Subgroups — #11675973

Order 768.

1794 conjugacy classes of subgroups.

The subgroup lattice has 1628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#86949	C₂	1	1	yes	maximal, characteristic, complemented
2	#86926	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#3389	C₂	1	1	yes	maximal, characteristic, complemented
4	#83633	C₂	1	1	yes	maximal, characteristic, complemented
5	#83631	C₂	1	1	yes	maximal, characteristic, complemented
6	#81976	C₂	1	1	yes	maximal, characteristic, complemented
7	#81975	C₂	1	1	yes	maximal, characteristic, complemented
8	#81966	C₂	1	1	yes	maximal, characteristic, complemented
9	#81965	C₂	1	1	yes	maximal, characteristic, complemented
10	#81918	C₂	1	1	yes	maximal, characteristic, complemented
11	#81913	C₂	1	1	yes	maximal, characteristic, complemented
12	#81170	C₂	1	1	yes	maximal, characteristic, complemented
13	#81169	C₂	1	1	yes	maximal, characteristic, complemented
14	#81168	C₂	1	1	yes	maximal, characteristic, complemented
15	#81165	C₂	1	1	yes	maximal, characteristic, complemented
16	#81163	C₂	1	1	yes	maximal, characteristic, complemented
17	#81159	C₂	1	1	yes	maximal, characteristic, complemented
18	#81158	C₂	1	1	yes	maximal, characteristic, complemented
19	#81157	C₂	1	1	yes	maximal, characteristic, complemented
20	#80968	C₂	1	1	yes	maximal, characteristic, complemented
21	D₃×#474	C₂	1	1	yes	maximal, characteristic, complemented
22	#80960	C₂	1	1	yes	maximal, characteristic, complemented
23	#80957	C₂	1	1	yes	maximal, characteristic, complemented
24	#79976	C₂	1	1	yes	maximal, characteristic, complemented
25	#79961	C₂	1	1	yes	maximal, characteristic, complemented
26	#79866	C₂	1	1	yes	maximal, characteristic
27	#79865	C₂	1	1	yes	maximal, characteristic
28	#79856	C₂	1	1	yes	maximal, characteristic, complemented
29	#79855	C₂	1	1	yes	maximal, characteristic, complemented
30	#79587	C₂	1	1	yes	maximal, characteristic
31	D₈×Dic₆	C₂	1	1	yes	maximal, characteristic, complemented
32	#61381	—	3	1	no	maximal, Sylow
33	C₃×#554	C₂²	1	1	yes	characteristic
34	C₃×#554	C₂²	1	1	yes	characteristic, complemented
35	C₂×#911	C₂²	1	1	yes	characteristic
36	#5729	C₂²	1	1	yes	characteristic
37	#5727	C₂²	1	1	yes	characteristic
38	D₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
39	#5722	C₂²	1	1	yes	characteristic, complemented
40	#5690	C₂²	1	1	yes	characteristic
41	#5690	C₂²	1	1	yes	characteristic
42	#5689	C₂²	1	1	yes	characteristic
43	#5689	C₂²	1	1	yes	characteristic
44	#5689	C₂²	1	1	yes	characteristic
45	#5688	C₂²	1	1	yes	characteristic
46	#5685	C₂²	1	1	yes	characteristic, complemented
47	#5685	C₂²	1	1	yes	characteristic, complemented
48	#5636	—	2	1	no	—
49	#5636	—	2	1	no	—
50	#5635	—	2	1	no	—
51	#5634	—	2	1	no	—
52	#5634	—	2	1	no	—
53	#5632	—	2	1	no	—
54	#5632	—	2	1	no	—
55	#5632	—	2	1	no	—
56	D₃×C₂²⋊Q₈	—	2	1	no	—
57	#5623	—	2	1	no	—
58	#5623	—	2	1	no	—
