Subgroups — #6388649

Order 512.

1786 conjugacy classes of subgroups.

The subgroup lattice has 1351 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#60536	C₂	1	1	yes	maximal, characteristic
2	#60269	C₂	1	1	yes	maximal, characteristic, complemented
3	#60128	C₂	1	1	yes	maximal, characteristic, complemented
4	#22950	C₂	1	2	yes	maximal, complemented
5	#22948	C₂	1	2	yes	maximal, complemented
6	#22888	C₂	1	2	yes	maximal, complemented
7	#22886	C₂	1	2	yes	maximal, complemented
8	#22803	C₂	1	1	yes	maximal, characteristic, complemented
9	#22802	C₂	1	1	yes	maximal, characteristic, complemented
10	#22783	C₂	1	1	yes	maximal, characteristic, complemented
11	#22783	C₂	1	1	yes	maximal, characteristic, complemented
12	#22782	C₂	1	1	yes	maximal, characteristic, complemented
13	#22782	C₂	1	1	yes	maximal, characteristic, complemented
14	#22688	C₂	1	1	yes	maximal, characteristic, complemented
15	#22686	C₂	1	1	yes	maximal, characteristic, complemented
16	#22167	C₂	1	2	yes	maximal, complemented
17	#22132	C₂	1	2	yes	maximal, complemented
18	#21993	C₂	1	1	yes	maximal, characteristic, complemented
19	#21899	C₂	1	1	yes	maximal, characteristic, complemented
20	#21629	C₂	1	2	yes	maximal, complemented
21	#21519	C₂	1	2	yes	maximal, complemented
22	C₂×#1806	C₂	1	1	yes	maximal, characteristic, complemented
23	#20535	C₂	1	1	yes	maximal, characteristic, complemented
24	#3444	C₂²	1	1	yes	characteristic
25	C₂×C₄×#41	C₂²	1	1	yes	characteristic
26	#3108	C₄	1	1	yes	characteristic, complemented
27	#3108	C₄	1	1	yes	characteristic, complemented
28	#3107	C₄	1	1	yes	characteristic, complemented
29	#3107	C₄	1	1	yes	characteristic, complemented
30	#3106	C₄	1	1	yes	characteristic, complemented
31	#3106	C₄	1	1	yes	characteristic, complemented
32	#3105	C₄	1	1	yes	characteristic, complemented
33	#3105	C₄	1	1	yes	characteristic, complemented
34	#3104	C₄	1	1	yes	characteristic, complemented
35	#3103	C₄	1	1	yes	characteristic, complemented
36	#3102	C₄	1	1	yes	characteristic, complemented
37	#3102	C₄	1	1	yes	characteristic, complemented
38	#3102	C₄	1	1	yes	characteristic, complemented
39	#3102	C₄	1	1	yes	characteristic, complemented
40	#3101	C₄	1	1	yes	characteristic, complemented
41	#3100	C₄	1	1	yes	characteristic, complemented
42	#3091	C₂²	1	1	yes	characteristic
43	#3091	C₂²	1	1	yes	characteristic
44	#3076	C₂²	1	1	yes	characteristic
45	#3076	C₂²	1	1	yes	characteristic
46	#3035	C₂²	1	1	yes	characteristic
47	#3035	C₂²	1	1	yes	characteristic
48	#3002	C₂²	1	1	yes	characteristic
49	#3002	C₂²	1	1	yes	characteristic
50	#2995	—	2	2	no	—
51	#2992	—	2	2	no	—
52	#2990	—	2	1	no	—
53	#2990	—	2	1	no	—
54	#2989	—	2	1	no	—
55	#2989	—	2	1	no	—
56	#2961	C₂²	1	2	yes	complemented
57	C₂×#444	C₂²	1	2	yes	—
58	C₂×#443	C₂²	1	2	yes	—
59	C₄×#135	C₂²	1	1	yes	characteristic
60	C₄×#135	C₂²	1	1	yes	characteristic
61	C₄×#135	C₂²	1	1	yes	characteristic
62	C₄×#135	C₂²	1	1	yes	characteristic
63	#2933	C₂²	1	2	yes	—
64	#2933	C₂²	1	2	yes	—
65	#2932	C₂²	1	2	yes	complemented
66	#2925	—	2	1	no	—
67	#2925	—	2	1	no	—
68	#2925	C₂²	1	1	yes	characteristic
69	#2925	C₂²	1	1	yes	characteristic
70	#2925	C₂²	1	1	yes	characteristic, complemented
71	#2925	C₂²	1	1	yes	characteristic, complemented
72	#2924	—	2	2	no	—
73	#2924	C₂²	1	2	yes	—
74	#2923	—	2	2	no	—
75	#2923	C₂²	1	2	yes	—
76	#2920	—	2	1	no	—
77	#2920	C₂²	1	1	yes	characteristic
78	C₂×#432	—	2	1	no	—
79	C₂×#432	C₂²	1	1	yes	characteristic
80	C₂×#431	C₂²	1	1	yes	characteristic
81	#2906	C₂²	1	1	yes	characteristic
82	#2906	C₂²	1	1	yes	characteristic
83	#2906	C₂²	1	1	yes	characteristic, complemented
84	#2906	C₂²	1	1	yes	characteristic, complemented
85	C₂×#423	C₂²	1	1	yes	characteristic
86	C₂²×#104	C₂²	1	2	yes	—
87	#2880	C₂²	1	2	yes	—
88	#2875	C₂²	1	2	yes	—
89	C₂×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
90	#1986	C₂²	1	2	yes	complemented
91	#1980	C₂²	1	2	yes	complemented
92	#1975	C₂²	1	2	yes	—
93	#1974	C₂²	1	2	yes	—
94	#1950	C₂²	1	2	yes	complemented
95	#1950	C₂²	1	2	yes	complemented
96	#1946	C₂²	1	2	yes	complemented
97	#1945	C₂²	1	2	yes	complemented
98	#1938	C₂²	1	2	yes	—
99	#1938	C₂²	1	2	yes	complemented
100	#1937	C₂²	1	2	yes	—
101	#1937	C₂²	1	2	yes	complemented
102	#1929	C₂²	1	2	yes	—
103	#1929	C₂²	1	2	yes	—
104	#1929	C₂²	1	2	yes	complemented
105	#1929	C₂²	1	2	yes	complemented
106	#1922	C₂²	1	2	yes	complemented
107	#1922	C₂²	1	2	yes	complemented
108	#1922	C₂²	1	2	yes	complemented
109	#1922	C₂²	1	2	yes	complemented
110	#1896	C₂²	1	2	yes	—
111	#1896	C₂²	1	2	yes	—
112	#1876	C₂²	1	2	yes	—
113	#1876	C₂²	1	2	yes	—
114	#1876	C₂²	1	2	yes	—
115	#1876	C₂²	1	2	yes	—
116	#1866	C₂²	1	2	yes	—
117	#1866	C₂²	1	2	yes	—
118	#1866	C₂²	1	2	yes	complemented
119	#1866	C₂²	1	2	yes	complemented
120	#1855	C₂²	1	2	yes	—
121	#1855	C₂²	1	2	yes	—
122	#1848	C₂²	1	1	yes	characteristic, complemented
123	#1848	C₂²	1	1	yes	characteristic, complemented
124	#1837	C₂²	1	1	yes	characteristic, complemented
125	#1837	C₂²	1	1	yes	characteristic, complemented
126	#1806	C₂²	1	2	yes	—
127	#1806	C₂²	1	1	yes	characteristic
128	#1806	C₂²	1	1	yes	characteristic
129	#1806	C₂²	1	2	yes	—
130	#1806	C₂²	1	1	yes	characteristic
131	#1806	C₂²	1	1	yes	characteristic
132	#1806	C₂²	1	1	yes	characteristic, complemented
133	#1806	C₂²	1	1	yes	characteristic, complemented
134	#1806	C₂²	1	1	yes	characteristic, complemented
135	#1806	C₂²	1	1	yes	characteristic, complemented
136	#1773	C₂²	1	2	yes	complemented
137	#1772	C₂²	1	2	yes	complemented
138	#1771	C₂²	1	2	yes	complemented
139	#1771	C₂²	1	2	yes	complemented
140	#1770	C₂²	1	1	yes	characteristic, complemented
141	#1770	C₂²	1	1	yes	characteristic, complemented
142	C₈×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
