—	2	1	no	—
290	#399	—	2	1	no	—
291	#399	—	2	1	no	—
292	#399	—	2	1	no	—
293	#396	—	2	1	no	—
294	#396	—	2	1	no	—
295	#396	—	2	1	no	—
296	#396	—	2	1	no	—
297	#396	—	2	1	no	—
298	#396	—	2	1	no	—
299	#396	—	2	1	no	—
300	#396	—	2	1	no	—
301	#393	—	2	1	no	—
302	#393	—	2	1	no	—
303	#393	—	2	1	no	—
304	#393	—	2	1	no	—
305	#391	—	2	1	no	—
306	#391	—	2	1	no	—
307	#391	—	2	1	no	—
308	#391	—	2	1	no	—
309	#391	—	2	1	no	—
310	#391	—	2	1	no	—
311	#390	—	2	1	no	—
312	#390	—	2	1	no	—
313	#390	—	2	1	no	—
314	#390	—	2	1	no	—
315	#390	C₂³	1	1	yes	characteristic
316	#390	C₂³	1	1	yes	characteristic
317	#390	C₂³	1	1	yes	characteristic
318	#390	C₂³	1	1	yes	characteristic
319	#390	C₂³	1	1	yes	characteristic
320	#390	C₂³	1	1	yes	characteristic
321	#390	C₂³	1	1	yes	characteristic
322	#390	C₂³	1	1	yes	characteristic
323	#389	—	2	1	no	—
324	#389	—	2	1	no	—
325	#389	—	2	1	no	—
326	#389	—	2	1	no	—
327	#389	—	2	1	no	—
328	#389	—	2	1	no	—
329	#389	—	2	1	no	—
330	#389	—	2	1	no	—
331	#389	—	2	1	no	—
332	#389	—	2	1	no	—
333	#389	C₂³	1	1	yes	characteristic
334	#389	C₂³	1	1	yes	characteristic
335	#389	C₂³	1	1	yes	characteristic
336	#389	C₂³	1	1	yes	characteristic
337	#389	C₂³	1	1	yes	characteristic
338	#389	C₂³	1	1	yes	characteristic
339	#389	C₂³	1	1	yes	characteristic
340	#389	C₂³	1	1	yes	characteristic
341	#388	—	2	1	no	—
342	#388	—	2	1	no	—
343	#388	—	2	1	no	—
344	#388	—	2	1	no	—
345	#388	—	2	1	no	—
346	#388	—	2	1	no	—
347	#388	—	2	1	no	—
348	#388	—	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	#387	—	2	1	no	—
355	#387	—	2	1	no	—
356	#387	—	2	1	no	—
357	#387	—	2	1	no	—
358	#387	—	2	1	no	—
359	#387	—	2	1	no	—
360	#387	—	2	1	no	—
361	#387	—	2	1	no	—
362	#387	—	2	1	no	—
363	#387	—	2	1	no	—
364	#387	—	2	1	no	—
365	#387	—	2	1	no	—
366	#387	—	2	1	no	—
367	#387	—	2	1	no	—
368	#387	—	2	1	no	—
369	#385	—	2	1	no	—
370	#385	—	2	1	no	—
371	#385	—	2	1	no	—
372	#385	—	2	1	no	—
373	#385	—	2	1	no	—
374	#385	—	2	1	no	—
375	#385	—	2	1	no	—
376	#385	—	2	1	no	—
377	#385	—	2	1	no	—
378	#385	—	2	1	no	—
379	#385	—	2	1	no	—
380	#385	—	2	1	no	—
381	#384	C₂³	1	1	yes	characteristic
382	#384	C₂³	1	1	yes	characteristic
383	#384	C₂³	1	1	yes	characteristic
384	#384	C₂³	1	1	yes	characteristic
385	#384	C₂³	1	1	yes	characteristic
386	#384	C₂³	1	1	yes	characteristic
387	#384	C₂³	1	1	yes	characteristic
388	#384	C₂³	1	1	yes	characteristic
389	#383	—	2	1	no	—
390	#382	—	2	1	no	—
391	#382	C₂³	1	1	yes	characteristic
392	#382	C₂³	1	1	yes	characteristic
393	#382	C₂³	1	1	yes	characteristic