59	#5622	—	2	1	no	—
60	#5579	C₂²	1	1	yes	characteristic
61	#5578	C₂²	1	1	yes	characteristic
62	Q₈×Dic₆	C₂²	1	1	yes	characteristic, complemented
63	#5546	C₂²	1	1	yes	characteristic
64	#5546	C₂²	1	1	yes	characteristic
65	#5545	C₂²	1	1	yes	characteristic
66	#5545	C₂²	1	1	yes	characteristic
67	C₄×D₃×D₄	C₂²	1	1	yes	characteristic
68	#5543	C₂²	1	1	yes	characteristic, complemented
69	#5539	C₂²	1	1	yes	characteristic
70	#5539	C₂²	1	1	yes	characteristic
71	D₄×Dic₆	C₂²	1	1	yes	characteristic
72	D₄×Dic₆	C₂²	1	1	yes	characteristic, complemented
73	D₄×Dic₆	C₂²	1	1	yes	characteristic, complemented
74	C₄×#237	C₂²	1	1	yes	characteristic
75	#5511	—	2	1	no	—
76	#5511	—	2	1	no	—
77	C₂×#896	—	2	1	no	—
78	C₂×#888	—	2	1	no	—
79	C₃×#501	C₂²	1	1	yes	characteristic, complemented
80	C₃×#501	C₂²	1	1	yes	characteristic, complemented
81	C₃×#499	C₂²	1	1	yes	characteristic, complemented
82	C₃×#478	C₂²	1	1	yes	characteristic
83	C₃×#478	C₂²	1	1	yes	characteristic
84	C₃×#478	C₂²	1	1	yes	characteristic, complemented
85	C₃×#478	C₂²	1	1	yes	characteristic, complemented
86	C₃×#474	C₂²	1	1	yes	characteristic
87	C₃×#474	C₂²	1	1	yes	characteristic, complemented
88	C₃×#446	C₂²	1	1	yes	characteristic, complemented
89	C₃×#442	C₂²	1	1	yes	characteristic
90	C₃×#442	C₂²	1	1	yes	characteristic
91	C₃×C₄×D₈	C₂²	1	1	yes	characteristic
92	#5152	C₂²	1	1	yes	characteristic
93	Dic₃×D₈	C₂²	1	1	yes	characteristic
94	Dic₃×D₈	C₂²	1	1	yes	characteristic
95	#5091	C₂²	1	1	yes	characteristic, complemented
96	#5087	C₂²	1	1	yes	characteristic
97	#5081	C₂²	1	1	yes	characteristic, complemented
98	#5078	C₂²	1	1	yes	characteristic, complemented
99	#5066	C₂²	1	1	yes	characteristic
100	#5066	C₂²	1	1	yes	characteristic
101	#5065	C₂²	1	1	yes	characteristic, complemented
102	#5064	C₂²	1	1	yes	characteristic, complemented
103	#5064	C₂²	1	1	yes	characteristic, complemented
104	#5064	C₂²	1	1	yes	characteristic, complemented
105	#5063	C₂²	1	1	yes	characteristic, complemented
106	#5063	C₂²	1	1	yes	characteristic, complemented
107	#5024	C₂²	1	1	yes	characteristic, complemented
108	#5018	C₂²	1	1	yes	characteristic
109	#5018	C₂²	1	1	yes	characteristic
110	C₄×#214	C₂²	1	1	yes	characteristic
111	#5014	C₂²	1	1	yes	characteristic
112	#5014	C₂²	1	1	yes	characteristic
113	C₄×#213	C₂²	1	1	yes	characteristic
114	#5009	C₂²	1	1	yes	characteristic, complemented
115	#5009	C₂²	1	1	yes	characteristic, complemented
116	#5008	C₂²	1	1	yes	characteristic
117	#5007	C₂²	1	1	yes	characteristic
118	#5007	C₂²	1	1	yes	characteristic
119	#5007	C₂²	1	1	yes	characteristic, complemented
120	#4891	C₂²	1	1	yes	characteristic
121	#4890	C₂²	1	1	yes	characteristic
122	#4890	C₂²	1	1	yes	characteristic
123	#4890	C₂²	1	1	yes	characteristic
124	#4889	C₂²	1	1	yes	characteristic
125	#4881	C₂²	1	1	yes	characteristic
126	#4881	C₂²	1	1	yes	characteristic
127	#4880	C₂²	1	1	yes	characteristic