143	C₈×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
144	#1765	C₂²	1	2	yes	—
145	#1765	C₂²	1	2	yes	complemented
146	#1764	C₂²	1	2	yes	—
147	#1764	C₂²	1	2	yes	complemented
148	#1749	C₂²	1	2	yes	—
149	C₄×C₂²⋊C₈	C₂²	1	2	yes	—
150	C₂×#339	C₂²	1	2	yes	—
151	C₂²×#41	C₂³	1	1	yes	characteristic
152	C₂×#135	C₂³	1	1	yes	characteristic
153	C₂×#135	C₂³	1	1	yes	characteristic
154	C₂×#135	C₂³	1	1	yes	characteristic
155	C₂×#135	C₂³	1	1	yes	characteristic
156	C₂×#131	C₂³	1	2	yes	—
157	C₂×#131	C₂³	1	2	yes	—
158	C₂×#131	C₂³	1	2	yes	—
159	C₂×#131	C₂³	1	2	yes	—
160	C₂²×M₁₆	C₂³	1	2	yes	—
161	#533	C₂×C₄	1	1	yes	characteristic
162	#533	C₂×C₄	1	1	yes	characteristic
163	#533	C₂³	1	1	yes	characteristic
164	#532	C₂×C₄	1	1	yes	characteristic
165	#532	C₂×C₄	1	1	yes	characteristic
166	#532	C₂³	1	1	yes	characteristic
167	#529	—	2	1	no	—
168	#529	—	2	1	no	—
169	#529	—	2	1	no	—
170	#529	—	2	1	no	—
171	#529	C₂×C₄	1	1	yes	characteristic
172	#529	C₂×C₄	1	1	yes	characteristic
173	#529	C₂×C₄	1	1	yes	characteristic
174	#529	C₂×C₄	1	1	yes	characteristic
175	#525	—	2	1	no	—
176	#525	—	2	1	no	—
177	#525	C₂³	1	1	yes	characteristic
178	#525	C₂³	1	1	yes	characteristic
179	C₄×#41	—	2	1	no	—
180	C₄×#41	—	2	1	no	—
181	C₄×#41	—	2	1	no	—
182	C₄×#41	—	2	1	no	—
183	C₄×#41	—	2	1	no	—
184	C₄×#41	—	2	1	no	—
185	C₄×#41	C₂×C₄	1	1	yes	characteristic
186	C₄×#41	C₂×C₄	1	1	yes	characteristic
187	C₄×#41	C₂×C₄	1	1	yes	characteristic
188	C₄×#41	C₂×C₄	1	1	yes	characteristic
189	C₄×#41	C₂³	1	1	yes	characteristic
190	C₄×#41	C₂³	1	1	yes	characteristic
191	C₄×#41	C₂³	1	1	yes	characteristic
192	C₄×#41	C₂³	1	1	yes	characteristic
193	C₄×#41	C₂³	1	1	yes	characteristic
194	C₄×#41	C₂³	1	1	yes	characteristic
195	C₂×C₄×Q₈	C₂×C₄	1	1	yes	characteristic
196	C₂×C₄×Q₈	C₂×C₄	1	1	yes	characteristic
197	C₂×C₄×D₄	—	2	1	no	—
198	C₂×C₄×D₄	—	2	1	no	—
199	C₂×C₄×D₄	C₂×C₄	1	1	yes	characteristic
200	C₂×C₄×D₄	C₂×C₄	1	1	yes	characteristic
201	C₂×#117	—	2	1	no	—
202	C₂×#117	C₂³	1	1	yes	characteristic
203	C₂²×C₄⋊C₄	—	2	1	no	—
204	C₂²×C₄²	—	2	1	no	—
205	C₂²×C₄²	C₂³	1	2	yes	—
206	C₂²×C₄²	C₂³	1	1	yes	characteristic
207	#485	C₂×C₄	1	1	yes	characteristic
208	#485	C₂×C₄	1	1	yes	characteristic
209	#485	C₂×C₄	1	1	yes	characteristic
210	#485	C₂×C₄	1	1	yes	characteristic
211	#484	C₂×C₄	1	1	yes	characteristic
212	#484	C₂×C₄	1	1	yes	characteristic
213	#483	C₂×C₄	1	1	yes	characteristic
214	#483	C₂×C₄	1	1	yes	characteristic
215	#482	C₂×C₄	1	1	yes	characteristic
216	#482	C₂×C₄	1	1	yes	characteristic
217	#482	C₂×C₄	1	1	yes	characteristic
218	#482	C₂×C₄	1	1	yes	characteristic
219	#481	C₂×C₄	1	1	yes	characteristic
220	#481	C₂×C₄	1	1	yes	characteristic
221	#480	C₂×C₄	1	1	yes	characteristic
222	#480	C₂×C₄	1	1	yes	characteristic
223	#479	C₂×C₄	1	1	yes	characteristic, complemented
224	#479	C₂×C₄	1	1	yes	characteristic, complemented
225	#479	C₂×C₄	1	1	yes	characteristic, complemented
226	#479	C₂×C₄	1	1	yes	characteristic, complemented
227	#478	C₂×C₄	1	1	yes	characteristic, complemented
228	#478	C₂×C₄	1	1	yes	characteristic, complemented
229	#478	C₂×C₄	1	1	yes	characteristic, complemented
230	#478	C₂×C₄	1	1	yes	characteristic, complemented
231	#477	C₂×C₄	1	1	yes	characteristic, complemented
232	#477	C₂×C₄	1	1	yes	characteristic, complemented
233	#476	C₂×C₄	1	1	yes	characteristic, complemented
234	#476	C₂×C₄	1	1	yes	characteristic, complemented
235	#475	C₂×C₄	1	1	yes	characteristic, complemented
236	#475	C₂×C₄	1	1	yes	characteristic, complemented
237	#474	C₂×C₄	1	1	yes	characteristic, complemented
238	#474	C₂×C₄	1	1	yes	characteristic, complemented
239	#464	C₂×C₄	1	1	yes	characteristic, complemented
240	#464	C₂×C₄	1	1	yes	characteristic, complemented
241	#464	C₂×C₄	1	1	yes	characteristic, complemented
242	#464	C₂×C₄	1	1	yes	characteristic, complemented
243	#463	C₂×C₄	1	1	yes	characteristic, complemented
244	#463	C₂×C₄	1	1	yes	characteristic, complemented
245	#463	C₂×C₄	1	1	yes	characteristic, complemented
246	#463	C₂×C₄	1	1	yes	characteristic, complemented
247	#462	C₂×C₄	1	1	yes	characteristic, complemented
248	#462	C₂×C₄	1	1	yes	characteristic, complemented
249	#461	C₂×C₄	1	1	yes	characteristic, complemented
250	#461	C₂×C₄	1	1	yes	characteristic, complemented
251	#460	C₂×C₄	1	1	yes	characteristic, complemented
252	#460	C₂×C₄	1	1	yes	characteristic, complemented
253	#459	C₂×C₄	1	1	yes	characteristic, complemented
254	#459	C₂×C₄	1	1	yes	characteristic, complemented
255	#452	C₂×C₄	1	1	yes	characteristic
256	#452	C₂×C₄	1	1	yes	characteristic
257	#452	C₂×C₄	1	1	yes	characteristic
258	#452	C₂×C₄	1	1	yes	characteristic
259	#451	C₂×C₄	1	1	yes	characteristic
260	#451	C₂×C₄	1	1	yes	characteristic
261	#450	C₂×C₄	1	1	yes	characteristic
262	#450	C₂×C₄	1	1	yes	characteristic
263	#449	C₂×C₄	1	1	yes	characteristic
264	#449	C₂×C₄	1	1	yes	characteristic
265	#449	C₂×C₄	1	1	yes	characteristic
266	#449	C₂×C₄	1	1	yes	characteristic
267	#448	C₂×C₄	1	1	yes	characteristic
268	#448	C₂×C₄	1	1	yes	characteristic
269	#447	C₂×C₄	1	1	yes	characteristic
270	#447	C₂×C₄	1	1	yes	characteristic
271	#446	—	2	2	no	—
272	#446	—	2	2	no	—
273	#446	—	2	2	no	—
274	#446	—	2	2	no	—
275	#444	—	4	4	no	—
276	#443	—	4	4	no	—
277	C₄×Q₁₆	C₂×C₄	1	1	yes	characteristic, complemented
278	C₄×Q₁₆	C₂×C₄	1	1	yes	characteristic, complemented
279	C₄×Q₁₆	C₂×C₄	1	1	yes	characteristic, complemented
280	C₄×Q₁₆	C₂×C₄	1	1	yes	characteristic, complemented
281	C₄×Q₁₆	C₂×C₄	1	1	yes	characteristic, complemented
282	C₄×Q₁₆	C₂×C₄	1	1	yes	characteristic, complemented
283	C₄×Q₁₆	C₂×C₄	1	1	yes	characteristic, complemented
284	C₄×Q₁₆	C₂×C₄	1	1	yes	characteristic, complemented
285	C₄×SD₁₆	C₂×C₄	1	1	yes	characteristic, complemented