394	#382	C₂³	1	1	yes	characteristic
395	#382	C₂³	1	1	yes	characteristic
396	#382	C₂³	1	1	yes	characteristic
397	#382	C₂³	1	1	yes	characteristic
398	#382	C₂³	1	1	yes	characteristic
399	#381	—	2	1	no	—
400	#380	—	2	1	no	—
401	#380	—	2	1	no	—
402	#380	—	2	1	no	—
403	#380	—	2	1	no	—
404	#380	—	2	1	no	—
405	#380	—	2	1	no	—
406	#380	—	2	1	no	—
407	#380	C₂³	1	1	yes	characteristic
408	#380	C₂³	1	1	yes	characteristic
409	#380	C₂³	1	1	yes	characteristic
410	#380	C₂³	1	1	yes	characteristic
411	#379	—	2	1	no	—
412	#379	—	2	1	no	—
413	C₄×C₄⋊C₄	—	2	1	no	—
414	C₄×C₄⋊C₄	—	2	1	no	—
415	C₄×C₄⋊C₄	—	2	1	no	—
416	C₄×C₄⋊C₄	—	2	1	no	—
417	C₄×C₄⋊C₄	—	2	1	no	—
418	C₄×C₄⋊C₄	—	2	1	no	—
419	C₄×C₄⋊C₄	—	2	1	no	—
420	C₄×C₄⋊C₄	—	2	1	no	—
421	C₄×C₄⋊C₄	—	2	1	no	—
422	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
423	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
424	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
425	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
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×C₄⋊C₄	C₂³	1	1	yes	characteristic
434	C₄×C₂²⋊C₄	—	2	1	no	—
435	#376	—	2	1	no	—
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	#336	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	#336	C₂³	1	1	yes	characteristic
482	#336	C₂³	1	1	yes	characteristic
483	#336	C₂³	1	1	yes	characteristic
484	C₂⁵	—	2	1	no	—
485	C₂²×Q₈	C₂×D₄	1	1	yes	characteristic
486	C₂²×Q₈	C₂×D₄	1	1	yes	characteristic
487	C₂²×Q₈	C₂×D₄	1	1	yes	characteristic
488	C₂²×Q₈	C₂×D₄	1	1	yes	characteristic
489	C₂²×D₄	—	2	2	no	—
490	C₂²×D₄	—	2	2	no	—
491	C₂²×D₄	—	2	1	no	—
492	C₂²×D₄	—	2	2	no	—
493	C₂²×D₄	—	2	2	no	—
494	C₂²×D₄	—	4	1	no	—
495	C₂²×D₄	—	4	1	no	—
496	C₂²×D₄	C₂⁴	1	1	yes	characteristic
497	C₂²×D₄	C₂⁴	1	1	yes	characteristic
498	C₂³×C₄	—	2	1	no	—
499	C₂³×C₄	—	2	1	no	—
500	C₂³×C₄	—	2	1	no	—
501	C₂³×C₄	—	2	1	no	—
502	C₂³×C₄	—	2	1	no	—
503	C₂³×C₄	C₂×D₄	1	1	yes	characteristic
504	C₂³×C₄	C₂×D₄	1	1	yes	characteristic
505	C₂³×C₄	C₂⁴	1	1	yes	characteristic
506	C₂²×C₈	C₂⁴	1	1	yes	characteristic
507	C₂²×C₈	C₂⁴	1	1	yes	characteristic
508	C₂²×C₈	C₂⁴	1	1	yes	characteristic
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	C₄⋊Q₈	—	2	4	no	—
515	C₄⋊Q₈	—	2	4	no	—
516	#125	—	2	4	no	—
517	#125	—	2	4	no	—
518	C₂²⋊Q₈	—	2	4	no	—
519	C₂²⋊Q₈	—	2	4	no	—
520	C₂²⋊Q₈	—	2	4	no	—
521	C₂²⋊Q₈	—	2	4	no	—
522	C₂²⋊Q₈	—	8	2	no	—
523	C₂²⋊Q₈	—	8	2	no	—
524	C₂²⋊Q₈	—	8	2	no	—
525	C₂²⋊Q₈	—	8	2	no	—
526	C₄×Q₈	—	2	2	no	—
527	C₄×Q₈	—	2	2	no	—
528	C₄×Q₈	—	2	2	no	—
529	C₄×Q₈	—	2	2	no	—