128	D₃×#107	C₂²	1	1	yes	characteristic
129	D₃×#107	C₂²	1	1	yes	characteristic
130	#4878	C₂²	1	1	yes	characteristic, complemented
131	#4877	C₂²	1	1	yes	characteristic, complemented
132	#4876	C₂²	1	1	yes	characteristic, complemented
133	#4875	C₂²	1	1	yes	characteristic, complemented
134	#4875	C₂²	1	1	yes	characteristic, complemented
135	#4875	C₂²	1	1	yes	characteristic, complemented
136	#4874	C₂²	1	1	yes	characteristic, complemented
137	#4874	C₂²	1	1	yes	characteristic, complemented
138	#4874	C₂²	1	1	yes	characteristic, complemented
139	#4874	C₂²	1	1	yes	characteristic, complemented
140	#4871	C₂²	1	1	yes	characteristic
141	#4870	C₂²	1	1	yes	characteristic
142	#4861	C₂²	1	1	yes	characteristic
143	#4861	C₂²	1	1	yes	characteristic
144	#4861	C₂²	1	1	yes	characteristic
145	#4860	C₂²	1	1	yes	characteristic
146	#4858	C₂²	1	1	yes	characteristic, complemented
147	#4857	C₂²	1	1	yes	characteristic, complemented
148	#4856	C₂²	1	1	yes	characteristic, complemented
149	#4856	C₂²	1	1	yes	characteristic, complemented
150	#4856	C₂²	1	1	yes	characteristic, complemented
151	#4855	C₂²	1	1	yes	characteristic, complemented
152	#4855	C₂²	1	1	yes	characteristic, complemented
153	#4854	C₂²	1	1	yes	characteristic, complemented
154	#4852	C₂²	1	1	yes	characteristic
155	#4852	C₂²	1	1	yes	characteristic
156	#4850	C₂²	1	1	yes	characteristic, complemented
157	#4846	C₂²	1	1	yes	characteristic
158	#4846	C₂²	1	1	yes	characteristic
159	#4842	C₂²	1	1	yes	characteristic
160	#4839	C₂²	1	1	yes	characteristic
161	#4839	C₂²	1	1	yes	characteristic
162	D₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
163	#4830	C₂²	1	1	yes	characteristic, complemented
164	#4829	C₂²	1	1	yes	characteristic, complemented
165	#4829	C₂²	1	1	yes	characteristic, complemented
166	#4828	C₂²	1	1	yes	characteristic, complemented
167	#4828	C₂²	1	1	yes	characteristic, complemented
168	#4785	C₂²	1	1	yes	characteristic
169	#4772	C₂²	1	1	yes	characteristic
170	#4772	C₂²	1	1	yes	characteristic
171	#4771	C₂²	1	1	yes	characteristic
172	#4770	C₂²	1	1	yes	characteristic
173	D₃×#102	C₂²	1	1	yes	characteristic
174	D₃×#102	C₂²	1	1	yes	characteristic
175	#4766	C₂²	1	1	yes	characteristic
176	#4766	C₂²	1	1	yes	characteristic, complemented
177	#4763	C₂²	1	1	yes	characteristic
178	#4763	C₂²	1	1	yes	characteristic, complemented
179	#4761	C₂²	1	1	yes	characteristic
180	#4761	C₂²	1	1	yes	characteristic, complemented
181	#4759	C₂²	1	1	yes	characteristic
182	#4759	C₂²	1	1	yes	characteristic
183	#4759	C₂²	1	1	yes	characteristic
184	#4759	C₂²	1	1	yes	characteristic, complemented
185	#4759	C₂²	1	1	yes	characteristic, complemented
186	#4759	C₂²	1	1	yes	characteristic, complemented
187	#4758	C₂²	1	1	yes	characteristic
188	#4758	C₂²	1	1	yes	characteristic
189	#4757	C₂²	1	1	yes	characteristic
190	#4756	C₂²	1	1	yes	characteristic
191	#4756	C₂²	1	1	yes	characteristic