286	C₄×SD₁₆	C₂×C₄	1	1	yes	characteristic, complemented
287	C₄×SD₁₆	C₂×C₄	1	1	yes	characteristic, complemented
288	C₄×SD₁₆	C₂×C₄	1	1	yes	characteristic, complemented
289	C₄×SD₁₆	C₂×C₄	1	1	yes	characteristic, complemented
290	C₄×SD₁₆	C₂×C₄	1	1	yes	characteristic, complemented
291	C₄×SD₁₆	C₂×C₄	1	1	yes	characteristic, complemented
292	C₄×SD₁₆	C₂×C₄	1	1	yes	characteristic, complemented
293	C₄×SD₁₆	C₂×C₄	1	1	yes	characteristic, complemented
294	C₄×SD₁₆	C₂×C₄	1	1	yes	characteristic, complemented
295	C₄×SD₁₆	C₂×C₄	1	1	yes	characteristic, complemented
296	C₄×SD₁₆	C₂×C₄	1	1	yes	characteristic, complemented
297	C₄×SD₁₆	C₂×C₄	1	1	yes	characteristic, complemented
298	C₄×SD₁₆	C₂×C₄	1	1	yes	characteristic, complemented
299	C₄×SD₁₆	C₂×C₄	1	1	yes	characteristic, complemented
300	C₄×SD₁₆	C₂×C₄	1	1	yes	characteristic, complemented
301	C₄×D₈	C₂×C₄	1	1	yes	characteristic, complemented
302	C₄×D₈	C₂×C₄	1	1	yes	characteristic, complemented
303	C₄×D₈	C₂×C₄	1	1	yes	characteristic, complemented
304	C₄×D₈	C₂×C₄	1	1	yes	characteristic, complemented
305	C₄×D₈	C₂×C₄	1	1	yes	characteristic, complemented
306	C₄×D₈	C₂×C₄	1	1	yes	characteristic, complemented
307	C₄×D₈	C₂×C₄	1	1	yes	characteristic, complemented
308	C₄×D₈	C₂×C₄	1	1	yes	characteristic, complemented
309	#436	—	2	2	no	—
310	#436	—	2	2	no	—
311	#435	—	2	2	no	—
312	#435	—	2	2	no	—
313	#435	—	2	2	no	—
314	#435	—	2	2	no	—
315	#435	—	2	2	no	—
316	#435	—	2	2	no	—
317	#435	—	2	2	no	—
318	#435	—	2	2	no	—
319	C₈×D₄	—	2	2	no	—
320	C₈×D₄	—	2	2	no	—
321	#433	—	2	2	no	—
322	#433	—	2	2	no	—
323	#433	—	2	2	no	—
324	#433	—	2	2	no	—
325	#433	—	2	2	no	—
326	#433	—	2	2	no	—
327	#433	—	2	2	no	—
328	#433	—	2	2	no	—
329	#432	—	2	1	no	—
330	#432	—	2	1	no	—
331	#432	—	2	1	no	—
332	#432	—	2	1	no	—
333	#432	—	2	1	no	—
334	#432	—	2	1	no	—
335	#432	—	2	2	no	—
336	#432	—	2	2	no	—
337	#432	—	2	2	no	—
338	#432	D₄	1	1	yes	characteristic
339	#432	D₄	1	1	yes	characteristic
340	#432	D₄	1	2	yes	—
341	#432	D₄	1	2	yes	—
342	#432	D₄	1	1	yes	characteristic
343	#432	D₄	1	1	yes	characteristic
344	#431	—	2	1	no	—
345	#431	—	2	1	no	—
346	#431	—	2	1	no	—
347	#431	—	2	1	no	—
348	#431	—	2	1	no	—
349	#431	—	2	1	no	—
350	#431	—	2	2	no	—
351	#431	C₂×C₄	1	1	yes	characteristic
352	#431	C₂×C₄	1	1	yes	characteristic
353	#431	C₂×C₄	1	1	yes	characteristic
354	#431	C₂×C₄	1	1	yes	characteristic
355	#431	C₂×C₄	1	1	yes	characteristic
356	#431	C₂×C₄	1	1	yes	characteristic
357	#431	C₂×C₄	1	1	yes	characteristic
358	#431	C₂×C₄	1	1	yes	characteristic
359	C₂×#108	C₂³	1	2	yes	—
360	C₂×#108	C₂³	1	2	yes	—
361	C₂×#108	C₂³	1	2	yes	—
362	C₂×#108	C₂³	1	2	yes	—
363	#427	C₂³	1	1	yes	characteristic
364	#427	C₂³	1	1	yes	characteristic
365	#427	C₂³	1	1	yes	characteristic
366	#427	C₂³	1	1	yes	characteristic
367	#424	—	2	2	no	—
368	#424	—	2	2	no	—
369	#424	—	2	2	no	—
370	#424	—	2	2	no	—
371	#424	C₂³	1	2	yes	—
372	#424	C₂³	1	2	yes	—
373	#424	C₂³	1	2	yes	—
374	#424	C₂³	1	2	yes	—
375	#423	—	2	1	no	—
376	#423	—	2	1	no	—
377	#423	—	2	1	no	—
378	#423	—	2	1	no	—
379	#423	—	2	1	no	—
380	#423	—	2	1	no	—
381	#423	C₂³	1	1	yes	characteristic
382	#423	C₂³	1	1	yes	characteristic
383	#423	C₂³	1	2	yes	—
384	#423	C₂³	1	1	yes	characteristic
385	#423	C₂³	1	1	yes	characteristic
386	C₂×C₄⋊C₈	—	2	1	no	—
387	C₂×C₄⋊C₈	—	2	1	no	—
388	C₂×C₄⋊C₈	—	2	1	no	—
389	C₂×C₄⋊C₈	—	2	1	no	—
390	C₂×C₄⋊C₈	—	2	1	no	—
391	C₂×C₄⋊C₈	—	2	1	no	—
392	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
393	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
394	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
395	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
396	C₂×#104	—	4	4	no	—
397	C₂×#104	C₂³	1	2	yes	—
398	C₂×#104	C₂³	1	2	yes	—
399	C₂×#104	C₂³	1	2	yes	—
400	C₂×#104	C₂³	1	2	yes	—
401	C₂×#104	C₂³	1	2	yes	—
402	C₂×#104	C₂³	1	2	yes	—
403	C₂×#104	C₂³	1	2	yes	—
404	C₂×#104	C₂³	1	2	yes	—
405	#416	C₂³	1	1	yes	characteristic
406	#416	C₂³	1	1	yes	characteristic
407	#416	C₂³	1	1	yes	characteristic
408	#416	C₂³	1	1	yes	characteristic
409	#416	C₂³	1	1	yes	characteristic
410	#416	C₂³	1	1	yes	characteristic
411	#416	C₂³	1	1	yes	characteristic
412	#416	C₂³	1	1	yes	characteristic
413	#408	—	2	2	no	—
414	#408	—	2	2	no	—
415	#408	C₂³	1	2	yes	—
416	#408	C₂³	1	2	yes	—
417	#408	C₂³	1	2	yes	—
418	#408	C₂³	1	2	yes	—
419	#407	—	2	2	no	—
420	#407	C₂³	1	2	yes	—
421	C₂×C₂²⋊C₈	—	2	2	no	—
422	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
423	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
424	C₂×C₂²⋊C₈	C₂³	1	2	yes	—
425	#405	—	2	2	no	—
426	#405	—	2	2	no	—
427	#405	C₂³	1	2	yes	—
428	#405	C₂³	1	2	yes	—
429	#405	C₂³	1	2	yes	—
430	#405	C₂³	1	2	yes	—
431	C₄×M₁₆	—	2	2	no	—
432	C₄×M₁₆	C₂³	1	2	yes	—
433	C₂×#97	—	2	2	no	—
434	C₂×#97	C₂³	1	2	yes	—
435	C₂×#97	C₂³	1	2	yes	—
436	C₂×#97	C₂³	1	2	yes	—
437	C₂×C₄×C₈	C₂³	1	2	yes	—
438	C₂×C₄×C₈	C₂³	1	2	yes	—
439	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
440	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
441	C₄×C₄⋊C₄	—	2	1	no	—
442	C₄×C₄⋊C₄	—	2	1	no	—
443	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
444	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
445	C₄×C₄⋊C₄	C₂³	1	2	yes	—
446	C₂×#95	—	2	1	no	—
447	#341	C₂³	1	2	yes	—
448	#341	C₂³	1	2	yes	—
449	#341	C₂³	1	2	yes	—
450	#341	C₂³	1	2	yes	—
451	#339	C₂³	1	2	yes	—
452	#339	C₂³	1	2	yes	—
453	#339	C₂³	1	2	yes	—
454	#339	C₂³	1	2	yes	—
455	#339	C₂³	1	2	yes	—
456	#339	C₂³	1	2	yes	—
457	#339	C₂³	1	2	yes	—
458	#339	C₂³	1	2	yes	—
459	#336	C₂³	1	2	yes	—
460	#336	C₂³	1	2	yes	—
461	#336	C₂³	1	2	yes	—
462	#336	C₂³	1	2	yes	—
463	C₂×#41	—	2	1	no	—
464	C₂×#41	—	2	1	no	—
465	C₂×#41	—	2	1	no	—
466	C₂×#41	—	2	1	no	—
467	C₂×#41	—	2	2	no	—
468	C₂×#41	—	2	2	no	—
469	C₂×#41	—	4	1	no	—