530	C₄×Q₈	—	2	2	no	—
531	C₄×Q₈	—	2	2	no	—
532	C₄×Q₈	—	2	2	no	—
533	C₄×Q₈	—	2	2	no	—
534	C₄×Q₈	—	8	2	no	—
535	C₄×Q₈	—	8	2	no	—
536	C₄×D₄	—	2	2	no	—
537	C₄×D₄	—	2	2	no	—
538	C₄×D₄	—	2	2	no	—
539	C₄×D₄	—	2	2	no	—
540	C₄×D₄	—	2	2	no	—
541	C₄×D₄	—	2	2	no	—
542	C₄×D₄	—	2	2	no	—
543	C₄×D₄	—	2	2	no	—
544	C₄×D₄	—	4	4	no	—
545	C₄×D₄	—	4	4	no	—
546	#117	—	2	2	no	—
547	#117	—	2	2	no	—
548	#117	—	2	2	no	—
549	#117	—	2	2	no	—
550	#117	—	4	1	no	—
551	#117	—	4	1	no	—
552	#117	—	8	2	no	—
553	#117	#41	1	4	yes	—
554	#117	#41	1	4	yes	—
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	—	2	1	no	—
580	C₂×C₄⋊C₄	—	4	1	no	—
581	C₂×C₄⋊C₄	—	4	1	no	—
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	C₂×D₄	1	1	yes	characteristic
586	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
587	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
588	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
589	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
590	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
591	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
592	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
593	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
594	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
595	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
596	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
597	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
598	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
599	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
600	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
601	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
602	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
603	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
604	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
605	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
606	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
607	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
608	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
609	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
610	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
611	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
612	C₂×C₂²⋊C₄	—	2	1	no	—
613	C₂×C₂²⋊C₄	—	2	1	no	—
614	C₂×C₂²⋊C₄	—	2	1	no	—
615	C₂×C₂²⋊C₄	—	2	1	no	—
616	C₂×C₂²⋊C₄	—	2	1	no	—
617	C₂×C₂²⋊C₄	—	2	1	no	—
618	C₂×C₂²⋊C₄	—	2	1	no	—
619	C₂×C₂²⋊C₄	—	2	1	no	—
620	C₂×C₂²⋊C₄	—	2	1	no	—