192	#4710	C₂²	1	1	yes	characteristic
193	#4710	C₂²	1	1	yes	characteristic
194	#4708	C₂²	1	1	yes	characteristic
195	#4707	C₂²	1	1	yes	characteristic
196	#4702	C₂²	1	1	yes	characteristic, complemented
197	#4702	C₂²	1	1	yes	characteristic, complemented
198	#4701	C₂²	1	1	yes	characteristic, complemented
199	#4701	C₂²	1	1	yes	characteristic, complemented
200	C₄×#204	C₂²	1	1	yes	characteristic
201	#4689	C₂²	1	1	yes	characteristic
202	#4682	C₂²	1	1	yes	characteristic, complemented
203	C₈×Dic₆	C₂²	1	1	yes	characteristic, complemented
204	#3503	—	3	1	no	—
205	#3501	—	3	1	no	—
206	#3389	—	3	1	no	—
207	#3389	—	3	1	no	—
208	#3389	—	3	1	no	—
209	#3389	D₃	1	1	yes	characteristic, complemented
210	#3386	—	3	1	no	—
211	#3386	—	3	1	no	—
212	#3385	—	3	1	no	—
213	#3385	—	3	1	no	—
214	#3385	—	3	1	no	—
215	#3385	—	3	1	no	—
216	#3384	—	3	1	no	—
217	#3384	—	3	1	no	—
218	#3381	—	3	1	no	—
219	#3381	—	3	1	no	—
220	Q₈×D₈	—	3	1	no	—
221	Q₈×D₈	—	3	1	no	—
222	#3165	—	3	1	no	—
223	#3164	—	3	1	no	—
224	#3164	—	3	1	no	—
225	#3083	—	3	1	no	—
226	#3083	—	3	1	no	—
227	#3081	—	3	1	no	—
228	#3081	—	3	1	no	—
229	#3076	—	3	1	no	—
230	C₂×#474	—	3	1	no	—
231	#2962	—	3	1	no	—
232	#2946	—	3	1	no	—
233	#2946	—	3	1	no	—
234	C₄×AGL(1,ℤ/8)	—	3	1	no	—
235	C₂×D₃×Q₈	—	2	1	no	—
236	C₂×D₃×Q₈	—	2	1	no	—
237	C₂×#237	C₂³	1	1	yes	characteristic
238	C₂×D₃×D₄	C₂³	1	1	yes	characteristic
239	C₂²×C₄×D₃	—	2	1	no	—
240	C₂²×Dic₆	—	2	1	no	—
241	C₂²×Dic₆	—	2	1	no	—
242	C₂²×Dic₆	—	2	1	no	—
243	C₂×C₃×D₈	C₂³	1	1	yes	characteristic
244	C₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
245	C₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
246	C₃×#125	C₂³	1	1	yes	characteristic
247	C₃×#125	C₂³	1	1	yes	characteristic
248	C₃×#125	C₂³	1	1	yes	characteristic
249	C₃×#125	C₂³	1	1	yes	characteristic
250	C₃×C₂²⋊Q₈	—	2	1	no	—
251	C₃×C₂²⋊Q₈	—	2	1	no	—
252	C₃×C₂²⋊Q₈	—	2	1	no	—
253	C₃×C₂²⋊Q₈	—	2	1	no	—
254	C₃×C₂²⋊Q₈	—	2	1	no	—
255	C₃×C₂²⋊Q₈	—	2	1	no	—
256	C₃×C₄×Q₈	C₂³	1	1	yes	characteristic
257	C₃×C₄×D₄	C₂³	1	1	yes	characteristic
258	C₃×C₄×D₄	C₂³	1	1	yes	characteristic
259	C₃×C₄×D₄	C₂³	1	1	yes	characteristic
260	C₃×C₄×D₄	C₂³	1	1	yes	characteristic
261	C₃×C₄×D₄	C₂³	1	1	yes	characteristic
262	C₃×C₄×D₄	C₂³	1	1	yes	characteristic
263	C₂×C₃×C₄⋊C₄	—	2	1	no	—
264	C₂×C₃×C₄⋊C₄	—	2	1	no	—
265	#946	—	2	1	no	—
266	#946	—	2	1	no	—
267	#946	—	2	1	no	—
268	#946	D₄	1	1	yes	characteristic
269	Q₈×Dic₃	—	2	1	no	—
270	#944	—	2	1	no	—
271	#944	—	2	1	no	—
272	#944	—	2	1	no	—
273	#944	—	2	1	no	—
274	#944	D₄	1	1	yes	characteristic
275	D₄×Dic₃	C₂³	1	1	yes	characteristic
276	D₄×Dic₃	C₂³	1	1	yes	characteristic
277	D₄×Dic₃	C₂³	1	1	yes	characteristic
278	D₄×Dic₃	C₂³	1	1	yes	characteristic
279	D₄×Dic₃	C₂³	1	1	yes	characteristic
280	D₄×Dic₃	C₂³	1	1	yes	characteristic
281	C₂×#214	C₂³	1	1	yes	characteristic
282	C₂×#213	C₂³	1	1	yes	characteristic
283	C₄×#67	—	2	1	no	—
