Subgroups — #6526885

Order 512.

2006 conjugacy classes of subgroups.

The subgroup lattice has 1196 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#3240	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#3233	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#3117	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#3108	C₂	1	1	yes	maximal, characteristic, complemented
5	#37542	C₂	1	1	yes	maximal, characteristic
6	#35179	C₂	1	1	yes	maximal, characteristic, complemented
7	#28550	C₂	1	1	yes	maximal, characteristic, complemented
8	#28547	C₂	1	1	yes	maximal, characteristic, complemented
9	#28546	C₂	1	1	yes	maximal, characteristic, complemented
10	#28543	C₂	1	1	yes	maximal, characteristic, complemented
11	#28538	C₂	1	1	yes	maximal, characteristic, complemented
12	#28537	C₂	1	1	yes	maximal, characteristic, complemented
13	#28535	C₂	1	1	yes	maximal, characteristic, complemented
14	#28533	C₂	1	1	yes	maximal, characteristic, complemented
15	#28436	C₂	1	1	yes	maximal, characteristic, complemented
16	#28432	C₂	1	1	yes	maximal, characteristic, complemented
17	#28428	C₂	1	1	yes	maximal, characteristic, complemented
18	#28424	C₂	1	1	yes	maximal, characteristic, complemented
19	#28412	C₂	1	1	yes	maximal, characteristic, complemented
20	#28411	C₂	1	1	yes	maximal, characteristic, complemented
21	#28408	C₂	1	1	yes	maximal, characteristic, complemented
22	#28407	C₂	1	1	yes	maximal, characteristic, complemented
23	#28324	C₂	1	1	yes	maximal, characteristic, complemented
24	#28324	C₂	1	1	yes	maximal, characteristic, complemented
25	#28323	C₂	1	1	yes	maximal, characteristic
26	#28322	C₂	1	1	yes	maximal, characteristic, complemented
27	#27923	C₂	1	1	yes	maximal, characteristic
28	#27922	C₂	1	1	yes	maximal, characteristic, complemented
29	#27921	C₂	1	1	yes	maximal, characteristic, complemented
30	#27920	C₂	1	1	yes	maximal, characteristic, complemented
31	#20537	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×#533	C₂²	1	1	yes	characteristic
33	C₂×#529	C₂²	1	1	yes	characteristic
34	C₂×#529	C₂²	1	1	yes	characteristic
35	C₂²×C₄×Q₈	C₂²	1	1	yes	characteristic
36	#3240	—	2	8	no	—
37	#3233	—	2	8	no	—
38	C₂×#501	C₂²	1	1	yes	characteristic
39	C₂×#501	C₂²	1	1	yes	characteristic
40	C₂×#499	C₂²	1	1	yes	characteristic
41	C₂×#499	C₂²	1	1	yes	characteristic
42	C₂×#489	C₂²	1	1	yes	characteristic
43	C₂×#489	C₂²	1	1	yes	characteristic
44	C₂×#488	C₂²	1	1	yes	characteristic
45	C₂×#488	C₂²	1	1	yes	characteristic
46	#3117	—	2	8	no	—
47	#3108	—	2	8	no	—
48	C₂×#484	C₂²	1	1	yes	characteristic
49	C₂×#481	C₂²	1	1	yes	characteristic
50	C₂×#485	C₂²	1	1	yes	characteristic
51	C₂×#485	C₂²	1	1	yes	characteristic
52	C₂×#485	C₂²	1	1	yes	characteristic
53	C₂×#485	C₂²	1	1	yes	characteristic
54	C₂×#482	C₂²	1	1	yes	characteristic
55	C₂×#482	C₂²	1	1	yes	characteristic
56	C₂×#482	C₂²	1	1	yes	characteristic
57	C₂×#482	C₂²	1	1	yes	characteristic
58	C₂×#483	C₂²	1	1	yes	characteristic
59	C₂×#480	C₂²	1	1	yes	characteristic
60	C₂×#479	C₂²	1	1	yes	characteristic
61	C₂×#479	C₂²	1	1	yes	characteristic
62	C₂×#479	C₂²	1	1	yes	characteristic
63	C₂×#479	C₂²	1	1	yes	characteristic
64	C₂×#479	C₂²	1	1	yes	characteristic
65	C₂×#479	C₂²	1	1	yes	characteristic
66	C₂×#477	C₂²	1	1	yes	characteristic
67	C₂×#475	C₂²	1	1	yes	characteristic
68	C₂×#478	C₂²	1	1	yes	characteristic
69	C₂×#478	C₂²	1	1	yes	characteristic
70	C₂×#476	C₂²	1	1	yes	characteristic
71	C₂×#474	C₂²	1	1	yes	characteristic
72	C₂×#464	C₂²	1	1	yes	characteristic
73	C₂×#464	C₂²	1	1	yes	characteristic
74	C₂×#464	C₂²	1	1	yes	characteristic
75	C₂×#464	C₂²	1	1	yes	characteristic
76	C₂×#451	C₂²	1	1	yes	characteristic
77	C₂×#451	C₂²	1	1	yes	characteristic
78	C₂×#448	C₂²	1	1	yes	characteristic
79	C₂×#448	C₂²	1	1	yes	characteristic
80	C₂×#441	C₂²	1	1	yes	characteristic
81	C₂×#441	C₂²	1	1	yes	characteristic
82	C₂×#440	C₂²	1	1	yes	characteristic
83	C₂×#440	C₂²	1	1	yes	characteristic
84	C₂×C₄×Q₁₆	C₂²	1	1	yes	characteristic
85	C₂×C₄×Q₁₆	C₂²	1	1	yes	characteristic
86	C₂×C₄×SD₁₆	C₂²	1	1	yes	characteristic
87	C₂×C₄×SD₁₆	C₂²	1	1	yes	characteristic
88	C₂×#432	C₂²	1	1	yes	characteristic
89	C₂×#431	C₂²	1	1	yes	characteristic
90	#2855	—	2	2	no	—
91	#2823	—	2	2	no	—
92	#2630	—	2	2	no	—
93	#2630	—	2	2	no	—
94	#2627	—	2	2	no	—
95	#2621	C₂²	1	1	yes	characteristic
96	#2620	C₂²	1	1	yes	characteristic
97	#2620	C₂²	1	1	yes	characteristic