621	C₂×C₂²⋊C₄	—	2	1	no	—
622	C₂×C₂²⋊C₄	—	2	1	no	—
623	C₂×C₂²⋊C₄	—	2	1	no	—
624	C₂×C₂²⋊C₄	—	2	1	no	—
625	C₂×C₂²⋊C₄	—	2	1	no	—
626	C₂×C₂²⋊C₄	—	2	1	no	—
627	C₂×C₂²⋊C₄	—	2	1	no	—
628	C₂×C₂²⋊C₄	—	2	1	no	—
629	C₂×C₂²⋊C₄	—	2	1	no	—
630	C₂×C₂²⋊C₄	—	2	1	no	—
631	C₂×C₂²⋊C₄	—	2	1	no	—
632	C₂×C₂²⋊C₄	—	2	1	no	—
633	C₂×C₂²⋊C₄	—	2	1	no	—
634	C₂×C₂²⋊C₄	—	2	1	no	—
635	C₂×C₂²⋊C₄	—	2	1	no	—
636	C₂×C₂²⋊C₄	—	2	1	no	—
637	C₂×C₂²⋊C₄	—	2	1	no	—
638	C₂×C₂²⋊C₄	—	4	4	no	—
639	C₂×C₂²⋊C₄	—	4	4	no	—
640	C₂×C₂²⋊C₄	—	8	2	no	—
641	C₂×C₂²⋊C₄	—	8	2	no	—
642	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
643	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
644	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
645	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
646	C₂×C₄²	—	2	2	no	—
647	C₂×C₄²	—	2	2	no	—
648	C₂×C₄²	—	2	1	no	—
649	C₂×C₄²	—	2	1	no	—
650	C₂×C₄²	—	2	1	no	—
651	C₂×C₄²	—	2	1	no	—
652	C₂×C₄²	—	2	1	no	—
653	C₂×C₄²	—	2	1	no	—
654	C₂×C₄²	—	2	1	no	—
655	C₂×C₄²	—	2	1	no	—
656	C₂×C₄²	—	2	1	no	—
657	C₂×C₄²	—	2	1	no	—
658	C₂×C₄²	—	2	1	no	—
659	C₂×C₄²	—	2	1	no	—
660	C₂×C₄²	—	2	1	no	—
661	C₂×C₄²	—	2	1	no	—
662	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
663	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
664	C₂×C₄²	C₂⁴	1	1	yes	characteristic
665	C₂×C₄²	C₂⁴	1	1	yes	characteristic
666	C₂×C₄²	C₂⁴	1	1	yes	characteristic
667	C₂×C₄²	C₂⁴	1	1	yes	characteristic
668	C₂×C₄²	C₂⁴	1	1	yes	characteristic
669	C₂×C₄²	C₂⁴	1	1	yes	characteristic
670	#107	—	4	1	no	—
671	#107	—	4	1	no	—
672	#107	—	4	1	no	—
673	#107	—	4	1	no	—
674	#107	—	4	1	no	—
675	#107	—	4	1	no	—
676	#107	—	4	1	no	—
677	#107	—	4	1	no	—
678	#107	—	4	1	no	—
679	#107	—	4	1	no	—
680	#106	—	4	1	no	—
681	#106	—	4	1	no	—
682	#106	—	4	1	no	—
683	#106	—	4	1	no	—
684	#106	—	4	1	no	—
685	#106	—	4	1	no	—
686	C₄⋊C₈	—	2	2	no	—
687	C₄⋊C₈	—	2	2	no	—
688	C₄⋊C₈	—	2	2	no	—
689	C₄⋊C₈	—	2	2	no	—
690	#102	—	2	2	no	—
691	#102	—	2	2	no	—
692	#102	—	2	2	no	—
693	#102	—	2	2	no	—
694	#102	—	2	2	no	—
695	#102	—	2	2	no	—
696	#102	—	2	2	no	—
697	#102	—	2	2	no	—
698	#102	—	4	1	no	—
699	#102	—	4	1	no	—
700	#102	—	4	1	no	—
701	#102	—	4	1	no	—
702	#102	—	4	1	no	—
703	#102	—	4	1	no	—
704	#102	—	4	1	no	—
705	#102	—	4	1	no	—
706	C₂²⋊C₈	—	2	2	no	—
707	C₂²⋊C₈	—	2	2	no	—
708	C₂²⋊C₈	—	2	2	no	—
709	C₂²⋊C₈	—	2	2	no	—
710	#97	—	2	2	no	—
711	#97	—	2	2	no	—
712	C₄×C₈	—	2	2	no	—
713	C₄×C₈	—	2	2	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	—	2	1	no	—
748	#95	—	2	1	no	—
749	#95	—	2	1	no	—
750	#95	—	2	1	no	—
751	#95	—	2	1	no	—