470	C₂×#41	—	4	1	no	—
471	C₂×#41	C₂²×C₄	1	1	yes	characteristic
472	C₂×#41	C₂²×C₄	1	1	yes	characteristic
473	C₂×#41	C₂⁴	1	1	yes	characteristic
474	C₂×#41	C₂⁴	1	1	yes	characteristic
475	C₂×#41	C₂⁴	1	1	yes	characteristic
476	C₂×#41	C₂⁴	1	1	yes	characteristic
477	C₂²×Q₈	C₂²×C₄	1	1	yes	characteristic
478	C₂²×D₄	—	2	1	no	—
479	C₂²×D₄	C₂²×C₄	1	1	yes	characteristic
480	C₂³×C₄	—	2	1	no	—
481	C₂³×C₄	—	2	1	no	—
482	C₂³×C₄	—	2	1	no	—
483	C₂³×C₄	—	2	2	no	—
484	C₂³×C₄	#41	1	1	yes	characteristic
485	C₂³×C₄	#41	1	1	yes	characteristic
486	C₂³×C₄	C₂⁴	1	1	yes	characteristic
487	#135	—	2	2	no	—
488	#135	—	2	2	no	—
489	#135	—	2	2	no	—
490	#135	—	2	2	no	—
491	#135	—	4	1	no	—
492	#135	—	4	1	no	—
493	#135	—	4	1	no	—
494	#135	—	4	1	no	—
495	C₂×Q₁₆	C₂²×C₄	1	1	yes	characteristic
496	C₂×Q₁₆	C₂²×C₄	1	1	yes	characteristic
497	C₂×Q₁₆	C₂²×C₄	1	1	yes	characteristic
498	C₂×Q₁₆	C₂²×C₄	1	1	yes	characteristic
499	C₂×SD₁₆	C₂²×C₄	1	1	yes	characteristic
500	C₂×SD₁₆	C₂²×C₄	1	1	yes	characteristic
501	C₂×SD₁₆	C₂²×C₄	1	1	yes	characteristic
502	C₂×SD₁₆	C₂²×C₄	1	1	yes	characteristic
503	C₂×SD₁₆	C₂²×C₄	1	1	yes	characteristic
504	C₂×SD₁₆	C₂²×C₄	1	1	yes	characteristic
505	C₂×SD₁₆	C₂²×C₄	1	1	yes	characteristic
506	C₂×SD₁₆	C₂²×C₄	1	1	yes	characteristic
507	C₂×D₈	C₂²×C₄	1	1	yes	characteristic
508	C₂×D₈	C₂²×C₄	1	1	yes	characteristic
509	C₂×D₈	C₂²×C₄	1	1	yes	characteristic
510	C₂×D₈	C₂²×C₄	1	1	yes	characteristic
511	#131	—	2	4	no	—
512	#131	—	2	4	no	—
513	#131	—	4	2	no	—
514	#131	—	4	2	no	—
515	#131	—	4	2	no	—
516	#131	—	4	2	no	—
517	#131	—	4	2	no	—
518	#131	—	4	2	no	—
519	C₂×M₁₆	—	2	2	no	—
520	C₂×M₁₆	—	2	2	no	—
521	C₂×M₁₆	—	2	2	no	—
522	C₂×M₁₆	—	2	2	no	—
523	C₂×M₁₆	—	2	2	no	—
524	C₂×M₁₆	—	4	2	no	—
525	C₂×M₁₆	—	4	2	no	—
526	C₂×M₁₆	C₂⁴	1	2	yes	—
527	C₂×M₁₆	C₂⁴	1	2	yes	—
528	C₂×M₁₆	C₂⁴	1	2	yes	—
529	C₂×M₁₆	C₂⁴	1	2	yes	—
530	C₂²×C₈	—	2	2	no	—
531	C₂²×C₈	—	2	2	no	—
532	C₂²×C₈	—	2	2	no	—
533	C₂²×C₈	—	2	2	no	—
534	C₂²×C₈	—	2	2	no	—
535	C₂²×C₈	C₂⁴	1	1	yes	characteristic
536	C₂²×C₈	C₂⁴	1	1	yes	characteristic
537	C₂²×C₈	C₂⁴	1	1	yes	characteristic
538	C₂²×C₈	C₂⁴	1	1	yes	characteristic
539	C₂²×C₈	C₂⁴	1	2	yes	—
540	C₂²×C₈	C₂⁴	1	2	yes	—
541	C₄⋊Q₈	C₂²×C₄	1	1	yes	characteristic
542	C₄⋊Q₈	C₂²×C₄	1	1	yes	characteristic
543	C₄⋊Q₈	C₂²×C₄	1	1	yes	characteristic
544	#127	C₂²×C₄	1	1	yes	characteristic
545	#126	—	2	1	no	—
546	#126	—	2	1	no	—
547	#126	—	2	1	no	—
548	#126	—	2	1	no	—
549	#125	—	2	1	no	—
550	#125	—	2	1	no	—
551	#125	C₂²×C₄	1	1	yes	characteristic
552	#125	C₂²×C₄	1	1	yes	characteristic
553	#124	—	2	1	no	—
554	#124	—	2	1	no	—
555	#124	C₂²×C₄	1	1	yes	characteristic
556	#124	C₂²×C₄	1	1	yes	characteristic
557	#123	—	2	1	no	—
558	#123	—	2	1	no	—
559	#123	—	2	1	no	—
560	#123	—	2	1	no	—
561	#123	—	2	1	no	—
562	#123	—	2	1	no	—
563	C₂²⋊Q₈	—	2	1	no	—
564	C₂²⋊Q₈	—	2	1	no	—
565	C₂²⋊Q₈	—	2	1	no	—
566	C₂²⋊Q₈	—	2	1	no	—
567	C₂²⋊Q₈	C₂²×C₄	1	1	yes	characteristic
568	C₂²⋊Q₈	C₂²×C₄	1	1	yes	characteristic
569	C₂²⋊Q₈	C₂²×C₄	1	1	yes	characteristic
570	C₂²⋊Q₈	C₂²×C₄	1	1	yes	characteristic
571	#121	—	2	1	no	—
572	#121	—	2	1	no	—
573	#121	—	2	1	no	—
574	#121	—	2	1	no	—
575	#121	C₂²×C₄	1	1	yes	characteristic
576	#121	C₂²×C₄	1	1	yes	characteristic
577	#121	C₂²×C₄	1	1	yes	characteristic
578	#121	C₂²×C₄	1	1	yes	characteristic
579	#120	—	2	1	no	—
580	#120	—	2	1	no	—
581	C₄×Q₈	—	2	1	no	—
582	C₄×Q₈	—	2	1	no	—
583	C₄×Q₈	—	2	1	no	—
584	C₄×Q₈	—	2	1	no	—
585	C₄×Q₈	—	2	1	no	—
586	C₄×Q₈	—	2	1	no	—
587	C₄×Q₈	—	2	1	no	—
588	C₄×Q₈	—	2	1	no	—
589	C₄×Q₈	C₂²×C₄	1	1	yes	characteristic
590	C₄×Q₈	C₂²×C₄	1	1	yes	characteristic
591	C₄×Q₈	C₂²×C₄	1	1	yes	characteristic
592	C₄×Q₈	C₂²×C₄	1	1	yes	characteristic
593	C₄×Q₈	C₂²×C₄	1	1	yes	characteristic
594	C₄×Q₈	C₂²×C₄	1	1	yes	characteristic
595	C₄×Q₈	C₂²×C₄	1	1	yes	characteristic
596	C₄×Q₈	C₂²×C₄	1	1	yes	characteristic
597	C₄×Q₈	C₂²×C₄	1	1	yes	characteristic
598	C₄×Q₈	C₂²×C₄	1	1	yes	characteristic
599	C₄×Q₈	C₂²×C₄	1	1	yes	characteristic
600	C₄×Q₈	C₂²×C₄	1	1	yes	characteristic
601	C₄×D₄	—	2	1	no	—
602	C₄×D₄	—	2	1	no	—
603	C₄×D₄	—	2	1	no	—
604	C₄×D₄	—	2	1	no	—
605	C₄×D₄	—	2	1	no	—
606	C₄×D₄	—	2	1	no	—
607	C₄×D₄	—	2	1	no	—
608	C₄×D₄	—	2	1	no	—
609	C₄×D₄	—	2	1	no	—
610	C₄×D₄	—	2	1	no	—
611	C₄×D₄	—	2	1	no	—
612	C₄×D₄	—	2	1	no	—
613	C₄×D₄	—	2	1	no	—
614	C₄×D₄	—	2	1	no	—
615	C₄×D₄	—	2	1	no	—
616	C₄×D₄	—	2	1	no	—
617	C₄×D₄	—	2	1	no	—
618	C₄×D₄	—	2	1	no	—
619	C₄×D₄	—	2	1	no	—
620	C₄×D₄	—	2	1	no	—
621	C₄×D₄	—	2	1	no	—
622	C₄×D₄	—	2	1	no	—
623	C₄×D₄	—	2	1	no	—
624	C₄×D₄	—	2	1	no	—
625	C₄×D₄	—	2	1	no	—
626	C₄×D₄	—	2	1	no	—
627	C₄×D₄	—	2	1	no	—
628	C₄×D₄	—	2	1	no	—
629	C₄×D₄	—	2	1	no	—
630	C₄×D₄	—	2	1	no	—
631	C₄×D₄	—	2	1	no	—
632	C₄×D₄	—	2	1	no	—
633	C₄×D₄	—	2	1	no	—
634	C₄×D₄	—	2	1	no	—
635	C₄×D₄	—	2	1	no	—
636	C₄×D₄	—	2	1	no	—
637	C₄×D₄	C₂²×C₄	1	1	yes	characteristic
638	C₄×D₄	C₂²×C₄	1	1	yes	characteristic
639	C₄×D₄	C₂²×C₄	1	1	yes	characteristic
640	C₄×D₄	C₂²×C₄	1	1	yes	characteristic
641	C₄×D₄	C₂²×C₄	1	1	yes	characteristic
642	C₄×D₄	C₂²×C₄	1	1	yes	characteristic
643	C₄×D₄	C₂²×C₄	1	1	yes	characteristic
644	C₄×D₄	C₂²×C₄	1	1	yes	characteristic
645	C₄×D₄	C₂²×C₄	1	1	yes	characteristic
646	C₄×D₄	C₂²×C₄	1	1	yes	characteristic
647	C₄×D₄	C₂²×C₄	1	1	yes	characteristic
648	C₄×D₄	C₂²×C₄	1	1	yes	characteristic
649	#117	—	2	1	no	—
650	#117	—	2	1	no	—
651	#117	—	2	1	no	—
652	#117	—	2	1	no	—
653	#117	—	2	1	no	—
654	#117	—	2	1	no	—
655	#117	—	2	1	no	—
656	#117	—	2	1	no	—
657	#117	—	2	1	no	—
658	#117	—	2	1	no	—
659	#117	—	2	1	no	—
660	#117	—	2	1	no	—
661	#117	—	2	1	no	—
662	#117	—	2	1	no	—
663	#117	—	2	1	no	—
664	#117	—	2	1	no	—
665	#117	—	2	1	no	—
666	#117	—	2	1	no	—
667	#117	C₂²×C₄	1	1	yes	characteristic
668	#117	C₂²×C₄	1	1	yes	characteristic