98	#2619	C₂²	1	1	yes	characteristic
99	#2609	—	2	2	no	—
100	#2582	—	2	2	no	—
101	#2581	—	2	2	no	—
102	#2568	C₂²	1	1	yes	characteristic
103	#2568	C₂²	1	1	yes	characteristic
104	#2567	C₂²	1	1	yes	characteristic
105	#2567	C₂²	1	1	yes	characteristic
106	#2566	C₂²	1	1	yes	characteristic
107	#2566	C₂²	1	1	yes	characteristic
108	#2565	C₂²	1	1	yes	characteristic
109	#2565	C₂²	1	1	yes	characteristic
110	#2565	C₂²	1	1	yes	characteristic
111	#2565	C₂²	1	1	yes	characteristic
112	#2565	C₂²	1	1	yes	characteristic
113	#2565	C₂²	1	1	yes	characteristic
114	#2545	C₂²	1	1	yes	characteristic
115	#2545	C₂²	1	1	yes	characteristic
116	#2544	C₂²	1	1	yes	characteristic
117	#2544	C₂²	1	1	yes	characteristic
118	#2317	C₂²	1	1	yes	characteristic
119	#2317	C₂²	1	1	yes	characteristic
120	#2310	C₂²	1	1	yes	characteristic
121	#2310	C₂²	1	1	yes	characteristic
122	#2285	C₂²	1	1	yes	characteristic
123	#2097	C₂²	1	1	yes	characteristic
124	#2097	C₂²	1	1	yes	characteristic
125	#2097	C₂²	1	1	yes	characteristic
126	#2097	C₂²	1	1	yes	characteristic
127	#2097	C₂²	1	1	yes	characteristic
128	#2097	C₂²	1	1	yes	characteristic
129	#2097	C₂²	1	1	yes	characteristic
130	#2097	C₂²	1	1	yes	characteristic
131	#2096	C₂²	1	1	yes	characteristic
132	#2096	C₂²	1	1	yes	characteristic
133	#2096	C₂²	1	1	yes	characteristic
134	#2096	C₂²	1	1	yes	characteristic
135	#2095	C₂²	1	1	yes	characteristic
136	#2095	C₂²	1	1	yes	characteristic
137	#2095	C₂²	1	1	yes	characteristic
138	#2095	C₂²	1	1	yes	characteristic
139	#2094	C₂²	1	1	yes	characteristic
140	#2094	C₂²	1	1	yes	characteristic
141	#2093	C₂²	1	1	yes	characteristic
142	#2093	C₂²	1	1	yes	characteristic
143	#2092	C₂²	1	1	yes	characteristic
144	#2092	C₂²	1	1	yes	characteristic
145	#2092	C₂²	1	1	yes	characteristic
146	#2092	C₂²	1	1	yes	characteristic
147	#2016	C₂²	1	1	yes	characteristic
148	#2016	C₂²	1	1	yes	characteristic
149	#2015	C₂²	1	1	yes	characteristic
150	#2015	C₂²	1	1	yes	characteristic
151	#2015	C₂²	1	1	yes	characteristic
152	#2015	C₂²	1	1	yes	characteristic
153	#2014	C₂²	1	1	yes	characteristic
154	#2014	C₂²	1	1	yes	characteristic
155	#1973	C₂²	1	1	yes	characteristic
156	#1973	C₂²	1	1	yes	characteristic
157	#1973	C₂²	1	1	yes	characteristic
158	#1973	C₂²	1	1	yes	characteristic
159	#1971	C₂²	1	1	yes	characteristic
160	#1971	C₂²	1	1	yes	characteristic
161	#1971	C₂²	1	1	yes	characteristic
162	#1971	C₂²	1	1	yes	characteristic
163	#1969	C₂²	1	1	yes	characteristic
164	#1969	C₂²	1	1	yes	characteristic
165	#1969	C₂²	1	1	yes	characteristic
166	#1969	C₂²	1	1	yes	characteristic
167	#1968	C₂²	1	1	yes	characteristic
168	#1968	C₂²	1	1	yes	characteristic
169	#1968	C₂²	1	1	yes	characteristic
170	#1968	C₂²	1	1	yes	characteristic
171	#1961	C₂²	1	1	yes	characteristic
172	#1960	C₂²	1	1	yes	characteristic
173	#1959	C₂²	1	1	yes	characteristic
174	#1959	C₂²	1	1	yes	characteristic
175	#1958	C₂²	1	1	yes	characteristic
176	#1958	C₂²	1	1	yes	characteristic
177	#1957	C₂²	1	1	yes	characteristic
178	#1956	C₂²	1	1	yes	characteristic
179	#1847	C₂²	1	1	yes	characteristic
180	#1847	C₂²	1	1	yes	characteristic
181	#1847	C₂²	1	1	yes	characteristic
182	#1847	C₂²	1	1	yes	characteristic
183	#1846	C₂²	1	1	yes	characteristic
184	#1846	C₂²	1	1	yes	characteristic
185	#1845	C₂²	1	1	yes	characteristic
186	#1844	C₂²	1	1	yes	characteristic
187	#1771	C₂²	1	1	yes	characteristic
188	#1771	C₂²	1	1	yes	characteristic
189	#1771	C₂²	1	1	yes	characteristic
190	#1771	C₂²	1	1	yes	characteristic
191	#1770	C₂²	1	1	yes	characteristic
192	#1770	C₂²	1	1	yes	characteristic
193	C₈×C₄⋊C₄	C₂²	1	1	yes	characteristic
194	C₈×C₄⋊C₄	C₂²	1	1	yes	characteristic
195	#1750	C₂²	1	1	yes	characteristic
196	#1750	C₂²	1	1	yes	characteristic
197	#1750	C₂²	1	1	yes	characteristic
198	#1750	C₂²	1	1	yes	characteristic
199	C₂³×Q₈	C₂³	1	1	yes	characteristic
200	C₂²×Q₁₆	C₂³	1	1	yes	characteristic
201	C₂²×Q₁₆	C₂³	1	1	yes	characteristic
202	C₂²×Q₁₆	C₂³	1	1	yes	characteristic
203	C₂²×Q₁₆	C₂³	1	1	yes	characteristic
204	C₂²×SD₁₆	C₂³	1	1	yes	characteristic
205	C₂²×SD₁₆	C₂³	1	1	yes	characteristic
206	C₂²×SD₁₆	C₂³	1	1	yes	characteristic
207	C₂²×SD₁₆	C₂³	1	1	yes	characteristic
208	#533	—	2	4	no	—
209	#533	—	2	4	no	—
210	C₂×C₄⋊Q₈	C₂³	1	1	yes	characteristic
211	C₂×C₄⋊Q₈	C₂³	1	1	yes	characteristic
212	C₂×C₄⋊Q₈	C₂³	1	1	yes	characteristic
213	C₂×#127	C₂³	1	1	yes	characteristic
214	#529	—	2	4	no	—
215	#529	—	2	4	no	—
216	#529	—	2	4	no	—