752	#95	—	2	1	no	—
753	#95	—	2	1	no	—
754	C₂⁴	—	2	4	no	—
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	C₂²×D₄	1	1	yes	characteristic
764	C₂×Q₈	—	2	2	no	—
765	C₂×Q₈	—	2	2	no	—
766	C₂×Q₈	—	2	2	no	—
767	C₂×Q₈	—	2	2	no	—
768	C₂×Q₈	—	2	2	no	—
769	C₂×Q₈	—	2	2	no	—
770	C₂×Q₈	—	4	1	no	—
771	C₂×Q₈	—	4	1	no	—
772	C₂×Q₈	—	4	1	no	—
773	C₂×Q₈	—	4	1	no	—
774	C₂×Q₈	—	4	1	no	—
775	C₂×Q₈	—	4	1	no	—
776	C₂×D₄	—	2	4	no	—
777	C₂×D₄	—	2	1	no	—
778	C₂×D₄	—	2	1	no	—
779	C₂×D₄	—	2	1	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	—	4	4	no	—
788	C₂×D₄	—	4	4	no	—
789	C₂×D₄	—	4	4	no	—
790	C₂×D₄	—	4	4	no	—
791	C₂×D₄	—	4	2	no	—
792	C₂×D₄	—	4	2	no	—
793	C₂×D₄	2₋¹⁺⁴	1	2	yes	—
794	C₂×D₄	2₋¹⁺⁴	1	2	yes	—
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	2	no	—
800	C₂²×C₄	—	2	2	no	—
801	C₂²×C₄	—	2	2	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	—	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	—	4	1	no	—
817	C₂²×C₄	—	4	1	no	—
818	C₂²×C₄	—	4	1	no	—
819	C₂²×C₄	—	4	2	no	—
820	C₂²×C₄	—	4	2	no	—
821	C₂²×C₄	—	4	2	no	—
822	C₂²×C₄	—	4	2	no	—
823	C₂²×C₄	—	4	2	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	—	8	1	no	—
829	C₂²×C₄	—	8	1	no	—
830	C₂²×C₄	—	8	1	no	—
831	C₂²×C₄	—	8	1	no	—
832	C₂²×C₄	—	8	1	no	—
833	C₂²×C₄	—	8	1	no	—
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	C₂²×D₄	1	1	yes	characteristic
839	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
840	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
841	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
842	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
843	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
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	C₂×#41	1	2	yes	—
848	C₂²×C₄	C₂×#41	1	2	yes	—
849	C₂²×C₄	C₂⁵	1	1	yes	characteristic
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	—	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	C₄⋊C₄	—	2	2	no	—
875	C₄⋊C₄	—	2	2	no	—
876	C₄⋊C₄	—	2	2	no	—
877	C₄⋊C₄	—	2	2	no	—
878	C₄⋊C₄	—	2	2	no	—
879	C₄⋊C₄	—	2	2	no	—
880	C₄⋊C₄	—	2	2	no	—
881	C₄⋊C₄	—	2	2	no	—
882	C₄⋊C₄	—	2	2	no	—
883	C₄⋊C₄	—	2	2	no	—
884	C₄⋊C₄	—	2	2	no	—
885	C₄⋊C₄	—	2	2	no	—
886	C₄⋊C₄	—	2	2	no	—
887	C₄⋊C₄	—	2	2	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	—	2	1	no	—
909	C₄⋊C₄	—	2	1	no	—
910	C₄⋊C₄	—	2	1	no	—
911	C₄⋊C₄	—	2	1	no	—
912	C₄⋊C₄	—	2	1	no	—
913	C₄⋊C₄	—	2	1	no	—
914	C₄⋊C₄	—	2	1	no	—
915	C₄⋊C₄	—	2	1	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	—	4	2	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	—	8	1	no	—