669	#117	C₂⁴	1	1	yes	characteristic
670	#117	C₂⁴	1	1	yes	characteristic
671	#117	C₂⁴	1	1	yes	characteristic
672	#117	C₂⁴	1	1	yes	characteristic
673	C₂×C₄⋊C₄	—	2	1	no	—
674	C₂×C₄⋊C₄	—	2	1	no	—
675	C₂×C₄⋊C₄	—	2	1	no	—
676	C₂×C₄⋊C₄	—	2	2	no	—
677	C₂×C₄⋊C₄	—	2	1	no	—
678	C₂×C₄⋊C₄	—	4	4	no	—
679	C₂×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
680	C₂×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
681	C₂×C₂²⋊C₄	—	2	1	no	—
682	C₂×C₂²⋊C₄	—	2	1	no	—
683	C₂×C₂²⋊C₄	—	2	1	no	—
684	C₂×C₄²	—	2	1	no	—
685	C₂×C₄²	—	2	1	no	—
686	C₂×C₄²	—	2	1	no	—
687	C₂×C₄²	—	2	1	no	—
688	C₂×C₄²	—	2	1	no	—
689	C₂×C₄²	—	2	1	no	—
690	C₂×C₄²	—	2	1	no	—
691	C₂×C₄²	—	2	1	no	—
692	C₂×C₄²	—	2	1	no	—
693	C₂×C₄²	—	2	1	no	—
694	C₂×C₄²	—	2	1	no	—
695	C₂×C₄²	—	2	1	no	—
696	C₂×C₄²	—	2	1	no	—
697	C₂×C₄²	—	2	2	no	—
698	C₂×C₄²	—	4	2	no	—
699	C₂×C₄²	—	4	2	no	—
700	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
701	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
702	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
703	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
704	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
705	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
706	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
707	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
708	C₂×C₄²	#41	1	1	yes	characteristic
709	C₂×C₄²	#41	1	1	yes	characteristic
710	C₂×C₄²	C₂⁴	1	2	yes	—
711	C₂×C₄²	C₂⁴	1	2	yes	—
712	C₂×C₄²	C₂⁴	1	1	yes	characteristic
713	C₂×C₄²	C₂⁴	1	1	yes	characteristic
714	#108	—	4	2	no	—
715	#108	—	4	2	no	—
716	#108	—	4	2	no	—
717	#108	—	4	2	no	—
718	#107	C₂²×C₄	1	1	yes	characteristic
719	#107	C₂²×C₄	1	1	yes	characteristic
720	#107	C₂²×C₄	1	1	yes	characteristic
721	#107	C₂²×C₄	1	1	yes	characteristic
722	#107	C₂²×C₄	1	1	yes	characteristic
723	#107	C₂²×C₄	1	1	yes	characteristic
724	#107	C₂²×C₄	1	1	yes	characteristic
725	#107	C₂²×C₄	1	1	yes	characteristic
726	#106	C₂²×C₄	1	1	yes	characteristic
727	#106	C₂²×C₄	1	1	yes	characteristic
728	#106	C₂²×C₄	1	1	yes	characteristic
729	#106	C₂²×C₄	1	1	yes	characteristic
730	#106	C₂²×C₄	1	1	yes	characteristic
731	#106	C₂²×C₄	1	1	yes	characteristic
732	#106	C₂²×C₄	1	1	yes	characteristic
733	#106	C₂²×C₄	1	1	yes	characteristic
734	C₄⋊C₈	—	2	2	no	—
735	C₄⋊C₈	—	2	2	no	—
736	C₄⋊C₈	—	2	2	no	—
737	C₄⋊C₈	—	2	2	no	—
738	C₄⋊C₈	—	2	2	no	—
739	C₄⋊C₈	—	2	2	no	—
740	C₄⋊C₈	—	2	2	no	—
741	C₄⋊C₈	—	2	2	no	—
742	C₄⋊C₈	—	2	1	no	—
743	C₄⋊C₈	—	2	1	no	—
744	C₄⋊C₈	—	2	1	no	—
745	C₄⋊C₈	—	2	1	no	—
746	C₄⋊C₈	—	2	1	no	—
747	C₄⋊C₈	—	2	1	no	—
748	C₄⋊C₈	—	2	2	no	—
749	C₄⋊C₈	—	2	2	no	—
750	C₄⋊C₈	—	2	1	no	—
751	C₄⋊C₈	—	2	1	no	—
752	C₄⋊C₈	C₂²×C₄	1	1	yes	characteristic
753	C₄⋊C₈	C₂²×C₄	1	1	yes	characteristic
754	C₄⋊C₈	C₂²×C₄	1	1	yes	characteristic
755	C₄⋊C₈	C₂²×C₄	1	1	yes	characteristic
756	C₄⋊C₈	C₂²×C₄	1	1	yes	characteristic
757	C₄⋊C₈	C₂²×C₄	1	1	yes	characteristic
758	C₄⋊C₈	C₂²×C₄	1	1	yes	characteristic
759	C₄⋊C₈	C₂²×C₄	1	1	yes	characteristic
760	C₄⋊C₈	C₂×D₄	1	1	yes	characteristic
761	C₄⋊C₈	C₂×D₄	1	1	yes	characteristic
762	C₄⋊C₈	C₂×D₄	1	1	yes	characteristic
763	C₄⋊C₈	C₂×D₄	1	1	yes	characteristic
764	C₄⋊C₈	C₂×D₄	1	2	yes	—
765	C₄⋊C₈	C₂×D₄	1	2	yes	—
766	#104	—	2	4	no	—
767	#104	—	2	4	no	—
768	#104	—	4	2	no	—
769	#104	—	4	2	no	—
770	#104	—	4	2	no	—
771	#104	—	4	2	no	—
772	#104	—	4	2	no	—
773	#104	—	4	2	no	—
774	#103	C₂²×C₄	1	1	yes	characteristic
775	#103	C₂²×C₄	1	1	yes	characteristic
776	#103	C₂²×C₄	1	1	yes	characteristic
777	#103	C₂²×C₄	1	1	yes	characteristic
778	#103	C₂²×C₄	1	1	yes	characteristic
779	#103	C₂²×C₄	1	1	yes	characteristic
780	#103	C₂²×C₄	1	1	yes	characteristic
781	#103	C₂²×C₄	1	1	yes	characteristic
782	#103	C₂²×C₄	1	1	yes	characteristic
783	#103	C₂²×C₄	1	1	yes	characteristic
784	#103	C₂²×C₄	1	1	yes	characteristic
785	#103	C₂²×C₄	1	1	yes	characteristic
786	#103	C₂²×C₄	1	1	yes	characteristic
787	#103	C₂²×C₄	1	1	yes	characteristic
788	#103	C₂²×C₄	1	1	yes	characteristic
789	#103	C₂²×C₄	1	1	yes	characteristic
790	#102	C₂²×C₄	1	1	yes	characteristic
791	#102	C₂²×C₄	1	1	yes	characteristic
792	#102	C₂²×C₄	1	1	yes	characteristic
793	#102	C₂²×C₄	1	1	yes	characteristic
794	#102	C₂²×C₄	1	1	yes	characteristic
795	#102	C₂²×C₄	1	1	yes	characteristic
796	#102	C₂²×C₄	1	1	yes	characteristic
797	#102	C₂²×C₄	1	1	yes	characteristic
798	#102	C₂²×C₄	1	1	yes	characteristic
799	#102	C₂²×C₄	1	1	yes	characteristic
800	#102	C₂²×C₄	1	1	yes	characteristic
801	#102	C₂²×C₄	1	1	yes	characteristic
802	#102	C₂²×C₄	1	1	yes	characteristic
803	#102	C₂²×C₄	1	1	yes	characteristic
804	#102	C₂²×C₄	1	1	yes	characteristic
805	#102	C₂²×C₄	1	1	yes	characteristic
806	C₂²⋊C₈	—	2	2	no	—
807	C₂²⋊C₈	—	2	2	no	—
808	C₂²⋊C₈	—	2	2	no	—
809	C₂²⋊C₈	—	2	2	no	—
810	C₂²⋊C₈	—	2	2	no	—
811	C₂²⋊C₈	—	2	2	no	—
812	C₂²⋊C₈	—	2	2	no	—
813	C₂²⋊C₈	—	2	2	no	—
814	C₂²⋊C₈	—	2	2	no	—
815	C₂²⋊C₈	—	2	2	no	—
816	C₂²⋊C₈	C₂²×C₄	1	1	yes	characteristic
817	C₂²⋊C₈	C₂²×C₄	1	1	yes	characteristic
818	C₂²⋊C₈	C₂²×C₄	1	1	yes	characteristic
819	C₂²⋊C₈	C₂²×C₄	1	1	yes	characteristic
820	C₂²⋊C₈	C₂²×C₄	1	1	yes	characteristic
821	C₂²⋊C₈	C₂²×C₄	1	1	yes	characteristic
822	C₂²⋊C₈	C₂²×C₄	1	1	yes	characteristic
823	C₂²⋊C₈	C₂²×C₄	1	1	yes	characteristic
824	C₂²⋊C₈	C₂×D₄	1	2	yes	—
825	C₂²⋊C₈	C₂×D₄	1	2	yes	—
826	C₂²⋊C₈	C₂×D₄	1	2	yes	—
827	C₂²⋊C₈	C₂×D₄	1	2	yes	—
828	#97	—	2	2	no	—
829	#97	—	2	2	no	—
830	#97	—	2	2	no	—
831	#97	—	2	2	no	—
832	#97	—	2	2	no	—
833	#97	—	4	2	no	—
834	#97	—	4	2	no	—
835	#97	C₂×D₄	1	2	yes	—
836	#97	C₂×D₄	1	2	yes	—
837	#97	C₂×D₄	1	2	yes	—
838	#97	C₂×D₄	1	2	yes	—
839	C₄×C₈	—	2	2	no	—
840	C₄×C₈	—	2	2	no	—
841	C₄×C₈	—	2	2	no	—
842	C₄×C₈	—	2	2	no	—
843	C₄×C₈	—	2	2	no	—
844	C₄×C₈	—	4	2	no	—
845	C₄×C₈	—	4	2	no	—
846	C₄×C₈	C₂²×C₄	1	1	yes	characteristic