217	#529	—	2	4	no	—
218	C₂×#126	—	2	1	no	—
219	C₂×#126	—	2	1	no	—
220	C₂×#125	C₂³	1	1	yes	characteristic
221	C₂×#125	C₂³	1	1	yes	characteristic
222	C₂×#125	C₂³	1	1	yes	characteristic
223	C₂×#125	C₂³	1	1	yes	characteristic
224	C₂×#124	C₂³	1	1	yes	characteristic
225	C₂×#124	C₂³	1	1	yes	characteristic
226	C₂×#124	C₂³	1	1	yes	characteristic
227	C₂×#124	C₂³	1	1	yes	characteristic
228	C₂×#123	—	2	1	no	—
229	C₂×#123	—	2	1	no	—
230	C₂×C₂²⋊Q₈	—	2	1	no	—
231	C₂×C₂²⋊Q₈	—	2	1	no	—
232	C₂×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
233	C₂×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
234	C₂×#121	C₂³	1	1	yes	characteristic
235	C₂×#121	C₂³	1	1	yes	characteristic
236	C₂×C₄×Q₈	—	2	1	no	—
237	C₂×C₄×Q₈	—	2	1	no	—
238	C₂×C₄×Q₈	—	2	1	no	—
239	C₂×C₄×Q₈	—	2	1	no	—
240	C₂×C₄×Q₈	—	2	4	no	—
241	C₂×C₄×Q₈	—	2	4	no	—
242	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
243	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
244	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
245	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
246	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
247	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
248	C₂×C₄×D₄	—	2	1	no	—
249	C₂×C₄×D₄	—	2	1	no	—
250	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
251	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
252	C₂×#117	—	2	1	no	—
253	C₂×#117	—	2	1	no	—
254	C₂×#117	C₂³	1	1	yes	characteristic
255	C₂×#117	C₂³	1	1	yes	characteristic
256	C₂×#117	C₂³	1	1	yes	characteristic
257	C₂×#117	C₂³	1	1	yes	characteristic
258	C₂²×C₄⋊C₄	—	2	1	no	—
259	C₂²×C₄⋊C₄	C₂³	1	1	yes	characteristic
260	C₂²×C₄²	—	2	1	no	—
261	C₂²×C₄²	C₂³	1	1	yes	characteristic
262	#501	—	2	4	no	—
263	#501	—	2	4	no	—
264	#499	—	2	4	no	—
265	#499	—	2	4	no	—
266	#489	—	2	4	no	—
267	#489	—	2	4	no	—
268	#488	—	2	4	no	—
269	#488	—	2	4	no	—
270	#485	—	2	4	no	—
271	#485	—	2	4	no	—
272	#485	—	2	4	no	—
273	#485	—	2	4	no	—
274	#484	—	2	4	no	—
275	#483	—	2	4	no	—
276	#482	—	2	4	no	—
277	#482	—	2	4	no	—
278	#482	—	2	4	no	—
279	#482	—	2	4	no	—
280	#481	—	2	4	no	—
281	#480	—	2	4	no	—
282	#479	—	2	4	no	—
283	#479	—	2	4	no	—
284	#479	—	2	4	no	—
285	#479	—	2	4	no	—
286	#479	—	2	4	no	—
287	#479	—	2	4	no	—
288	#478	—	2	4	no	—
289	#478	—	2	4	no	—
290	#477	—	2	4	no	—
291	#476	—	2	4	no	—
292	#475	—	2	4	no	—
293	#474	—	2	4	no	—
294	#464	—	2	4	no	—
295	#464	—	2	4	no	—
296	#464	—	2	4	no	—
297	#464	—	2	4	no	—
298	#451	—	2	4	no	—
299	#451	—	2	4	no	—
300	#448	—	2	4	no	—
301	#448	—	2	4	no	—
302	#441	—	2	4	no	—
303	#441	—	2	4	no	—
304	#440	—	2	4	no	—
305	#440	—	2	4	no	—
306	C₄×Q₁₆	—	2	4	no	—
307	C₄×Q₁₆	—	2	4	no	—
308	C₄×SD₁₆	—	2	4	no	—
309	C₄×SD₁₆	—	2	4	no	—
310	#432	D₄	1	8	yes	complemented
311	#431	D₄	1	8	yes	complemented
312	C₂×#107	C₂³	1	1	yes	characteristic
313	C₂×#107	C₂³	1	1	yes	characteristic
314	C₂×#107	C₂³	1	1	yes	characteristic
315	C₂×#107	C₂³	1	1	yes	characteristic
316	C₂×#107	C₂³	1	1	yes	characteristic
317	C₂×#107	C₂³	1	1	yes	characteristic
318	C₂×#107	C₂³	1	1	yes	characteristic
319	C₂×#107	C₂³	1	1	yes	characteristic
320	C₂×#107	C₂³	1	1	yes	characteristic
321	C₂×#107	C₂³	1	1	yes	characteristic
322	C₂×#107	C₂³	1	1	yes	characteristic
323	C₂×#107	C₂³	1	1	yes	characteristic
324	C₂×#106	C₂³	1	1	yes	characteristic
325	C₂×#106	C₂³	1	1	yes	characteristic
326	C₂×#106	C₂³	1	1	yes	characteristic
327	C₂×#106	C₂³	1	1	yes	characteristic
328	C₂×#106	C₂³	1	1	yes	characteristic
329	C₂×#106	C₂³	1	1	yes	characteristic
330	C₂×#106	C₂³	1	1	yes	characteristic
331	C₂×#106	C₂³	1	1	yes	characteristic
332	C₂×#106	C₂³	1	1	yes	characteristic
333	C₂×#106	C₂³	1	1	yes	characteristic
334	C₂×#106	C₂³	1	1	yes	characteristic
335	C₂×#106	C₂³	1	1	yes	characteristic
336	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
337	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
338	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
339	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
340	C₂×#103	C₂³	1	1	yes	characteristic
341	C₂×#103	C₂³	1	1	yes	characteristic
342	C₂×#103	C₂³	1	1	yes	characteristic
343	C₂×#103	C₂³	1	1	yes	characteristic
344	C₂×#103	C₂³	1	1	yes	characteristic
345	C₂×#103	C₂³	1	1	yes	characteristic
346	C₂×#103	C₂³	1	1	yes	characteristic
347	C₂×#103	C₂³	1	1	yes	characteristic
348	C₂×#103	C₂³	1	1	yes	characteristic
349	C₂×#103	C₂³	1	1	yes	characteristic
350	C₂×#103	C₂³	1	1	yes	characteristic