284	C₄×#67	—	2	1	no	—
285	C₄×#67	—	2	1	no	—
286	C₄×#67	—	2	1	no	—
287	C₄×#67	—	2	1	no	—
288	C₄×#67	—	2	1	no	—
289	C₂×(C₂×D₃)⋊C₄	—	2	1	no	—
290	C₂×(C₂×D₃)⋊C₄	—	2	1	no	—
291	C₂×C₄⋊Dic₃	—	2	1	no	—
292	#924	—	2	1	no	—
293	#924	—	2	1	no	—
294	#924	—	2	1	no	—
295	#924	—	2	1	no	—
296	#924	—	2	1	no	—
297	#924	—	2	1	no	—
298	C₂×Dic₃⋊C₄	—	2	1	no	—
299	C₂×Dic₃⋊C₄	—	2	1	no	—
300	C₂×Dic₃⋊C₄	—	2	1	no	—
301	C₂×Dic₃⋊C₄	—	2	1	no	—
302	C₂×C₄×Dic₃	—	2	1	no	—
303	#911	Q₈	1	8	yes	complemented
304	C₂×#204	C₂³	1	1	yes	characteristic
305	C₂×ΓL(1,𝔽₂₅)	C₂³	1	1	yes	characteristic
306	C₂×ΓL(1,𝔽₂₅)	C₂³	1	1	yes	characteristic
307	C₂×D₃×C₈	C₂³	1	1	yes	characteristic
308	C₂×D₃×C₈	C₂³	1	1	yes	characteristic
309	#897	—	2	1	no	—
310	#897	—	2	1	no	—
311	#897	—	2	1	no	—
312	#897	—	2	1	no	—
313	#897	—	2	1	no	—
314	#897	D₄	1	1	yes	characteristic
315	#896	—	2	1	no	—
316	#896	—	2	1	no	—
317	#896	—	2	1	no	—
318	#896	—	2	1	no	—
319	#896	—	2	1	no	—
320	#896	—	2	1	no	—
321	#896	—	2	1	no	—
322	#896	—	2	1	no	—
323	#896	—	2	1	no	—
324	#896	—	2	1	no	—
325	#896	—	2	1	no	—
326	#896	—	2	1	no	—
327	#896	—	2	1	no	—
328	#896	—	2	1	no	—
329	#896	D₄	1	1	yes	characteristic
330	#896	D₄	1	1	yes	characteristic
331	#893	C₂³	1	1	yes	characteristic
332	#893	C₂³	1	1	yes	characteristic
333	#893	C₂³	1	1	yes	characteristic
334	#892	C₂³	1	1	yes	characteristic
335	#892	C₂³	1	1	yes	characteristic
336	#892	C₂³	1	1	yes	characteristic
337	D₃×C₄⋊C₄	—	2	1	no	—
338	D₃×C₄⋊C₄	—	2	1	no	—
339	D₃×C₄⋊C₄	—	2	1	no	—
340	D₃×C₄⋊C₄	—	2	1	no	—
341	D₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
342	D₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
343	D₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
344	#890	C₂³	1	1	yes	characteristic
345	#890	C₂³	1	1	yes	characteristic
346	#890	C₂³	1	1	yes	characteristic
347	#890	C₂³	1	1	yes	characteristic
348	#889	—	2	1	no	—
349	#889	—	2	1	no	—
350	#889	—	2	1	no	—
351	#889	—	2	1	no	—
352	#889	—	2	1	no	—
353	#889	—	2	1	no	—
354	#889	—	2	1	no	—
355	#889	—	2	1	no	—
356	#889	D₄	1	1	yes	characteristic
357	#889	D₄	1	1	yes	characteristic
358	#888	—	2	1	no	—
359	#888	—	2	1	no	—
360	#888	—	2	1	no	—
361	#888	—	2	1	no	—
362	#888	—	2	1	no	—
363	#888	—	2	1	no	—
364	#888	—	2	1	no	—
365	#888	—	2	1	no	—
366	#888	—	2	1	no	—
367	#888	—	2	1	no	—
368	#888	D₄	1	1	yes	characteristic
369	#888	C₂³	1	1	yes	characteristic
370	#888	C₂³	1	1	yes	characteristic
371	#888	C₂³	1	1	yes	characteristic
372	#888	C₂³	1	1	yes	characteristic
373	#888	C₂³	1	1	yes	characteristic
374	#888	C₂³	1	1	yes	characteristic
375	#888	C₂³	1	1	yes	characteristic
376	#888	C₂³	1	1	yes	characteristic
377	#887	—	2	1	no	—
378	#887	—	2	1	no	—
379	#887	—	2	1	no	—
380	#887	—	2	1	no	—
381	#887	—	2	1	no	—
382	#887	C₂³	1	1	yes	characteristic
383	#887	C₂³	1	1	yes	characteristic
384	#887	C₂³	1	1	yes	characteristic
385	#67⋊C₄	—	2	1	no	—
386	#67⋊C₄	—	2	1	no	—
387	#67⋊C₄	—	2	1	no	—