937	C₄⋊C₄	—	8	1	no	—
938	C₄⋊C₄	—	8	1	no	—
939	C₄⋊C₄	—	8	1	no	—
940	C₄⋊C₄	—	8	1	no	—
941	C₄⋊C₄	#123	1	4	yes	—
942	C₄⋊C₄	#123	1	4	yes	—
943	C₂²⋊C₄	—	2	2	no	—
944	C₂²⋊C₄	—	2	2	no	—
945	C₂²⋊C₄	—	4	2	no	—
946	C₂²⋊C₄	—	4	2	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	—	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	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	#123	1	4	yes	—
972	C₂²⋊C₄	#123	1	4	yes	—
973	C₄²	—	2	2	no	—
974	C₄²	—	2	2	no	—
975	C₄²	—	2	1	no	—
976	C₄²	—	2	1	no	—
977	C₄²	—	2	1	no	—
978	C₄²	—	2	1	no	—
979	C₄²	—	2	1	no	—
980	C₄²	—	2	1	no	—
981	C₄²	—	2	1	no	—
982	C₄²	—	2	1	no	—
983	C₄²	—	4	2	no	—
984	C₄²	—	4	2	no	—
985	C₄²	—	4	2	no	—
986	C₄²	—	4	2	no	—
987	C₄²	—	8	1	no	—
988	C₄²	—	8	1	no	—
989	C₄²	—	8	1	no	—
990	C₄²	—	8	1	no	—
991	C₄²	—	8	1	no	—
992	C₄²	—	8	1	no	—
993	C₄²	—	8	1	no	—
994	C₄²	—	8	1	no	—
995	C₄²	—	8	1	no	—
996	C₄²	—	8	1	no	—
997	C₄²	C₂×#41	1	2	yes	—
998	C₄²	C₂×#41	1	2	yes	—
999	C₄²	C₂×#41	1	2	yes	—
1000	C₄²	C₂×#41	1	2	yes	—
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	2	no	—
1008	C₂³	—	2	2	no	—
1009	C₂³	—	4	8	no	—
1010	C₂³	—	4	1	no	—
1011	C₂³	—	4	1	no	—
1012	C₂³	—	4	1	no	—
1013	C₂³	—	4	1	no	—
1014	C₂³	—	4	1	no	—
1015	C₂³	—	4	1	no	—
1016	C₂³	—	4	1	no	—
1017	C₂³	—	4	1	no	—
1018	C₂³	—	4	1	no	—
1019	C₂³	—	4	1	no	—
1020	C₂³	—	4	1	no	—
1021	C₂³	—	4	1	no	—
1022	C₂³	—	8	4	no	—
1023	C₂³	—	8	4	no	—
1024	C₂³	—	16	2	no	—
1025	C₂³	—	16	2	no	—
1026	C₂³	—	16	2	no	—
1027	C₂³	—	16	2	no	—
1028	C₂³	C₂×#123	1	2	yes	—
1029	C₂³	C₂³×D₄	1	1	yes	characteristic
1030	Q₈	—	4	4	no	—
1031	Q₈	—	4	4	no	—
1032	Q₈	—	8	2	no	—
1033	Q₈	—	8	2	no	—
1034	D₄	—	2	2	no	—
1035	D₄	—	2	2	no	—
1036	D₄	—	2	2	no	—
1037	D₄	—	2	2	no	—
1038	D₄	—	4	8	no	—
1039	D₄	—	4	1	no	—
1040	D₄	—	4	1	no	—
1041	D₄	—	4	1	no	—
1042	D₄	—	4	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	2	no	—
1056	C₂×C₄	—	2	2	no	—
1057	C₂×C₄	—	2	2	no	—
1058	C₂×C₄	—	2	2	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	1	no	—
1071	C₂×C₄	—	2	1	no	—
1072	C₂×C₄	—	2	1	no	—
1073	C₂×C₄	—	2	1	no	—
1074	C₂×C₄	—	2	1	no	—
1075	C₂×C₄	—	2	1	no	—
1076	C₂×C₄	—	2	1	no	—
1077	C₂×C₄	—	2	1	no	—
1078	C₂×C₄	—	2	1	no	—
1079	C₂×C₄	—	2	1	no	—
1080	C₂×C₄	—	4	4	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	—	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	—	8	2	no	—
1124	C₂×C₄	—	16	2	no	—
1125	C₂×C₄	—	16	2	no	—
1126	C₂×C₄	—	16	2	no	—
1127	C₂×C₄	—	16	2	no	—
1128	C₂×C₄	—	16	2	no	—
1129	C₂×C₄	C₂×#123	1	2	yes	—
1130	C₂×C₄	C₂×#123	1	2	yes	—