351	C₂×#103	C₂³	1	1	yes	characteristic
352	C₂×#103	C₂³	1	1	yes	characteristic
353	C₂×#103	C₂³	1	1	yes	characteristic
354	C₂×#103	C₂³	1	1	yes	characteristic
355	C₂×#103	C₂³	1	1	yes	characteristic
356	C₂×#103	C₂³	1	1	yes	characteristic
357	C₂×#103	C₂³	1	1	yes	characteristic
358	C₂×#103	C₂³	1	1	yes	characteristic
359	C₂×#103	C₂³	1	1	yes	characteristic
360	C₂×#102	C₂³	1	1	yes	characteristic
361	C₂×#102	C₂³	1	1	yes	characteristic
362	C₂×#102	C₂³	1	1	yes	characteristic
363	C₂×#102	C₂³	1	1	yes	characteristic
364	C₂×#102	C₂³	1	1	yes	characteristic
365	C₂×#102	C₂³	1	1	yes	characteristic
366	C₂×#102	C₂³	1	1	yes	characteristic
367	C₂×#102	C₂³	1	1	yes	characteristic
368	C₂×#102	C₂³	1	1	yes	characteristic
369	C₂×#102	C₂³	1	1	yes	characteristic
370	C₂×#102	C₂³	1	1	yes	characteristic
371	C₂×#102	C₂³	1	1	yes	characteristic
372	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
373	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
374	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
375	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
376	C₂×#97	C₂³	1	1	yes	characteristic
377	C₂×#97	C₂³	1	1	yes	characteristic
378	C₂×#97	C₂³	1	1	yes	characteristic
379	C₂×#97	C₂³	1	1	yes	characteristic
380	C₂×#97	C₂³	1	1	yes	characteristic
381	C₂×#97	C₂³	1	1	yes	characteristic
382	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
383	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
384	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
385	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
386	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
387	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
388	#400	—	2	2	no	—
389	#400	—	2	2	no	—
390	#398	—	2	2	no	—
391	#398	—	2	2	no	—
392	#398	—	2	2	no	—
393	#398	—	2	2	no	—
394	#398	—	2	2	no	—
395	#398	—	2	2	no	—
396	#398	—	2	2	no	—
397	#397	—	2	2	no	—
398	#396	—	2	2	no	—
399	#396	—	2	2	no	—
400	#396	—	2	2	no	—
401	#396	—	2	2	no	—
402	#396	—	2	2	no	—
403	#396	—	2	2	no	—
404	#395	—	2	2	no	—
405	#395	—	2	2	no	—
406	#394	—	2	2	no	—
407	#394	—	2	2	no	—
408	#394	—	2	2	no	—
409	#394	—	2	2	no	—
410	#394	—	2	2	no	—
411	#392	—	2	2	no	—
412	#391	—	2	2	no	—
413	#391	—	2	2	no	—
414	#391	—	2	2	no	—
415	#391	—	2	2	no	—
416	#391	C₂³	1	1	yes	characteristic
417	#391	C₂³	1	1	yes	characteristic
418	#391	C₂³	1	1	yes	characteristic
419	#391	C₂³	1	1	yes	characteristic
420	#391	C₂³	1	1	yes	characteristic
421	#391	C₂³	1	1	yes	characteristic
422	#391	C₂³	1	1	yes	characteristic
423	#391	C₂³	1	1	yes	characteristic
424	#391	C₂³	1	1	yes	characteristic
425	#391	C₂³	1	1	yes	characteristic
426	#391	C₂³	1	1	yes	characteristic
427	#391	C₂³	1	1	yes	characteristic
428	#390	C₂³	1	1	yes	characteristic
429	#390	C₂³	1	1	yes	characteristic
430	#390	C₂³	1	1	yes	characteristic
431	#390	C₂³	1	1	yes	characteristic
432	#389	—	2	2	no	—
433	#389	—	2	2	no	—
434	#389	—	2	2	no	—
435	#389	—	2	2	no	—
436	#388	—	2	2	no	—
437	#388	—	2	2	no	—
438	#387	—	2	2	no	—
439	#387	—	2	2	no	—
440	#387	—	2	2	no	—
441	#387	—	2	2	no	—
442	#387	—	2	2	no	—
443	#387	—	2	2	no	—
444	#386	—	2	2	no	—
445	#386	—	2	2	no	—
446	#385	—	2	2	no	—
447	#385	—	2	2	no	—
448	#385	—	2	2	no	—
449	#385	—	2	2	no	—
450	#384	D₄	1	2	yes	—
451	#384	C₂³	1	1	yes	characteristic
452	#384	C₂³	1	1	yes	characteristic
453	#384	C₂³	1	1	yes	characteristic
454	#384	C₂³	1	1	yes	characteristic
455	#384	C₂³	1	1	yes	characteristic
456	#384	C₂³	1	1	yes	characteristic
457	#382	D₄	1	2	yes	—
458	#382	C₂³	1	1	yes	characteristic
459	#382	C₂³	1	1	yes	characteristic
460	#382	C₂³	1	1	yes	characteristic
461	#382	C₂³	1	1	yes	characteristic
462	#382	C₂³	1	1	yes	characteristic
463	#382	C₂³	1	1	yes	characteristic
464	#381	—	2	2	no	—
465	#381	—	2	2	no	—
466	#380	D₄	1	2	yes	—
467	#380	D₄	1	2	yes	—
468	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
469	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
470	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
471	C₄×C₄⋊C₄	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	C₂²×Q₈	—	2	2	no	—
481	C₂²×Q₈	—	2	2	no	—
482	C₂²×Q₈	—	2	1	no	—
483	C₂²×Q₈	—	2	1	no	—
484	C₂²×Q₈	—	2	1	no	—
485	C₂²×Q₈	—	2	2	no	—
486	C₂²×Q₈	—	2	2	no	—
487	C₂²×Q₈	—	4	1	no	—
488	C₂²×Q₈	—	4	1	no	—
489	C₂²×Q₈	C₂⁴	1	1	yes	characteristic
490	C₂²×Q₈	C₂⁴	1	1	yes	characteristic
491	C₂²×Q₈	C₂⁴	1	1	yes	characteristic
492	C₂²×Q₈	C₂⁴	1	1	yes	characteristic
493	C₂²×D₄	—	2	1	no	—