388	#67⋊C₄	—	2	1	no	—
389	#67⋊C₄	—	2	1	no	—
390	#67⋊C₄	—	2	1	no	—
391	D₃×C₂²⋊C₄	—	2	1	no	—
392	D₃×C₂²⋊C₄	—	2	1	no	—
393	D₃×C₂²⋊C₄	—	2	1	no	—
394	#878	—	2	1	no	—
395	#878	—	2	1	no	—
396	#878	—	2	1	no	—
397	#878	—	2	1	no	—
398	#878	—	2	1	no	—
399	#878	—	2	1	no	—
400	#878	—	2	1	no	—
401	#878	—	2	1	no	—
402	#878	—	2	1	no	—
403	#878	—	2	1	no	—
404	#878	—	2	1	no	—
405	#878	—	2	1	no	—
406	#877	—	2	1	no	—
407	#877	—	2	1	no	—
408	#877	—	2	1	no	—
409	C₄×D₁₂	C₂³	1	1	yes	characteristic
410	C₄×D₁₂	C₂³	1	1	yes	characteristic
411	C₄×D₁₂	C₂³	1	1	yes	characteristic
412	#872	C₂³	1	1	yes	characteristic
413	#872	C₂³	1	1	yes	characteristic
414	C₄²×D₃	C₂³	1	1	yes	characteristic
415	#870	C₂³	1	1	yes	characteristic
416	#870	C₂³	1	1	yes	characteristic
417	#869	C₂³	1	1	yes	characteristic
418	#869	C₂³	1	1	yes	characteristic
419	#869	C₂³	1	1	yes	characteristic
420	#869	C₂³	1	1	yes	characteristic
421	C₄×Dic₆	C₂³	1	1	yes	characteristic
422	C₄×Dic₆	C₂³	1	1	yes	characteristic
423	C₄×Dic₆	C₂³	1	1	yes	characteristic
424	C₄×Dic₆	C₂³	1	1	yes	characteristic
425	C₄×Dic₆	C₂³	1	1	yes	characteristic
426	C₄×Dic₆	C₂³	1	1	yes	characteristic
427	C₃×#107	C₂³	1	1	yes	characteristic
428	C₃×#107	C₂³	1	1	yes	characteristic
429	C₃×#107	C₂³	1	1	yes	characteristic
430	C₃×#107	C₂³	1	1	yes	characteristic
431	C₃×#107	C₂³	1	1	yes	characteristic
432	C₃×#106	C₂³	1	1	yes	characteristic
433	C₃×#106	C₂³	1	1	yes	characteristic
434	C₃×#106	C₂³	1	1	yes	characteristic
435	C₃×#106	C₂³	1	1	yes	characteristic
436	C₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
437	C₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
438	C₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
439	C₃×#102	C₂³	1	1	yes	characteristic
440	C₃×#102	C₂³	1	1	yes	characteristic
441	C₃×#102	C₂³	1	1	yes	characteristic
442	C₃×#102	C₂³	1	1	yes	characteristic
443	C₃×#102	C₂³	1	1	yes	characteristic
444	C₃×#102	C₂³	1	1	yes	characteristic
445	C₃×#97	C₂³	1	1	yes	characteristic
446	C₃×#97	C₂³	1	1	yes	characteristic
447	C₃×C₄×C₈	C₂³	1	1	yes	characteristic
448	#832	C₂³	1	1	yes	characteristic
449	#832	C₂³	1	1	yes	characteristic
450	#832	C₂³	1	1	yes	characteristic
451	#832	C₂³	1	1	yes	characteristic
452	#832	C₂³	1	1	yes	characteristic
453	#832	C₂³	1	1	yes	characteristic
454	#821	C₂³	1	1	yes	characteristic
455	#821	C₂³	1	1	yes	characteristic
456	#821	C₂³	1	1	yes	characteristic
457	#818	C₂³	1	1	yes	characteristic
458	#818	C₂³	1	1	yes	characteristic
459	#818	C₂³	1	1	yes	characteristic
460	#818	C₂³	1	1	yes	characteristic
461	#818	C₂³	1	1	yes	characteristic
462	#818	C₂³	1	1	yes	characteristic
463	#817	C₂³	1	1	yes	characteristic
464	#817	C₂³	1	1	yes	characteristic
465	#817	C₂³	1	1	yes	characteristic
466	#816	C₂³	1	1	yes	characteristic
467	#816	C₂³	1	1	yes	characteristic
468	#816	C₂³	1	1	yes	characteristic
469	#815	C₂³	1	1	yes	characteristic
470	#815	C₂³	1	1	yes	characteristic