1131	C₂×C₄	C₂×#123	1	2	yes	—
1132	C₂×C₄	C₂×#123	1	2	yes	—
1133	C₂×C₄	C₂×#123	1	2	yes	—
1134	C₂×C₄	#576	1	2	yes	—
1135	C₂×C₄	C₂²×#41	1	1	yes	characteristic
1136	C₂×C₄	C₂²×#41	1	1	yes	characteristic
1137	C₂×C₄	C₂×2₋¹⁺⁴	1	1	yes	characteristic
1138	C₂×C₄	C₂×2₋¹⁺⁴	1	1	yes	characteristic
1139	C₂×C₄	#585	1	1	yes	characteristic
1140	C₂×C₄	#585	1	1	yes	characteristic
1141	C₈	—	4	1	no	—
1142	C₈	—	4	1	no	—
1143	C₈	—	4	1	no	—
1144	C₈	—	4	1	no	—
1145	C₈	—	4	1	no	—
1146	C₈	—	4	1	no	—
1147	C₈	—	4	1	no	—
1148	C₈	—	4	1	no	—
1149	C₂²	—	2	2	no	—
1150	C₂²	—	2	2	no	—
1151	C₂²	—	2	2	no	—
1152	C₂²	—	4	1	no	—
1153	C₂²	—	4	1	no	—
1154	C₂²	—	4	1	no	—
1155	C₂²	—	4	1	no	—
1156	C₂²	—	4	2	no	—
1157	C₂²	—	4	2	no	—
1158	C₂²	—	4	2	no	—
1159	C₂²	—	4	2	no	—
1160	C₂²	—	4	2	no	—
1161	C₂²	—	4	2	no	—
1162	C₂²	—	8	1	no	—
1163	C₂²	—	8	1	no	—
1164	C₂²	—	8	1	no	—
1165	C₂²	—	8	1	no	—
1166	C₂²	—	8	1	no	—
1167	C₂²	—	8	1	no	—
1168	C₂²	—	8	1	no	—
1169	C₂²	—	8	1	no	—
1170	C₂²	—	16	8	no	—
1171	C₂²	C₂²×#123	1	1	yes	characteristic
1172	C₂²	#3486	1	1	yes	characteristic
1173	C₂²	#3487	1	1	yes	characteristic
1174	C₂²	C₂×#576	1	1	yes	characteristic
1175	C₂²	#3584	1	1	yes	characteristic
1176	C₂²	#3585	1	1	yes	characteristic
1177	C₂²	#3586	1	1	yes	characteristic
1178	C₄	—	2	2	no	—
1179	C₄	—	2	2	no	—
1180	C₄	—	2	2	no	—
1181	C₄	—	2	2	no	—
1182	C₄	—	2	2	no	—
1183	C₄	—	2	2	no	—
1184	C₄	—	4	1	no	—
1185	C₄	—	4	1	no	—
1186	C₄	—	4	1	no	—
1187	C₄	—	4	1	no	—
1188	C₄	—	4	1	no	—
1189	C₄	—	4	1	no	—
1190	C₄	—	4	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	—	8	1	no	—
1200	C₄	—	8	1	no	—
1201	C₄	—	8	1	no	—
1202	C₄	—	8	1	no	—
1203	C₄	—	8	1	no	—
1204	C₄	—	8	1	no	—
1205	C₄	#3495	1	1	yes	characteristic
1206	C₄	#3495	1	1	yes	characteristic
1207	C₄	#3495	1	1	yes	characteristic
1208	C₄	#3495	1	1	yes	characteristic
1209	C₂	—	4	2	no	—
1210	C₂	—	8	2	no	—
1211	C₂	—	8	2	no	—
1212	C₂	#35672	1	1	yes	characteristic
1213	C₂	#60521	1	1	yes	characteristic
1214	C₂	#60523	1	1	yes	characteristic
1215	C₂	#61863	1	1	yes	characteristic
1216	C₂	#61873	1	1	yes	characteristic
1217	C₂	#61920	1	1	yes	characteristic
1218	C₂	#61925	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³	C₂³×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁵
prime radical	C₂³×D₄	C₂³
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³ ◁ C₂×#533 ◁ G
LECS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
2. #34373	C₂	semidirect
3. #27623	C₂	semidirect
4. #27620	C₂	semidirect
5. #27618	C₂	semidirect
6. #27615	C₂	semidirect