494	C₂²×D₄	—	2	1	no	—
495	C₂²×D₄	—	2	2	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	C₂×D₄	1	1	yes	characteristic
503	C₂³×C₄	C₂×D₄	1	1	yes	characteristic
504	C₂³×C₄	C₂⁴	1	1	yes	characteristic
505	C₂×Q₁₆	—	2	2	no	—
506	C₂×Q₁₆	—	2	2	no	—
507	C₂×Q₁₆	—	2	2	no	—
508	C₂×Q₁₆	—	2	2	no	—
509	C₂×Q₁₆	—	2	2	no	—
510	C₂×Q₁₆	—	2	2	no	—
511	C₂×Q₁₆	—	2	2	no	—
512	C₂×Q₁₆	—	2	2	no	—
513	C₂×Q₁₆	—	4	1	no	—
514	C₂×Q₁₆	—	4	1	no	—
515	C₂×Q₁₆	—	4	1	no	—
516	C₂×Q₁₆	—	4	1	no	—
517	C₂×SD₁₆	—	2	2	no	—
518	C₂×SD₁₆	—	2	2	no	—
519	C₂×SD₁₆	—	2	2	no	—
520	C₂×SD₁₆	—	2	2	no	—
521	C₂×SD₁₆	—	2	2	no	—
522	C₂×SD₁₆	—	2	2	no	—
523	C₂×SD₁₆	—	2	2	no	—
524	C₂×SD₁₆	—	2	2	no	—
525	C₂×SD₁₆	—	4	1	no	—
526	C₂×SD₁₆	—	4	1	no	—
527	C₂×SD₁₆	—	4	1	no	—
528	C₂×SD₁₆	—	4	1	no	—
529	C₂²×C₈	C₂⁴	1	1	yes	characteristic
530	C₂²×C₈	C₂⁴	1	1	yes	characteristic
531	C₂²×C₈	C₂⁴	1	1	yes	characteristic
532	C₂²×C₈	C₂⁴	1	1	yes	characteristic
533	C₂²×C₈	C₂⁴	1	1	yes	characteristic
534	C₂²×C₈	C₂⁴	1	1	yes	characteristic
535	C₂²×C₈	C₂⁴	1	1	yes	characteristic
536	C₂²×C₈	C₂⁴	1	1	yes	characteristic
537	C₄⋊Q₈	—	2	2	no	—
538	C₄⋊Q₈	—	2	2	no	—
539	C₄⋊Q₈	—	2	2	no	—
540	C₄⋊Q₈	—	2	2	no	—
541	C₄⋊Q₈	—	4	1	no	—
542	C₄⋊Q₈	—	4	1	no	—
543	#127	—	4	1	no	—
544	#127	—	4	1	no	—
545	#126	—	4	4	no	—
546	#126	—	4	4	no	—
547	#125	—	2	2	no	—
548	#125	—	2	2	no	—
549	#125	—	2	2	no	—
550	#125	—	2	2	no	—
551	#125	—	2	2	no	—
552	#125	—	2	2	no	—
553	#125	—	2	2	no	—
554	#125	—	2	2	no	—
555	#124	—	2	2	no	—
556	#124	—	2	2	no	—
557	#124	—	2	2	no	—
558	#124	—	2	2	no	—
559	#124	—	4	1	no	—
560	#124	—	4	1	no	—
561	#124	—	4	1	no	—
562	#124	—	4	1	no	—
563	#123	—	4	4	no	—
564	#123	—	4	4	no	—
565	C₂²⋊Q₈	—	2	2	no	—
566	C₂²⋊Q₈	—	2	2	no	—
567	C₂²⋊Q₈	—	2	2	no	—
568	C₂²⋊Q₈	—	2	2	no	—
569	C₂²⋊Q₈	—	4	4	no	—
570	C₂²⋊Q₈	—	4	4	no	—
571	#121	—	2	2	no	—
572	#121	—	2	2	no	—
573	#121	—	2	2	no	—
574	#121	—	2	2	no	—
575	C₄×Q₈	—	2	2	no	—
576	C₄×Q₈	—	2	2	no	—
577	C₄×Q₈	—	2	2	no	—
578	C₄×Q₈	—	2	2	no	—
579	C₄×Q₈	—	2	2	no	—
580	C₄×Q₈	—	2	2	no	—
581	C₄×Q₈	—	2	2	no	—
582	C₄×Q₈	—	2	2	no	—
583	C₄×Q₈	—	2	2	no	—
584	C₄×Q₈	—	2	2	no	—
585	C₄×Q₈	—	2	2	no	—
586	C₄×Q₈	—	2	2	no	—
587	C₄×Q₈	—	4	4	no	—
588	C₄×Q₈	—	4	4	no	—
589	C₄×Q₈	—	4	4	no	—
590	C₄×Q₈	—	4	4	no	—
591	C₄×D₄	—	2	2	no	—
592	C₄×D₄	—	2	2	no	—
593	C₄×D₄	—	2	2	no	—
594	C₄×D₄	—	2	2	no	—
595	C₄×D₄	—	4	4	no	—
596	C₄×D₄	—	4	4	no	—
597	#117	—	2	2	no	—
598	#117	—	2	2	no	—
599	#117	—	2	2	no	—
600	#117	—	2	2	no	—
601	#117	—	4	1	no	—
602	#117	—	4	1	no	—
603	#117	—	4	1	no	—
604	#117	—	4	1	no	—
605	#117	—	4	4	no	—
606	#117	—	4	4	no	—
607	C₂×C₄⋊C₄	—	2	2	no	—
608	C₂×C₄⋊C₄	—	2	2	no	—
609	C₂×C₄⋊C₄	—	2	1	no	—
610	C₂×C₄⋊C₄	—	2	1	no	—
611	C₂×C₄⋊C₄	—	2	1	no	—
612	C₂×C₄⋊C₄	—	2	1	no	—
613	C₂×C₄⋊C₄	—	2	1	no	—
614	C₂×C₄⋊C₄	—	2	1	no	—
615	C₂×C₄⋊C₄	—	2	1	no	—
616	C₂×C₄⋊C₄	—	2	1	no	—
617	C₂×C₄⋊C₄	—	2	1	no	—
618	C₂×C₄⋊C₄	—	2	1	no	—
619	C₂×C₄⋊C₄	—	2	1	no	—
620	C₂×C₄⋊C₄	—	2	1	no	—
621	C₂×C₄⋊C₄	—	2	1	no	—
622	C₂×C₄⋊C₄	—	2	1	no	—
623	C₂×C₄⋊C₄	—	2	1	no	—
624	C₂×C₄⋊C₄	—	2	1	no	—
625	C₂×C₄⋊C₄	—	2	1	no	—
626	C₂×C₄⋊C₄	—	2	1	no	—
627	C₂×C₄⋊C₄	—	2	1	no	—
628	C₂×C₄⋊C₄	—	2	2	no	—
629	C₂×C₄⋊C₄	—	2	2	no	—
630	C₂×C₄⋊C₄	—	2	2	no	—
631	C₂×C₄⋊C₄	—	2	2	no	—
632	C₂×C₄⋊C₄	—	2	2	no	—
633	C₂×C₄⋊C₄	—	2	2	no	—
634	C₂×C₄⋊C₄	—	2	2	no	—
635	C₂×C₄⋊C₄	—	4	4	no	—
636	C₂×C₄⋊C₄	C₂×D₄	1	2	yes	—
637	C₂×C₄⋊C₄	C₂×D₄	1	2	yes	—
638	C₂×C₄⋊C₄	C₂×D₄	1	2	yes	—
639	C₂×C₄⋊C₄	C₂×D₄	1	2	yes	—
640	C₂×C₄⋊C₄	C₂×D₄	1	2	yes	—
641	C₂×C₄⋊C₄	C₂×D₄	1	2	yes	—
642	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
643	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
644	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
645	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
646	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
647	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
648	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
649	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
650	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
651	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
652	C₂×C₂²⋊C₄	—	2	1	no	—
653	C₂×C₂²⋊C₄	—	2	1	no	—
654	C₂×C₂²⋊C₄	—	2	1	no	—
655	C₂×C₂²⋊C₄	—	2	1	no	—
656	C₂×C₂²⋊C₄	—	2	1	no	—
657	C₂×C₂²⋊C₄	—	2	1	no	—
658	C₂×C₂²⋊C₄	—	2	1	no	—
659	C₂×C₂²⋊C₄	—	2	1	no	—
660	C₂×C₂²⋊C₄	—	2	1	no	—
661	C₂×C₂²⋊C₄	—	2	1	no	—
662	C₂×C₂²⋊C₄	—	2	1	no	—
663	C₂×C₂²⋊C₄	—	2	1	no	—
664	C₂×C₂²⋊C₄	—	2	2	no	—
665	C₂×C₂²⋊C₄	—	2	2	no	—