471	Dic₃⋊C₈	C₂³	1	1	yes	characteristic
472	Dic₃⋊C₈	C₂³	1	1	yes	characteristic
473	Dic₃⋊C₈	C₂³	1	1	yes	characteristic
474	Dic₃⋊C₈	C₂³	1	1	yes	characteristic
475	Dic₃⋊C₈	C₂³	1	1	yes	characteristic
476	Dic₃⋊C₈	C₂³	1	1	yes	characteristic
477	C₈×Dic₃	C₂³	1	1	yes	characteristic
478	C₈×Dic₃	C₂³	1	1	yes	characteristic
479	C₈×Dic₃	C₂³	1	1	yes	characteristic
480	C₈×Dic₃	C₂³	1	1	yes	characteristic
481	#810	C₂³	1	1	yes	characteristic
482	#810	C₂³	1	1	yes	characteristic
483	#810	C₂³	1	1	yes	characteristic
484	#809	C₂³	1	1	yes	characteristic
485	#809	C₂³	1	1	yes	characteristic
486	#809	C₂³	1	1	yes	characteristic
487	#808	C₂³	1	1	yes	characteristic
488	#808	C₂³	1	1	yes	characteristic
489	#808	C₂³	1	1	yes	characteristic
490	#808	C₂³	1	1	yes	characteristic
491	#808	C₂³	1	1	yes	characteristic
492	#808	C₂³	1	1	yes	characteristic
493	#808	C₂³	1	1	yes	characteristic
494	#807	C₂³	1	1	yes	characteristic
495	#807	C₂³	1	1	yes	characteristic
496	#807	C₂³	1	1	yes	characteristic
497	#807	C₂³	1	1	yes	characteristic
498	#807	C₂³	1	1	yes	characteristic
499	#807	C₂³	1	1	yes	characteristic
500	#807	C₂³	1	1	yes	characteristic
501	#807	C₂³	1	1	yes	characteristic
502	#807	C₂³	1	1	yes	characteristic
503	#807	C₂³	1	1	yes	characteristic
504	#807	C₂³	1	1	yes	characteristic
505	C₄⋊(C₃⋊C₈)	C₂³	1	1	yes	characteristic
506	C₄⋊(C₃⋊C₈)	C₂³	1	1	yes	characteristic
507	C₄⋊(C₃⋊C₈)	C₂³	1	1	yes	characteristic
508	#803	C₂³	1	1	yes	characteristic
509	#803	C₂³	1	1	yes	characteristic
510	C₄×C₃⋊C₈	C₂³	1	1	yes	characteristic
511	C₂×AGL(1,ℤ/8)	—	3	1	no	—
512	Q₈²	—	3	1	no	—
513	Q₈²	—	3	1	no	—
514	#557	—	3	1	no	—
515	#557	—	3	1	no	—
516	#554	—	3	1	no	—
517	#554	—	3	1	no	—
518	#554	—	3	1	no	—
519	#554	—	3	1	no	—
520	#554	—	3	1	no	—
521	#554	—	3	1	no	—
522	#554	—	6	1	no	—
523	#554	—	6	1	no	—
524	#554	—	6	1	no	—
525	#554	—	6	1	no	—
526	#554	—	6	1	no	—
527	#554	C₂×D₃	1	1	yes	characteristic
528	#554	C₂×D₃	1	1	yes	characteristic, complemented
529	D₄×Q₈	—	3	1	no	—
530	D₄×Q₈	—	3	1	no	—
531	D₄×Q₈	—	3	1	no	—
532	D₄×Q₈	—	3	1	no	—
533	D₄×Q₈	—	6	1	no	—
534	D₄×Q₈	—	6	1	no	—
535	D₄×Q₈	—	6	1	no	—
536	#544	—	3	1	no	—
537	#544	—	3	1	no	—
538	#544	—	3	1	no	—
539	#544	—	3	1	no	—
540	#544	—	6	1	no	—
541	#544	—	6	1	no	—
542	#543	—	6	1	no	—
543	#543	—	6	1	no	—
544	#533	—	3	1	no	—
545	#533	—	3	1	no	—
546	#533	—	6	1	no	—
547	C₂×C₄⋊Q₈	—	3	1	no	—
548	C₂×C₄⋊Q₈	—	6	1	no	—
549	C₂×C₂²⋊Q₈	—	6	1	no	—
550	C₂×C₂²⋊Q₈	—	6	1	no	—
551	#520	—	3	1	no	—
552	#520	—	3	1	no	—
553	#518	—	3	1	no	—
554	#518	—	3	1	no	—
555	C₄×#41	—	3	1	no	—
556	C₂×C₄×D₄	—	3	1	no	—
557	#501	—	3	1	no	—
558	#501	—	3	1	no	—
559	#501	—	3	1	no	—
560	#501	—	3	1	no	—
561	#501	—	3	1	no	—
562	#501	—	3	1	no	—
563	#501	—	3	1	no	—
564	#501	—	3	1	no	—
565	#501	—	3	1	no	—
566	#501	—	3	1	no	—
567	#501	C₂×D₃	1	1	yes	characteristic, complemented
568	#501	C₂×D₃	1	1	yes	characteristic, complemented