847	C₄×C₈	C₂²×C₄	1	1	yes	characteristic
848	C₄×C₈	C₂²×C₄	1	1	yes	characteristic
849	C₄×C₈	C₂²×C₄	1	1	yes	characteristic
850	C₄×C₈	C₂²×C₄	1	1	yes	characteristic
851	C₄×C₈	C₂²×C₄	1	1	yes	characteristic
852	C₄×C₈	C₂²×C₄	1	1	yes	characteristic
853	C₄×C₈	C₂²×C₄	1	1	yes	characteristic
854	#95	—	2	1	no	—
855	#95	—	2	2	no	—
856	#95	—	2	1	no	—
857	C₂⁴	—	2	1	no	—
858	C₂⁴	C₂×#41	1	1	yes	characteristic
859	#41	—	2	1	no	—
860	#41	—	2	1	no	—
861	#41	—	2	2	no	—
862	#41	—	2	2	no	—
863	#41	—	2	1	no	—
864	#41	—	2	1	no	—
865	#41	—	2	1	no	—
866	#41	—	2	1	no	—
867	#41	—	2	1	no	—
868	#41	—	2	1	no	—
869	#41	—	2	1	no	—
870	#41	—	2	1	no	—
871	#41	—	2	1	no	—
872	#41	—	2	1	no	—
873	#41	—	2	1	no	—
874	#41	—	2	1	no	—
875	#41	—	4	2	no	—
876	#41	—	4	2	no	—
877	#41	—	4	1	no	—
878	#41	—	4	1	no	—
879	#41	—	4	2	no	—
880	#41	—	4	2	no	—
881	#41	—	8	2	no	—
882	#41	—	8	2	no	—
883	#41	H(5,𝔽₂)	1	2	yes	—
884	#41	2₋¹⁺⁴	1	2	yes	—
885	C₂×Q₈	—	2	1	no	—
886	C₂×Q₈	—	2	1	no	—
887	C₂×Q₈	—	2	1	no	—
888	C₂×Q₈	—	2	2	no	—
889	C₂×Q₈	—	4	1	no	—
890	C₂×Q₈	C₂³×C₄	1	1	yes	characteristic
891	C₂×Q₈	C₂³×C₄	1	1	yes	characteristic
892	C₂×Q₈	C₂³×C₄	1	1	yes	characteristic
893	C₂×Q₈	C₂³×C₄	1	1	yes	characteristic
894	C₂×D₄	—	2	1	no	—
895	C₂×D₄	—	2	2	no	—
896	C₂×D₄	—	2	1	no	—
897	C₂×D₄	—	2	1	no	—
898	C₂×D₄	—	2	1	no	—
899	C₂×D₄	—	2	1	no	—
900	C₂×D₄	—	2	1	no	—
901	C₂×D₄	—	2	1	no	—
902	C₂×D₄	—	2	1	no	—
903	C₂×D₄	—	2	1	no	—
904	C₂×D₄	—	2	1	no	—
905	C₂×D₄	—	2	1	no	—
906	C₂×D₄	—	2	1	no	—
907	C₂×D₄	—	2	1	no	—
908	C₂×D₄	—	4	1	no	—
909	C₂×D₄	—	4	2	no	—
910	C₂×D₄	—	4	2	no	—
911	C₂×D₄	C₂³×C₄	1	1	yes	characteristic
912	C₂×D₄	C₂³×C₄	1	1	yes	characteristic
913	C₂×D₄	C₂³×C₄	1	1	yes	characteristic
914	C₂×D₄	C₂³×C₄	1	1	yes	characteristic
915	C₂²×C₄	—	2	1	no	—
916	C₂²×C₄	—	2	1	no	—
917	C₂²×C₄	—	2	1	no	—
918	C₂²×C₄	—	2	1	no	—
919	C₂²×C₄	—	2	1	no	—
920	C₂²×C₄	—	2	1	no	—
921	C₂²×C₄	—	2	1	no	—
922	C₂²×C₄	—	2	2	no	—
923	C₂²×C₄	—	2	1	no	—
924	C₂²×C₄	—	2	1	no	—
925	C₂²×C₄	—	2	1	no	—
926	C₂²×C₄	—	2	1	no	—
927	C₂²×C₄	—	2	1	no	—
928	C₂²×C₄	—	2	1	no	—
929	C₂²×C₄	—	2	1	no	—
930	C₂²×C₄	—	2	1	no	—
931	C₂²×C₄	—	2	1	no	—
932	C₂²×C₄	—	2	1	no	—
933	C₂²×C₄	—	2	1	no	—
934	C₂²×C₄	—	2	1	no	—
935	C₂²×C₄	—	2	1	no	—
936	C₂²×C₄	—	2	1	no	—
937	C₂²×C₄	—	2	1	no	—
938	C₂²×C₄	—	2	1	no	—
939	C₂²×C₄	—	2	1	no	—
940	C₂²×C₄	—	2	1	no	—
941	C₂²×C₄	—	2	2	no	—
942	C₂²×C₄	—	4	2	no	—
943	C₂²×C₄	—	4	2	no	—
944	C₂²×C₄	—	4	2	no	—
945	C₂²×C₄	—	4	2	no	—
946	C₂²×C₄	—	4	4	no	—
947	C₂²×C₄	—	4	4	no	—
948	C₂²×C₄	—	8	2	no	—
949	C₂²×C₄	—	8	2	no	—
950	C₂²×C₄	—	8	2	no	—
951	C₂²×C₄	C₄×D₄	1	1	yes	characteristic
952	C₂²×C₄	C₄×D₄	1	1	yes	characteristic
953	C₂²×C₄	C₄×D₄	1	1	yes	characteristic
954	C₂²×C₄	C₄×D₄	1	1	yes	characteristic
955	C₂²×C₄	C₄×D₄	1	1	yes	characteristic
956	C₂²×C₄	C₄×D₄	1	1	yes	characteristic
957	C₂²×C₄	C₄×D₄	1	1	yes	characteristic
958	C₂²×C₄	C₄×D₄	1	1	yes	characteristic
959	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
960	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
961	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
962	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
963	C₂²×C₄	C₂×#41	1	1	yes	characteristic
964	C₂²×C₄	C₂×#41	1	1	yes	characteristic
965	C₂²×C₄	C₂×#41	1	1	yes	characteristic
966	C₂²×C₄	C₂×#41	1	1	yes	characteristic
967	C₂²×C₄	C₂×#41	1	1	yes	characteristic
968	C₂²×C₄	C₂⁵	1	1	yes	characteristic
969	Q₁₆	—	2	2	no	—
970	Q₁₆	—	2	2	no	—
971	Q₁₆	—	4	1	no	—
972	Q₁₆	—	4	1	no	—
973	SD₁₆	—	2	2	no	—
974	SD₁₆	—	2	2	no	—
975	SD₁₆	—	2	2	no	—
976	SD₁₆	—	2	2	no	—
977	SD₁₆	—	4	1	no	—
978	SD₁₆	—	4	1	no	—
979	SD₁₆	—	4	1	no	—
980	SD₁₆	—	4	1	no	—
981	D₈	—	2	2	no	—
982	D₈	—	2	2	no	—
983	D₈	—	4	1	no	—
984	D₈	—	4	1	no	—
985	M₁₆	—	2	2	no	—
986	M₁₆	—	2	2	no	—
987	M₁₆	—	2	2	no	—
988	M₁₆	—	2	2	no	—
989	M₁₆	—	2	2	no	—
990	M₁₆	—	2	2	no	—
991	M₁₆	—	2	2	no	—
992	M₁₆	—	2	2	no	—
993	M₁₆	—	4	4	no	—
994	M₁₆	—	4	4	no	—
995	M₁₆	—	8	2	no	—
996	M₁₆	—	8	2	no	—
997	M₁₆	—	8	2	no	—
998	C₂×C₈	—	2	1	no	—
999	C₂×C₈	—	2	2	no	—
1000	C₂×C₈	—	2	1	no	—
1001	C₂×C₈	—	2	2	no	—
1002	C₂×C₈	—	2	1	no	—
1003	C₂×C₈	—	2	1	no	—
1004	C₂×C₈	—	2	1	no	—
1005	C₂×C₈	—	2	2	no	—
1006	C₂×C₈	—	2	1	no	—
1007	C₂×C₈	—	2	1	no	—
1008	C₂×C₈	—	2	1	no	—
1009	C₂×C₈	—	2	2	no	—
1010	C₂×C₈	—	2	2	no	—
1011	C₂×C₈	—	2	2	no	—
1012	C₂×C₈	—	2	2	no	—
1013	C₂×C₈	—	2	2	no	—
1014	C₂×C₈	—	4	4	no	—
1015	C₂×C₈	—	4	4	no	—
1016	C₂×C₈	—	8	2	no	—
1017	C₂×C₈	—	8	2	no	—
1018	C₂×C₈	—	8	2	no	—
1019	C₂×C₈	C₂³×C₄	1	1	yes	characteristic
1020	C₂×C₈	C₂³×C₄	1	1	yes	characteristic
1021	C₂×C₈	C₂³×C₄	1	1	yes	characteristic
1022	C₂×C₈	C₂³×C₄	1	1	yes	characteristic
1023	C₂×C₈	C₂³×C₄	1	1	yes	characteristic
1024	C₂×C₈	C₂³×C₄	1	1	yes	characteristic
1025	C₂×C₈	C₂³×C₄	1	1	yes	characteristic
1026	C₂×C₈	C₂³×C₄	1	1	yes	characteristic
1027	C₂×C₈	C₂²×D₄	1	2	yes	—
1028	C₂×C₈	C₂²×D₄	1	2	yes	—
1029	C₂×C₈	C₂²×D₄	1	2	yes	—
1030	C₂×C₈	C₂²×D₄	1	2	yes	—
1031	C₄⋊C₄	—	2	4	no	—
1032	C₄⋊C₄	—	2	1	no	—
1033	C₄⋊C₄	—	2	1	no	—
1034	C₄⋊C₄	—	2	1	no	—
1035	C₄⋊C₄	—	2	1	no	—
1036	C₄⋊C₄	—	2	1	no	—
1037	C₄⋊C₄	—	2	1	no	—
1038	C₄⋊C₄	—	2	1	no	—
1039	C₄⋊C₄	—	2	1	no	—
1040	C₄⋊C₄	—	2	1	no	—
1041	C₄⋊C₄	—	2	1	no	—
1042	C₄⋊C₄	—	2	1	no	—
1043	C₄⋊C₄	—	2	1	no	—
1044	C₄⋊C₄	—	2	1	no	—
1045	C₄⋊C₄	—	2	1	no	—
1046	C₄⋊C₄	—	2	1	no	—
1047	C₄⋊C₄	—	2	1	no	—
1048	C₄⋊C₄	—	2	1	no	—
1049	C₄⋊C₄	—	2	1	no	—
1050	C₄⋊C₄	—	2	1	no	—
1051	C₄⋊C₄	—	2	1	no	—
1052	C₄⋊C₄	—	2	1	no	—
1053	C₄⋊C₄	—	2	1	no	—
1054	C₄⋊C₄	—	2	1	no	—
1055	C₄⋊C₄	—	2	1	no	—
1056	C₄⋊C₄	—	2	1	no	—
1057	C₄⋊C₄	—	2	1	no	—
1058	C₄⋊C₄	—	4	2	no	—
1059	C₄⋊C₄	—	4	4	no	—
1060	C₄⋊C₄	C₂³×C₄	1	1	yes	characteristic
1061	C₄⋊C₄	C₂³×C₄	1	1	yes	characteristic
1062	C₄⋊C₄	C₂³×C₄	1	1	yes	characteristic
1063	C₄⋊C₄	C₂³×C₄	1	1	yes	characteristic
1064	C₄⋊C₄	C₂³×C₄	1	1	yes	characteristic