666	C₂×C₂²⋊C₄	—	2	2	no	—
667	C₂×C₂²⋊C₄	—	2	2	no	—
668	C₂×C₂²⋊C₄	—	2	2	no	—
669	C₂×C₂²⋊C₄	—	2	2	no	—
670	C₂×C₂²⋊C₄	C₂×D₄	1	2	yes	—
671	C₂×C₂²⋊C₄	C₂×D₄	1	2	yes	—
672	C₂×C₄²	—	2	1	no	—
673	C₂×C₄²	—	2	1	no	—
674	C₂×C₄²	—	2	1	no	—
675	C₂×C₄²	—	2	1	no	—
676	C₂×C₄²	—	2	1	no	—
677	C₂×C₄²	—	2	1	no	—
678	C₂×C₄²	—	2	1	no	—
679	C₂×C₄²	—	2	1	no	—
680	C₂×C₄²	—	4	4	no	—
681	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
682	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
683	C₂×C₄²	C₂×D₄	1	4	yes	—
684	C₂×C₄²	C₂×D₄	1	4	yes	—
685	C₂×C₄²	C₂⁴	1	1	yes	characteristic
686	C₂×C₄²	C₂⁴	1	1	yes	characteristic
687	C₂×C₄²	C₂⁴	1	1	yes	characteristic
688	C₂×C₄²	C₂⁴	1	1	yes	characteristic
689	C₂×C₄²	C₂⁴	1	1	yes	characteristic
690	C₂×C₄²	C₂⁴	1	1	yes	characteristic
691	#107	—	2	2	no	—
692	#107	—	2	2	no	—
693	#107	—	2	2	no	—
694	#107	—	2	2	no	—
695	#107	—	2	2	no	—
696	#107	—	2	2	no	—
697	#107	—	2	2	no	—
698	#107	—	2	2	no	—
699	#107	—	2	2	no	—
700	#107	—	2	2	no	—
701	#107	—	2	2	no	—
702	#107	—	2	2	no	—
703	#106	—	2	2	no	—
704	#106	—	2	2	no	—
705	#106	—	2	2	no	—
706	#106	—	2	2	no	—
707	#106	—	2	2	no	—
708	#106	—	2	2	no	—
709	#106	—	2	2	no	—
710	#106	—	2	2	no	—
711	#106	—	2	2	no	—
712	#106	—	2	2	no	—
713	#106	—	2	2	no	—
714	#106	—	2	2	no	—
715	C₄⋊C₈	C₂×D₄	1	4	yes	—
716	C₄⋊C₈	C₂×D₄	1	4	yes	—
717	C₄⋊C₈	C₂×D₄	1	4	yes	—
718	C₄⋊C₈	C₂×D₄	1	4	yes	—
719	#103	—	2	2	no	—
720	#103	—	2	2	no	—
721	#103	—	2	2	no	—
722	#103	—	2	2	no	—
723	#103	—	2	2	no	—
724	#103	—	2	2	no	—
725	#103	—	2	2	no	—
726	#103	—	2	2	no	—
727	#103	—	2	2	no	—
728	#103	—	2	2	no	—
729	#103	—	2	2	no	—
730	#103	—	2	2	no	—
731	#103	—	2	2	no	—
732	#103	—	2	2	no	—
733	#103	—	2	2	no	—
734	#103	—	2	2	no	—
735	#103	—	2	2	no	—
736	#103	—	2	2	no	—
737	#103	—	2	2	no	—
738	#103	—	2	2	no	—
739	#102	—	2	2	no	—
740	#102	—	2	2	no	—
741	#102	—	2	2	no	—
742	#102	—	2	2	no	—
743	#102	—	2	2	no	—
744	#102	—	2	2	no	—
745	#102	—	2	2	no	—
746	#102	—	2	2	no	—
747	#102	—	2	2	no	—
748	#102	—	2	2	no	—
749	#102	—	2	2	no	—
750	#102	—	2	2	no	—
751	C₂²⋊C₈	C₂×D₄	1	4	yes	—
752	C₂²⋊C₈	C₂×D₄	1	4	yes	—
753	C₂²⋊C₈	C₂×D₄	1	4	yes	—
754	C₂²⋊C₈	C₂×D₄	1	4	yes	—
755	#97	—	4	1	no	—
756	#97	—	4	1	no	—
757	#97	—	4	1	no	—
758	#97	—	4	1	no	—
759	#97	C₂×D₄	1	4	yes	—
760	#97	C₂×D₄	1	4	yes	—
761	C₄×C₈	—	4	1	no	—
762	C₄×C₈	—	4	1	no	—
763	C₄×C₈	—	4	1	no	—
764	C₄×C₈	—	4	1	no	—
765	C₄×C₈	C₂×D₄	1	4	yes	—
766	C₄×C₈	C₂×D₄	1	4	yes	—
767	#95	—	2	2	no	—
768	#95	—	2	2	no	—
769	#95	—	2	2	no	—
770	#95	—	2	2	no	—
771	#95	—	2	2	no	—
772	#95	—	2	2	no	—
773	#95	—	2	2	no	—
774	#95	—	2	2	no	—
775	#95	—	2	2	no	—
776	#95	—	2	2	no	—
777	#95	—	2	2	no	—
778	#95	—	2	2	no	—
779	#95	—	2	2	no	—
780	#95	—	2	2	no	—
781	#95	—	2	2	no	—
782	#95	—	2	2	no	—
783	#95	—	2	2	no	—
784	#95	—	2	2	no	—
785	#95	C₂×D₄	1	2	yes	—
786	#95	C₂×D₄	1	2	yes	—
787	#95	C₂×D₄	1	2	yes	—
788	#95	C₂×D₄	1	2	yes	—
789	C₂⁴	—	2	1	no	—
790	C₂⁴	—	2	1	no	—
791	C₂⁴	C₂²×D₄	1	1	yes	characteristic
792	C₂×Q₈	—	2	4	no	—
793	C₂×Q₈	—	2	1	no	—
794	C₂×Q₈	—	2	1	no	—
795	C₂×Q₈	—	2	1	no	—
796	C₂×Q₈	—	2	1	no	—
797	C₂×Q₈	—	2	1	no	—
798	C₂×Q₈	—	2	1	no	—
799	C₂×Q₈	—	2	1	no	—
800	C₂×Q₈	—	2	1	no	—
801	C₂×Q₈	—	2	1	no	—
802	C₂×Q₈	—	2	1	no	—
803	C₂×Q₈	—	2	1	no	—
804	C₂×Q₈	—	2	1	no	—
805	C₂×Q₈	—	2	1	no	—
806	C₂×Q₈	—	2	1	no	—
807	C₂×Q₈	—	2	1	no	—
808	C₂×Q₈	—	2	1	no	—
809	C₂×Q₈	—	2	1	no	—
810	C₂×Q₈	—	2	1	no	—
811	C₂×Q₈	—	2	1	no	—
812	C₂×Q₈	—	2	1	no	—
813	C₂×Q₈	—	2	1	no	—
814	C₂×Q₈	—	2	1	no	—
815	C₂×Q₈	—	4	4	no	—
816	C₂×Q₈	—	4	4	no	—
817	C₂×Q₈	—	4	4	no	—
818	C₂×Q₈	—	4	4	no	—
819	C₂×Q₈	—	4	2	no	—
820	C₂×Q₈	—	4	4	no	—
821	C₂×Q₈	—	4	2	no	—
822	C₂×Q₈	—	4	2	no	—
823	C₂×Q₈	—	4	2	no	—
824	C₂×Q₈	—	8	2	no	—
825	C₂×Q₈	2₋¹⁺⁴	1	2	yes	—
826	C₂×Q₈	2₋¹⁺⁴	1	2	yes	—
827	C₂×D₄	—	2	1	no	—
828	C₂×D₄	—	2	1	no	—
829	C₂×D₄	—	2	1	no	—
830	C₂×D₄	—	2	1	no	—
831	C₂×D₄	—	2	1	no	—
832	C₂×D₄	—	2	1	no	—
833	C₂×D₄	—	2	1	no	—
834	C₂×D₄	—	2	1	no	—
835	C₂×D₄	—	2	1	no	—
836	C₂×D₄	—	2	1	no	—
837	C₂×D₄	—	2	1	no	—
838	C₂×D₄	—	2	1	no	—
839	C₂×D₄	—	4	2	no	—
840	C₂×D₄	—	4	2	no	—
841	C₂×D₄	—	8	2	no	—
842	C₂×D₄	—	8	2	no	—
843	C₂×D₄	—	8	2	no	—
844	C₂×D₄	—	8	2	no	—
845	C₂×D₄	—	8	2	no	—
846	C₂²×C₄	—	2	1	no	—
847	C₂²×C₄	—	2	1	no	—
848	C₂²×C₄	—	2	1	no	—
849	C₂²×C₄	—	2	1	no	—
850	C₂²×C₄	—	2	4	no	—
851	C₂²×C₄	—	2	1	no	—
852	C₂²×C₄	—	2	1	no	—
853	C₂²×C₄	—	2	1	no	—
854	C₂²×C₄	—	2	1	no	—
855	C₂²×C₄	—	2	1	no	—
856	C₂²×C₄	—	2	1	no	—
857	C₂²×C₄	—	2	1	no	—
858	C₂²×C₄	—	2	1	no	—