11. #25072	C₂	semidirect
12. #25072	C₂	semidirect
13. #25069	C₂	semidirect
14. #25068	C₂	semidirect
15. #25065	C₂	semidirect
16. #25064	C₂	semidirect
17. #25057	C₂	semidirect
18. #25056	C₂	semidirect
19. #25007	C₂	semidirect
20. #25006	C₂	semidirect
21. #25003	C₂	semidirect
22. #25002	C₂	semidirect
23. #24998	C₂	semidirect
24. #24998	C₂	semidirect
25. #24993	C₂	semidirect
26. #24990	C₂	semidirect
27. #21992	C₂	semidirect
28. #21991	C₂	semidirect
29. #21824	C₂	semidirect
56. #2355	C₂²	semidirect
57. #2355	C₂²	semidirect
58. #2355	C₂²	semidirect
59. #2355	C₂²	semidirect
60. #2355	C₂²	semidirect
61. #2355	C₂²	semidirect
62. Q₈×C₄⋊C₄	C₂²	semidirect
63. Q₈×C₄⋊C₄	C₂²	semidirect
79. #2101	C₂²	semidirect
80. #2101	C₂²	semidirect
81. #2101	C₂²	semidirect
82. #2101	C₂²	semidirect
83. #2100	C₂²	semidirect
84. #2099	C₂²	semidirect
85. #2099	C₂²	semidirect
86. #2099	C₂²	semidirect
95. #2085	C₂²	semidirect
96. #2085	C₂²	semidirect
97. #2085	C₂²	semidirect
98. #2085	C₂²	semidirect
99. #2084	C₂²	semidirect
100. #2083	C₂²	semidirect
101. #2083	C₂²	semidirect
102. #2083	C₂²	semidirect
111. #1985	C₂²	semidirect
112. #1985	C₂²	semidirect
113. #1985	C₂²	semidirect
114. #1985	C₂²	semidirect
115. #1984	C₂²	semidirect
116. #1984	C₂²	semidirect
117. #1984	C₂²	semidirect
118. #1984	C₂²	semidirect
119. #1949	C₂²	semidirect
120. #1949	C₂²	semidirect
121. #1949	C₂²	semidirect
122. #1949	C₂²	semidirect
123. #1948	C₂²	semidirect
124. #1947	C₂²	semidirect
125. #1947	C₂²	semidirect
126. #1947	C₂²	semidirect
143. #1921	C₂²	semidirect
144. #1921	C₂²	semidirect
145. #1921	C₂²	semidirect
146. #1921	C₂²	semidirect
147. #1921	C₂²	semidirect
148. #1921	C₂²	semidirect
149. #1920	C₂²	semidirect
150. #1920	C₂²	semidirect
151. #1919	C₂²	semidirect
152. #1919	C₂²	semidirect
153. #1919	C₂²	semidirect
154. #1919	C₂²	semidirect
155. #1918	C₂²	semidirect
156. #1918	C₂²	semidirect
157. #1918	C₂²	semidirect
158. #1918	C₂²	semidirect
167. #1847	C₂²	semidirect
168. #1847	C₂²	semidirect
169. #1846	C₂²	semidirect
170. #1845	C₂²	semidirect
171. #1836	C₂²	semidirect
172. #1836	C₂²	semidirect
173. #1835	C₂²	semidirect
174. #1834	C₂²	semidirect

Maximal subgroups

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

subgroup	index
#35515	2
#34373	2
#27623	2
#27620	2
#27618	2
#27615	2
#27594	2
#27591	2
#27588	2
#27582	2
#25072	2
#25069	2
#25068	2
#25065	2
#25064	2
#25057	2
#25056	2
#25007	2
#25006	2
#25003	2
#25002	2
#24998	2
#24993	2
#24990	2
#21992	2
#21991	2
#21824	2
#20744	2