1065	C₄⋊C₄	C₂³×C₄	1	1	yes	characteristic
1066	C₄⋊C₄	C₂³×C₄	1	1	yes	characteristic
1067	C₄⋊C₄	C₂³×C₄	1	1	yes	characteristic
1068	C₂²⋊C₄	—	2	1	no	—
1069	C₂²⋊C₄	—	2	1	no	—
1070	C₂²⋊C₄	—	2	1	no	—
1071	C₂²⋊C₄	—	2	1	no	—
1072	C₂²⋊C₄	—	2	1	no	—
1073	C₂²⋊C₄	—	2	1	no	—
1074	C₂²⋊C₄	—	2	1	no	—
1075	C₂²⋊C₄	—	2	1	no	—
1076	C₂²⋊C₄	—	2	1	no	—
1077	C₂²⋊C₄	—	2	1	no	—
1078	C₂²⋊C₄	—	2	1	no	—
1079	C₂²⋊C₄	—	2	1	no	—
1080	C₂²⋊C₄	—	2	1	no	—
1081	C₂²⋊C₄	—	2	1	no	—
1082	C₂²⋊C₄	—	2	1	no	—
1083	C₂²⋊C₄	—	2	1	no	—
1084	C₂²⋊C₄	—	2	1	no	—
1085	C₂²⋊C₄	—	2	1	no	—
1086	C₂²⋊C₄	—	2	1	no	—
1087	C₂²⋊C₄	—	2	1	no	—
1088	C₂²⋊C₄	—	2	1	no	—
1089	C₂²⋊C₄	—	2	1	no	—
1090	C₂²⋊C₄	—	2	1	no	—
1091	C₂²⋊C₄	—	2	1	no	—
1092	C₂²⋊C₄	—	2	1	no	—
1093	C₂²⋊C₄	—	2	1	no	—
1094	C₂²⋊C₄	—	2	1	no	—
1095	C₂²⋊C₄	—	2	1	no	—
1096	C₂²⋊C₄	—	2	1	no	—
1097	C₂²⋊C₄	—	2	1	no	—
1098	C₄²	—	2	1	no	—
1099	C₄²	—	2	1	no	—
1100	C₄²	—	2	1	no	—
1101	C₄²	—	2	1	no	—
1102	C₄²	—	2	1	no	—
1103	C₄²	—	2	1	no	—
1104	C₄²	—	2	1	no	—
1105	C₄²	—	2	1	no	—
1106	C₄²	—	2	1	no	—
1107	C₄²	—	2	1	no	—
1108	C₄²	—	2	1	no	—
1109	C₄²	—	2	1	no	—
1110	C₄²	—	2	1	no	—
1111	C₄²	—	2	1	no	—
1112	C₄²	—	2	1	no	—
1113	C₄²	—	2	1	no	—
1114	C₄²	—	2	1	no	—
1115	C₄²	—	2	1	no	—
1116	C₄²	—	2	2	no	—
1117	C₄²	—	2	2	no	—
1118	C₄²	—	2	2	no	—
1119	C₄²	—	2	2	no	—
1120	C₄²	—	8	2	no	—
1121	C₄²	C₄×D₄	1	1	yes	characteristic
1122	C₄²	C₄×D₄	1	1	yes	characteristic
1123	C₄²	C₄×D₄	1	1	yes	characteristic
1124	C₄²	C₄×D₄	1	1	yes	characteristic
1125	C₄²	C₄×D₄	1	1	yes	characteristic
1126	C₄²	C₄×D₄	1	1	yes	characteristic
1127	C₄²	C₄×D₄	1	1	yes	characteristic
1128	C₄²	C₄×D₄	1	1	yes	characteristic
1129	C₄²	C₂³×C₄	1	1	yes	characteristic
1130	C₄²	C₂³×C₄	1	1	yes	characteristic
1131	C₄²	C₂³×C₄	1	1	yes	characteristic
1132	C₄²	C₂³×C₄	1	1	yes	characteristic
1133	C₄²	C₂²×D₄	1	1	yes	characteristic
1134	C₄²	C₂²×D₄	1	1	yes	characteristic
1135	C₄²	C₂²×D₄	1	1	yes	characteristic
1136	C₄²	C₂²×D₄	1	1	yes	characteristic
1137	C₂³	—	2	1	no	—
1138	C₂³	—	2	2	no	—
1139	C₂³	—	2	1	no	—
1140	C₂³	—	2	1	no	—
1141	C₂³	—	2	1	no	—
1142	C₂³	—	2	1	no	—
1143	C₂³	—	2	1	no	—
1144	C₂³	—	4	1	no	—
1145	C₂³	—	4	2	no	—
1146	C₂³	—	4	2	no	—
1147	C₂³	—	8	1	no	—
1148	C₂³	C₂×C₄×D₄	1	1	yes	characteristic
1149	C₂³	C₂×C₄×D₄	1	1	yes	characteristic
1150	C₂³	C₂²×#41	1	1	yes	characteristic
1151	Q₈	—	2	1	no	—
1152	Q₈	—	2	1	no	—
1153	Q₈	—	2	1	no	—
1154	Q₈	—	2	1	no	—
1155	Q₈	—	2	1	no	—
1156	Q₈	—	2	1	no	—
1157	Q₈	—	2	1	no	—
1158	Q₈	—	4	2	no	—
1159	Q₈	—	8	1	no	—
1160	Q₈	—	8	1	no	—
1161	Q₈	#520	1	2	yes	—
1162	D₄	—	2	2	no	—
1163	D₄	—	2	2	no	—
1164	D₄	—	2	1	no	—
1165	D₄	—	2	1	no	—
1166	D₄	—	2	1	no	—
1167	D₄	—	2	1	no	—
1168	D₄	—	2	1	no	—
1169	D₄	—	2	1	no	—
1170	D₄	—	2	1	no	—
1171	D₄	—	4	2	no	—
1172	D₄	—	4	2	no	—
1173	D₄	—	4	2	no	—
1174	D₄	—	4	2	no	—
1175	D₄	—	4	2	no	—
1176	D₄	—	4	1	no	—
1177	D₄	—	4	1	no	—
1178	D₄	—	4	1	no	—
1179	D₄	—	4	1	no	—
1180	D₄	—	4	1	no	—
1181	D₄	—	4	1	no	—
1182	D₄	—	8	1	no	—
1183	D₄	—	8	1	no	—
1184	D₄	—	8	1	no	—
1185	D₄	—	8	1	no	—
1186	D₄	#520	1	2	yes	—
1187	C₂×C₄	—	2	1	no	—
1188	C₂×C₄	—	2	2	no	—
1189	C₂×C₄	—	2	2	no	—
1190	C₂×C₄	—	2	1	no	—
1191	C₂×C₄	—	2	1	no	—
1192	C₂×C₄	—	2	1	no	—
1193	C₂×C₄	—	2	1	no	—
1194	C₂×C₄	—	2	1	no	—
1195	C₂×C₄	—	2	1	no	—
1196	C₂×C₄	—	2	2	no	—
1197	C₂×C₄	—	2	2	no	—
1198	C₂×C₄	—	2	2	no	—
1199	C₂×C₄	—	2	2	no	—
1200	C₂×C₄	—	2	1	no	—
1201	C₂×C₄	—	2	1	no	—
1202	C₂×C₄	—	2	2	no	—
1203	C₂×C₄	—	2	1	no	—
1204	C₂×C₄	—	2	1	no	—
1205	C₂×C₄	—	2	4	no	—
1206	C₂×C₄	—	2	1	no	—
1207	C₂×C₄	—	2	1	no	—
1208	C₂×C₄	—	2	1	no	—
1209	C₂×C₄	—	2	1	no	—
1210	C₂×C₄	—	2	1	no	—
1211	C₂×C₄	—	2	1	no	—
1212	C₂×C₄	—	2	1	no	—
1213	C₂×C₄	—	2	1	no	—
1214	C₂×C₄	—	2	1	no	—
1215	C₂×C₄	—	2	1	no	—
1216	C₂×C₄	—	2	1	no	—
1217	C₂×C₄	—	4	1	no	—
1218	C₂×C₄	—	4	1	no	—
1219	C₂×C₄	—	4	1	no	—
1220	C₂×C₄	—	4	1	no	—
1221	C₂×C₄	—	4	1	no	—
1222	C₂×C₄	—	4	1	no	—
1223	C₂×C₄	—	4	1	no	—
1224	C₂×C₄	—	4	2	no	—
1225	C₂×C₄	—	4	2	no	—
1226	C₂×C₄	—	4	2	no	—
1227	C₂×C₄	—	4	2	no	—
1228	C₂×C₄	—	4	2	no	—
1229	C₂×C₄	—	4	2	no	—
1230	C₂×C₄	—	4	2	no	—
1231	C₂×C₄	—	4	2	no	—
1232	C₂×C₄	—	4	2	no	—
1233	C₂×C₄	—	4	2	no	—
1234	C₂×C₄	—	4	1	no	—
1235	C₂×C₄	—	4	1	no	—
1236	C₂×C₄	—	4	1	no	—
1237	C₂×C₄	—	4	1	no	—
1238	C₂×C₄	—	4	1	no	—
1239	C₂×C₄	—	4	1	no	—
1240	C₂×C₄	—	4	2	no	—
1241	C₂×C₄	—	4	2	no	—
1242	C₂×C₄	—	4	2	no	—
1243	C₂×C₄	—	8	1	no	—
1244	C₂×C₄	—	8	1	no	—
1245	C₂×C₄	—	8	1	no	—
1246	C₂×C₄	—	8	1	no	—
1247	C₂×C₄	—	8	1	no	—
1248	C₂×C₄	—	8	1	no	—
1249	C₂×C₄	—	8	1	no	—
1250	C₂×C₄	—	8	1	no	—
1251	C₂×C₄	—	8	1	no	—
1252	C₂×C₄	—	8	8	no	—
1253	C₂×C₄	C₂×C₄×D₄	1	1	yes	characteristic
1254	C₂×C₄	C₂×C₄×D₄	1	1	yes	characteristic
1255	C₂×C₄	C₂×C₄×D₄	1	1	yes	characteristic
1256	C₂×C₄	C₂×C₄×D₄	1	1	yes	characteristic
1257	C₂×C₄	C₂×C₄×D₄	1	1	yes	characteristic
1258	C₂×C₄	C₂×C₄×D₄	1	1	yes	characteristic
1259	C₂×C₄	C₂×C₄×D₄	1	1	yes	characteristic
1260	C₂×C₄	C₂×C₄×D₄	1	1	yes	characteristic
1261	C₂×C₄	C₂×C₄×D₄	1	1	yes	characteristic
1262	C₂×C₄	C₂×C₄×D₄	1	1	yes	characteristic
1263	C₂×C₄	C₂⁴×C₄	1	1	yes	characteristic
1264	C₂×C₄	C₂³×D₄	1	1	yes	characteristic
1265	C₂×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
1266	C₂×C₄	C₂×2₋¹⁺⁴	1	1	yes	characteristic
1267	C₂×C₄	#585	1	1	yes	characteristic
1268	C₂×C₄	#585	1	1	yes	characteristic
1269	C₈	—	2	1	no	—
1270	C₈	—	2	1	no	—
1271	C₈	—	2	1	no	—
1272	C₈	—	2	1	no	—
1273	C₈	—	2	1	no	—
1274	C₈	—	2	1	no	—
1275	C₈	—	2	1	no	—
1276	C₈	—	2	1	no	—
1277	C₈	—	2	2	no	—
1278	C₈	—	2	2	no	—
1279	C₈	—	2	2	no	—
1280	C₈	—	2	2	no	—
1281	C₈	—	4	2	no	—
1282	C₈	—	4	2	no	—
1283	C₈	—	4	2	no	—
1284	C₈	—	4	2	no	—
1285	C₂²	—	2	1	no	—
1286	C₂²	—	2	1	no	—
1287	C₂²	—	2	1	no	—
1288	C₂²	—	2	1	no	—
1289	C₂²	—	2	1	no	—
1290	C₂²	—	2	1	no	—
1291	C₂²	—	2	1	no	—
1292	C₂²	—	2	2	no	—
1293	C₂²	—	4	2	no	—