859	C₂²×C₄	—	2	1	no	—
860	C₂²×C₄	—	2	1	no	—
861	C₂²×C₄	—	2	1	no	—
862	C₂²×C₄	—	2	1	no	—
863	C₂²×C₄	—	2	1	no	—
864	C₂²×C₄	—	2	1	no	—
865	C₂²×C₄	—	4	2	no	—
866	C₂²×C₄	—	4	2	no	—
867	C₂²×C₄	—	4	2	no	—
868	C₂²×C₄	—	4	2	no	—
869	C₂²×C₄	—	4	2	no	—
870	C₂²×C₄	—	4	2	no	—
871	C₂²×C₄	—	4	2	no	—
872	C₂²×C₄	—	8	2	no	—
873	C₂²×C₄	—	8	2	no	—
874	C₂²×C₄	—	8	2	no	—
875	C₂²×C₄	#127	1	4	yes	—
876	C₂²×C₄	#127	1	4	yes	—
877	C₂²×C₄	C₂²×D₄	1	2	yes	—
878	C₂²×C₄	C₂²×D₄	1	2	yes	—
879	C₂²×C₄	C₂²×D₄	1	2	yes	—
880	C₂²×C₄	C₂²×D₄	1	2	yes	—
881	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
882	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
883	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
884	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
885	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
886	C₂²×C₄	C₂²×D₄	1	2	yes	—
887	C₂²×C₄	C₂²×D₄	1	2	yes	—
888	C₂²×C₄	C₂⁵	1	1	yes	characteristic
889	Q₁₆	—	4	4	no	—
890	Q₁₆	—	4	4	no	—
891	Q₁₆	—	4	4	no	—
892	Q₁₆	—	4	4	no	—
893	SD₁₆	—	4	4	no	—
894	SD₁₆	—	4	4	no	—
895	SD₁₆	—	4	4	no	—
896	SD₁₆	—	4	4	no	—
897	C₂×C₈	—	2	1	no	—
898	C₂×C₈	—	2	1	no	—
899	C₂×C₈	—	2	1	no	—
900	C₂×C₈	—	2	1	no	—
901	C₂×C₈	—	2	1	no	—
902	C₂×C₈	—	2	1	no	—
903	C₂×C₈	—	2	1	no	—
904	C₂×C₈	—	2	1	no	—
905	C₂×C₈	—	2	1	no	—
906	C₂×C₈	—	2	1	no	—
907	C₂×C₈	—	2	1	no	—
908	C₂×C₈	—	2	1	no	—
909	C₂×C₈	—	2	1	no	—
910	C₂×C₈	—	2	1	no	—
911	C₂×C₈	—	2	1	no	—
912	C₂×C₈	—	2	1	no	—
913	C₂×C₈	C₂²×D₄	1	2	yes	—
914	C₂×C₈	C₂²×D₄	1	2	yes	—
915	C₂×C₈	C₂²×D₄	1	2	yes	—
916	C₂×C₈	C₂²×D₄	1	2	yes	—
917	C₂×C₈	C₂²×D₄	1	2	yes	—
918	C₂×C₈	C₂²×D₄	1	2	yes	—
919	C₂×C₈	C₂²×D₄	1	2	yes	—
920	C₂×C₈	C₂²×D₄	1	2	yes	—
921	C₄⋊C₄	—	2	1	no	—
922	C₄⋊C₄	—	2	1	no	—
923	C₄⋊C₄	—	2	1	no	—
924	C₄⋊C₄	—	2	1	no	—
925	C₄⋊C₄	—	2	1	no	—
926	C₄⋊C₄	—	2	1	no	—
927	C₄⋊C₄	—	2	1	no	—
928	C₄⋊C₄	—	2	1	no	—
929	C₄⋊C₄	—	2	1	no	—
930	C₄⋊C₄	—	2	1	no	—
931	C₄⋊C₄	—	2	1	no	—
932	C₄⋊C₄	—	2	1	no	—
933	C₄⋊C₄	—	2	1	no	—
934	C₄⋊C₄	—	2	1	no	—
935	C₄⋊C₄	—	2	1	no	—
936	C₄⋊C₄	—	2	1	no	—
937	C₄⋊C₄	—	2	1	no	—
938	C₄⋊C₄	—	2	1	no	—
939	C₄⋊C₄	—	2	1	no	—
940	C₄⋊C₄	—	2	1	no	—
941	C₄⋊C₄	—	4	2	no	—
942	C₄⋊C₄	—	4	2	no	—
943	C₄⋊C₄	—	4	2	no	—
944	C₄⋊C₄	—	4	2	no	—
945	C₄⋊C₄	—	4	2	no	—
946	C₄⋊C₄	—	4	2	no	—
947	C₄⋊C₄	—	4	2	no	—
948	C₄⋊C₄	—	4	2	no	—
949	C₄⋊C₄	—	4	2	no	—
950	C₄⋊C₄	—	4	2	no	—
951	C₄⋊C₄	—	4	2	no	—
952	C₄⋊C₄	—	4	2	no	—
953	C₄⋊C₄	—	4	2	no	—
954	C₄⋊C₄	—	4	2	no	—
955	C₄⋊C₄	—	4	2	no	—
956	C₄⋊C₄	—	4	2	no	—
957	C₄⋊C₄	—	4	2	no	—
958	C₄⋊C₄	—	4	2	no	—
959	C₄⋊C₄	—	4	2	no	—
960	C₄⋊C₄	—	4	2	no	—
961	C₄⋊C₄	—	4	2	no	—
962	C₄⋊C₄	—	4	2	no	—
963	C₄⋊C₄	—	4	2	no	—
964	C₄⋊C₄	—	4	2	no	—
965	C₄⋊C₄	—	4	2	no	—
966	C₄⋊C₄	—	8	2	no	—
967	C₄⋊C₄	—	8	2	no	—
968	C₄⋊C₄	—	8	2	no	—
969	C₄⋊C₄	—	8	2	no	—
970	C₄⋊C₄	—	8	2	no	—
971	C₄⋊C₄	—	8	2	no	—
972	C₄⋊C₄	—	8	2	no	—
973	C₂²⋊C₄	—	4	2	no	—
974	C₂²⋊C₄	—	4	2	no	—
975	C₂²⋊C₄	—	4	2	no	—
976	C₂²⋊C₄	—	4	2	no	—
977	C₂²⋊C₄	—	4	2	no	—
978	C₂²⋊C₄	—	4	2	no	—
979	C₂²⋊C₄	—	4	2	no	—
980	C₂²⋊C₄	—	4	2	no	—
981	C₂²⋊C₄	—	4	2	no	—
982	C₂²⋊C₄	—	4	2	no	—
983	C₂²⋊C₄	—	4	2	no	—
984	C₂²⋊C₄	—	4	2	no	—
985	C₂²⋊C₄	—	4	2	no	—
986	C₂²⋊C₄	—	4	2	no	—
987	C₂²⋊C₄	—	8	2	no	—
988	C₂²⋊C₄	—	8	2	no	—
989	C₂²⋊C₄	—	8	2	no	—
990	C₂²⋊C₄	—	8	2	no	—
991	C₂²⋊C₄	—	8	2	no	—
992	C₂²⋊C₄	—	8	2	no	—
993	C₄²	—	2	1	no	—
994	C₄²	—	2	1	no	—
995	C₄²	—	2	1	no	—
996	C₄²	—	2	1	no	—
997	C₄²	—	2	1	no	—
998	C₄²	—	2	1	no	—
999	C₄²	—	2	1	no	—
1000	C₄²	—	2	1	no	—
1001	C₄²	—	4	2	no	—
1002	C₄²	—	4	2	no	—
1003	C₄²	—	4	2	no	—
1004	C₄²	—	4	2	no	—
1005	C₄²	—	4	2	no	—
1006	C₄²	—	4	2	no	—
1007	C₄²	—	4	2	no	—
1008	C₄²	—	4	2	no	—
1009	C₄²	#127	1	4	yes	—
1010	C₄²	#127	1	4	yes	—
1011	C₄²	C₂²×D₄	1	2	yes	—
1012	C₄²	C₂²×D₄	1	2	yes	—
1013	C₄²	C₂²×D₄	1	2	yes	—
1014	C₄²	C₂²×D₄	1	2	yes	—
1015	C₂³	—	2	2	no	—
1016	C₂³	—	2	2	no	—
1017	C₂³	—	2	1	no	—
1018	C₂³	—	2	1	no	—
1019	C₂³	—	4	2	no	—
1020	C₂³	—	4	2	no	—
1021	C₂³	—	4	2	no	—
1022	C₂³	—	4	2	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	—	4	1	no	—
1029	C₂³	C₂×#127	1	2	yes	—
1030	C₂³	C₂³×D₄	1	1	yes	characteristic
1031	Q₈	—	2	2	no	—
1032	Q₈	—	2	2	no	—
1033	Q₈	—	2	2	no	—
1034	Q₈	—	2	2	no	—
1035	Q₈	—	4	8	no	—
1036	Q₈	—	4	1	no	—
1037	Q₈	—	4	1	no	—
1038	Q₈	—	4	1	no	—
1039	Q₈	—	4	1	no	—
1040	Q₈	—	4	1	no	—
1041	Q₈	—	4	1	no	—
1042	Q₈	—	4	1	no	—
1043	Q₈	—	4	1	no	—
1044	Q₈	—	4	1	no	—
1045	Q₈	—	4	1	no	—
1046	Q₈	—	4	1	no	—
1047	Q₈	—	4	1	no	—
1048	Q₈	—	8	4	no	—
1049	Q₈	—	8	4	no	—
1050	D₄	—	4	1	no	—
1051	D₄	—	4	1	no	—