1294	C₂²	—	4	2	no	—
1295	C₂²	—	4	1	no	—
1296	C₂²	—	4	1	no	—
1297	C₂²	—	4	1	no	—
1298	C₂²	—	4	1	no	—
1299	C₂²	—	4	1	no	—
1300	C₂²	—	4	1	no	—
1301	C₂²	—	4	1	no	—
1302	C₂²	—	4	1	no	—
1303	C₂²	—	4	1	no	—
1304	C₂²	—	4	1	no	—
1305	C₂²	—	4	1	no	—
1306	C₂²	—	8	4	no	—
1307	C₂²	#2957	1	2	yes	—
1308	C₂²	C₂²×C₄×D₄	1	1	yes	characteristic
1309	C₂²	#3494	1	1	yes	characteristic
1310	C₂²	#3495	1	1	yes	characteristic
1311	C₄	—	2	1	no	—
1312	C₄	—	2	1	no	—
1313	C₄	—	2	1	no	—
1314	C₄	—	2	1	no	—
1315	C₄	—	2	1	no	—
1316	C₄	—	2	1	no	—
1317	C₄	—	2	1	no	—
1318	C₄	—	2	1	no	—
1319	C₄	—	2	1	no	—
1320	C₄	—	2	2	no	—
1321	C₄	—	4	4	no	—
1322	C₄	—	4	1	no	—
1323	C₄	—	4	1	no	—
1324	C₄	—	4	1	no	—
1325	C₄	—	4	1	no	—
1326	C₄	—	4	1	no	—
1327	C₄	—	4	1	no	—
1328	C₄	—	4	1	no	—
1329	C₄	—	4	1	no	—
1330	C₄	—	4	1	no	—
1331	C₄	—	4	1	no	—
1332	C₄	—	4	1	no	—
1333	C₄	—	8	2	no	—
1334	C₄	#2956	1	2	yes	—
1335	C₄	C₂×#520	1	1	yes	characteristic
1336	C₄	#3428	1	1	yes	characteristic
1337	C₄	#3488	1	1	yes	characteristic
1338	C₄	#3489	1	1	yes	characteristic
1339	C₂	—	2	1	no	—
1340	C₂	—	2	2	no	—
1341	C₂	—	2	1	no	—
1342	C₂	—	4	1	no	—
1343	C₂	—	4	2	no	—
1344	C₂	—	8	1	no	—
1345	C₂	—	8	1	no	—
1346	C₂	—	8	1	no	—
1347	C₂	#34202	1	1	yes	characteristic
1348	C₂	C₂×#2956	1	1	yes	characteristic
1349	C₂	C₂×#2957	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂³×D₄
commutator	C₂×C₄	C₂⁴×C₄
Frattini, cosocle	C₂²×C₄	C₂⁵
socle	C₂²	C₂²×C₄×D₄
prime radical	#60536	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂×#432 ◁ G
LECS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
2. #60269	C₂	semidirect
3. #60128	C₂	semidirect
4. #22950	C₂	semidirect
5. #22948	C₂	semidirect
6. #22888	C₂	semidirect
7. #22886	C₂	semidirect
8. #22803	C₂	semidirect
9. #22802	C₂	semidirect
10. #22783	C₂	semidirect
11. #22783	C₂	semidirect
12. #22782	C₂	semidirect
13. #22782	C₂	semidirect
14. #22688	C₂	semidirect
15. #22686	C₂	semidirect
16. #22167	C₂	semidirect
17. #22132	C₂	semidirect
18. #21993	C₂	semidirect
19. #21899	C₂	semidirect
20. #21629	C₂	semidirect
21. #21519	C₂	semidirect
22. C₂×#1806	C₂	semidirect
23. #20535	C₂	semidirect
26. #3108	C₄	semidirect
27. #3108	C₄	semidirect
28. #3107	C₄	semidirect
29. #3107	C₄	semidirect
30. #3106	C₄	semidirect
31. #3106	C₄	semidirect
32. #3105	C₄	semidirect
33. #3105	C₄	semidirect
34. #3104	C₄	semidirect
35. #3103	C₄	semidirect
36. #3102	C₄	semidirect
37. #3102	C₄	semidirect
38. #3102	C₄	semidirect
39. #3102	C₄	semidirect
40. #3101	C₄	semidirect
41. #3100	C₄	semidirect
56. #2961	C₂²	semidirect
65. #2932	C₂²	semidirect
70. #2925	C₂²	semidirect
71. #2925	C₂²	semidirect
83. #2906	C₂²	semidirect
84. #2906	C₂²	semidirect
90. #1986	C₂²	semidirect
91. #1980	C₂²	semidirect
94. #1950	C₂²	semidirect
95. #1950	C₂²	semidirect
96. #1946	C₂²	semidirect
97. #1945	C₂²	semidirect
99. #1938	C₂²	semidirect
101. #1937	C₂²	semidirect
104. #1929	C₂²	semidirect
105. #1929	C₂²	semidirect
106. #1922	C₂²	semidirect
107. #1922	C₂²	semidirect
108. #1922	C₂²	semidirect
109. #1922	C₂²	semidirect
118. #1866	C₂²	semidirect
119. #1866	C₂²	semidirect
122. #1848	C₂²	semidirect
123. #1848	C₂²	semidirect
124. #1837	C₂²	semidirect
125. #1837	C₂²	semidirect
132. #1806	C₂²	semidirect
133. #1806	C₂²	semidirect
134. #1806	C₂²	semidirect
135. #1806	C₂²	semidirect
136. #1773	C₂²	semidirect
137. #1772	C₂²	semidirect
138. #1771	C₂²	semidirect
139. #1771	C₂²	semidirect
140. #1770	C₂²	semidirect
141. #1770	C₂²	semidirect
142. C₈×C₄⋊C₄	C₂²	semidirect
143. C₈×C₄⋊C₄	C₂²	semidirect
145. #1765	C₂²	semidirect
147. #1764	C₂²	semidirect
223. #479	C₂×C₄	semidirect
224. #479	C₂×C₄	semidirect
225. #479	C₂×C₄	semidirect
226. #479	C₂×C₄	semidirect
227. #478	C₂×C₄	semidirect
228. #478	C₂×C₄	semidirect
229. #478	C₂×C₄	semidirect
230. #478	C₂×C₄	semidirect
231. #477	C₂×C₄	semidirect
232. #477	C₂×C₄	semidirect
233. #476	C₂×C₄	semidirect
234. #476	C₂×C₄	semidirect
235. #475	C₂×C₄	semidirect
236. #475	C₂×C₄	semidirect
237. #474	C₂×C₄	semidirect
238. #474	C₂×C₄	semidirect
239. #464	C₂×C₄	semidirect
240. #464	C₂×C₄	semidirect
241. #464	C₂×C₄	semidirect
242. #464	C₂×C₄	semidirect
243. #463	C₂×C₄	semidirect
244. #463	C₂×C₄	semidirect
245. #463	C₂×C₄	semidirect
246. #463	C₂×C₄	semidirect
247. #462	C₂×C₄	semidirect
248. #462	C₂×C₄	semidirect
249. #461	C₂×C₄	semidirect
250. #461	C₂×C₄	semidirect
251. #460	C₂×C₄	semidirect
252. #460	C₂×C₄	semidirect
253. #459	C₂×C₄	semidirect
254. #459	C₂×C₄	semidirect
277. C₄×Q₁₆	C₂×C₄	semidirect
278. C₄×Q₁₆	C₂×C₄	semidirect
279. C₄×Q₁₆	C₂×C₄	semidirect
280. C₄×Q₁₆	C₂×C₄	semidirect
281. C₄×Q₁₆	C₂×C₄	semidirect
282. C₄×Q₁₆	C₂×C₄	semidirect
283. C₄×Q₁₆	C₂×C₄	semidirect
284. C₄×Q₁₆	C₂×C₄	semidirect
285. C₄×SD₁₆	C₂×C₄	semidirect
286. C₄×SD₁₆	C₂×C₄	semidirect
287. C₄×SD₁₆	C₂×C₄	semidirect
288. C₄×SD₁₆	C₂×C₄	semidirect
289. C₄×SD₁₆	C₂×C₄	semidirect
290. C₄×SD₁₆	C₂×C₄	semidirect
291. C₄×SD₁₆	C₂×C₄	semidirect
292. C₄×SD₁₆	C₂×C₄	semidirect
293. C₄×SD₁₆	C₂×C₄	semidirect
294. C₄×SD₁₆	C₂×C₄	semidirect
295. C₄×SD₁₆	C₂×C₄	semidirect
296. C₄×SD₁₆	C₂×C₄	semidirect
297. C₄×SD₁₆	C₂×C₄	semidirect
298. C₄×SD₁₆	C₂×C₄	semidirect
299. C₄×SD₁₆	C₂×C₄	semidirect
300. C₄×SD₁₆	C₂×C₄	semidirect
301. C₄×D₈	C₂×C₄	semidirect
302. C₄×D₈	C₂×C₄	semidirect
303. C₄×D₈	C₂×C₄	semidirect
304. C₄×D₈	C₂×C₄	semidirect
305. C₄×D₈	C₂×C₄	semidirect
306. C₄×D₈	C₂×C₄	semidirect
307. C₄×D₈	C₂×C₄	semidirect
308. C₄×D₈	C₂×C₄	semidirect

Maximal subgroups

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

subgroup	index
#60536	2
#60269	2
#60128	2
#22950	2
#22948	2
#22888	2
#22886	2
#22803	2
#22802	2
#22783	2
#22782	2
#22688	2
#22686	2
#22167	2
#22132	2
#21993	2
#21899	2
#21629	2
#21519	2
C₂×#1806	2
#20535	2