1052	D₄	—	4	1	no	—
1053	D₄	—	4	1	no	—
1054	D₄	—	4	1	no	—
1055	D₄	—	4	1	no	—
1056	D₄	—	4	1	no	—
1057	D₄	—	4	1	no	—
1058	D₄	—	8	4	no	—
1059	D₄	—	8	4	no	—
1060	D₄	—	16	4	no	—
1061	C₂×C₄	—	2	2	no	—
1062	C₂×C₄	—	2	2	no	—
1063	C₂×C₄	—	2	2	no	—
1064	C₂×C₄	—	2	2	no	—
1065	C₂×C₄	—	2	1	no	—
1066	C₂×C₄	—	2	1	no	—
1067	C₂×C₄	—	2	2	no	—
1068	C₂×C₄	—	2	2	no	—
1069	C₂×C₄	—	2	2	no	—
1070	C₂×C₄	—	2	2	no	—
1071	C₂×C₄	—	2	2	no	—
1072	C₂×C₄	—	2	2	no	—
1073	C₂×C₄	—	2	2	no	—
1074	C₂×C₄	—	2	2	no	—
1075	C₂×C₄	—	2	2	no	—
1076	C₂×C₄	—	2	2	no	—
1077	C₂×C₄	—	2	2	no	—
1078	C₂×C₄	—	2	2	no	—
1079	C₂×C₄	—	2	2	no	—
1080	C₂×C₄	—	2	2	no	—
1081	C₂×C₄	—	2	2	no	—
1082	C₂×C₄	—	2	2	no	—
1083	C₂×C₄	—	2	2	no	—
1084	C₂×C₄	—	2	2	no	—
1085	C₂×C₄	—	4	4	no	—
1086	C₂×C₄	—	4	4	no	—
1087	C₂×C₄	—	4	8	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	2	no	—
1093	C₂×C₄	—	4	2	no	—
1094	C₂×C₄	—	4	2	no	—
1095	C₂×C₄	—	4	2	no	—
1096	C₂×C₄	—	4	2	no	—
1097	C₂×C₄	—	4	2	no	—
1098	C₂×C₄	—	4	2	no	—
1099	C₂×C₄	—	4	2	no	—
1100	C₂×C₄	—	4	2	no	—
1101	C₂×C₄	—	4	2	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	—	8	4	no	—
1119	C₂×C₄	—	8	4	no	—
1120	C₂×C₄	—	8	4	no	—
1121	C₂×C₄	C₂×#127	1	2	yes	—
1122	C₂×C₄	C₂×#127	1	2	yes	—
1123	C₂×C₄	C₂×#127	1	2	yes	—
1124	C₂×C₄	C₂×#127	1	2	yes	—
1125	C₂×C₄	C₂×#127	1	2	yes	—
1126	C₂×C₄	C₂³×D₄	1	1	yes	characteristic
1127	C₂×C₄	C₂³×D₄	1	1	yes	characteristic
1128	C₂×C₄	C₂×2₋¹⁺⁴	1	1	yes	characteristic
1129	C₂×C₄	C₂×2₋¹⁺⁴	1	1	yes	characteristic
1130	C₂×C₄	#585	1	1	yes	characteristic
1131	C₂×C₄	#585	1	1	yes	characteristic
1132	C₈	—	2	2	no	—
1133	C₈	—	2	2	no	—
1134	C₈	—	2	2	no	—
1135	C₈	—	2	2	no	—
1136	C₈	—	2	2	no	—
1137	C₈	—	2	2	no	—
1138	C₈	—	2	2	no	—
1139	C₈	—	2	2	no	—
1140	C₂²	—	2	2	no	—
1141	C₂²	—	2	2	no	—
1142	C₂²	—	2	2	no	—
1143	C₂²	—	4	2	no	—
1144	C₂²	—	4	2	no	—
1145	C₂²	—	8	1	no	—
1146	C₂²	—	8	1	no	—
1147	C₂²	—	8	2	no	—
1148	C₂²	—	8	2	no	—
1149	C₂²	—	8	2	no	—
1150	C₂²	—	8	2	no	—
1151	C₂²	—	8	1	no	—
1152	C₂²	—	8	1	no	—
1153	C₂²	—	8	1	no	—
1154	C₂²	—	8	1	no	—
1155	C₂²	C₂²×#127	1	1	yes	characteristic
1156	C₂²	#3485	1	1	yes	characteristic
1157	C₂²	#3486	1	1	yes	characteristic
1158	C₂²	#3584	1	2	yes	—
1159	C₂²	#3586	1	2	yes	—
1160	C₄	—	2	2	no	—
1161	C₄	—	2	2	no	—
1162	C₄	—	2	2	no	—
1163	C₄	—	2	2	no	—
1164	C₄	—	2	2	no	—
1165	C₄	—	4	2	no	—
1166	C₄	—	4	2	no	—
1167	C₄	—	4	2	no	—
1168	C₄	—	4	2	no	—
1169	C₄	—	4	2	no	—
1170	C₄	—	4	2	no	—
1171	C₄	—	8	1	no	—
1172	C₄	—	8	1	no	—
1173	C₄	—	8	1	no	—
1174	C₄	—	8	1	no	—
1175	C₄	—	8	1	no	—
1176	C₄	—	8	1	no	—
1177	C₄	—	8	1	no	—
1178	C₄	—	8	1	no	—
1179	C₄	—	8	1	no	—
1180	C₄	—	8	1	no	—
1181	C₄	—	8	1	no	—
1182	C₄	—	8	1	no	—
1183	C₄	#3489	1	1	yes	characteristic
1184	C₄	#3489	1	1	yes	characteristic
1185	C₄	#3489	1	1	yes	characteristic
1186	C₄	#3489	1	1	yes	characteristic
1187	C₂	—	4	2	no	—
1188	C₂	—	16	1	no	—
1189	C₂	—	16	1	no	—
1190	C₂	#35634	1	1	yes	characteristic
1191	C₂	#60643	1	1	yes	characteristic
1192	C₂	#60645	1	1	yes	characteristic
1193	C₂	#61801	1	2	yes	—
1194	C₂	#61856	1	2	yes	—

	subgroup	G/H
center, socle	C₂³	C₂³×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁵
prime radical	#2619	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³ ◁ #2285 ◁ G
LECS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. C₂×#3240	C₂	semidirect
2. C₂×#3233	C₂	semidirect
3. C₂×#3117	C₂	semidirect
4. C₂×#3108	C₂	semidirect
6. #35179	C₂	semidirect
7. #28550	C₂	semidirect
8. #28547	C₂	semidirect
9. #28546	C₂	semidirect
10. #28543	C₂	semidirect
11. #28538	C₂	semidirect
12. #28537	C₂	semidirect
13. #28535	C₂	semidirect
14. #28533	C₂	semidirect
15. #28436	C₂	semidirect
16. #28432	C₂	semidirect
17. #28428	C₂	semidirect
18. #28424	C₂	semidirect
19. #28412	C₂	semidirect
20. #28411	C₂	semidirect
21. #28408	C₂	semidirect
22. #28407	C₂	semidirect
23. #28324	C₂	semidirect
24. #28324	C₂	semidirect
26. #28322	C₂	semidirect
28. #27922	C₂	semidirect
29. #27921	C₂	semidirect
30. #27920	C₂	semidirect
31. #20537	C₂	semidirect
310. #432	D₄	semidirect
311. #431	D₄	semidirect

Maximal subgroups

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

subgroup	index
C₂×#3240	2
C₂×#3233	2
C₂×#3117	2
C₂×#3108	2
#37542	2
#35179	2
#28550	2
#28547	2
#28546	2
#28543	2
#28538	2
#28537	2
#28535	2
#28533	2
#28436	2
#28432	2
#28428	2
#28424	2
#28412	2
#28411	2
#28408	2
#28407	2
#28324	2
#28323	2
#28322	2
#27923	2
#27922	2
#27921	2
#27920	2
#20537	2