569	#500	—	3	1	no	—
570	#500	—	3	1	no	—
571	#500	—	3	1	no	—
572	#500	—	3	1	no	—
573	#500	—	3	1	no	—
574	#500	—	3	1	no	—
575	#499	—	3	1	no	—
576	#499	—	3	1	no	—
577	#499	—	3	1	no	—
578	#499	C₂×D₃	1	1	yes	characteristic, complemented
579	#498	—	3	1	no	—
580	#498	—	3	1	no	—
581	#479	—	3	1	no	—
582	#479	—	3	1	no	—
583	#479	—	3	1	no	—
584	#479	—	3	1	no	—
585	#479	—	3	1	no	—
586	#479	—	3	1	no	—
587	#478	—	3	1	no	—
588	#478	—	3	1	no	—
589	#478	—	3	1	no	—
590	#478	—	3	1	no	—
591	#478	—	3	1	no	—
592	#478	—	3	1	no	—
593	#478	—	3	1	no	—
594	#478	—	3	1	no	—
595	#478	—	3	1	no	—
596	#478	—	3	1	no	—
597	#478	C₂×D₃	1	1	yes	characteristic
598	#478	C₂×D₃	1	1	yes	characteristic
599	#478	C₂×D₃	1	1	yes	characteristic, complemented
600	#478	C₂×D₃	1	1	yes	characteristic, complemented
601	#477	—	3	1	no	—
602	#477	—	3	1	no	—
603	#477	—	3	1	no	—
604	#477	—	3	1	no	—
605	#477	—	3	1	no	—
606	#476	—	3	1	no	—
607	#476	—	3	1	no	—
608	#476	—	3	1	no	—
609	#476	—	3	1	no	—
610	#476	—	3	1	no	—
611	#475	—	3	1	no	—
612	#474	—	3	1	no	—
613	#474	—	3	1	no	—
614	#474	—	3	1	no	—
615	#474	—	3	1	no	—
616	#474	—	3	1	no	—
617	#474	—	3	1	no	—
618	#474	—	3	1	no	—
619	#474	—	3	1	no	—
620	#474	—	3	1	no	—
621	#474	—	3	1	no	—
622	#474	—	3	1	no	—
623	#474	—	3	1	no	—
624	#474	—	3	1	no	—
625	#474	—	3	1	no	—
626	#474	—	3	1	no	—
627	#474	C₂×D₃	1	1	yes	characteristic
628	#474	C₂×D₃	1	1	yes	characteristic, complemented
629	#446	—	3	1	no	—
630	#446	—	3	1	no	—
631	#446	—	3	1	no	—
632	#446	—	3	1	no	—
633	#446	—	3	1	no	—
634	#446	C₂×D₃	1	1	yes	characteristic, complemented
635	C₈×Q₈	—	3	1	no	—
636	C₈×Q₈	—	3	1	no	—
637	#442	—	3	1	no	—
638	#442	—	3	1	no	—
639	#442	—	3	1	no	—
640	#442	—	3	1	no	—
641	#442	C₂×D₃	1	1	yes	characteristic
642	#442	C₂×D₃	1	1	yes	characteristic
643	#440	—	3	1	no	—
644	#440	—	3	1	no	—
645	#440	—	3	1	no	—
646	#440	—	3	1	no	—
647	#440	—	3	1	no	—
648	#440	—	3	1	no	—
649	C₄×SD₁₆	—	3	1	no	—
650	C₄×SD₁₆	—	3	1	no	—
651	C₄×SD₁₆	—	3	1	no	—
652	C₄×SD₁₆	—	3	1	no	—
653	C₄×SD₁₆	—	3	1	no	—
654	C₄×SD₁₆	—	3	1	no	—
655	C₄×D₈	—	3	1	no	—
656	C₄×D₈	—	3	1	no	—
657	C₄×D₈	—	3	1	no	—
658	C₄×D₈	—	3	1	no	—
659	C₄×D₈	—	3	1	no	—
660	C₄×D₈	C₂×D₃	1	1	yes	characteristic
661	#428	—	3	1	no	—
662	#428	—	3	1	no	—
663	#428	—	3	1	no	—
664	#428	—	3	1	no	—
665	#428	—	3	1	no	—
666	#427	—	3	1	no	—
667	#427	—	3	1	no	—
668	C₂×#107	—	3	1	no	—
669	C₂×#107	—	3	1	no	—
670	#424	—	3	1	no	—
671	#424	—	3	1	no	—
672	C₂×C₄⋊C₈	—	3	1	no	—
673	#418	—	3	1	no	—
674	#417	—	3	1	no	—
675	#416	—	3	1	no	—
676	#416	—	3	1	no	—
677	C₂×#102	—	3	1	no	—
678	C₂×#102	—	3	1	no	—
679	#405	—	3	1	no	—
680	#405	—	3	1	no	—
681	C₄×M₁₆	—	3	1	no	—
682	C₂³×D₃	—	2	1	no	—
683	C₂×C₃×Q₈	—	2	1	no	—
684	C₂×C₃×Q₈	—	2	1	no	—
685	C₂×C₃×Q₈	C₂×D₄	1	1	yes	characteristic
686	C₂×C₃×D₄	C₂⁴	1	1	yes	characteristic
687	C₂×C₃×D₄	C₂⁴	1	1	yes	characteristic
688	C₂²×C₃×C₄	—	2	1	no	—
689	C₂²×C₃×C₄	—	2	1	no	—
690	C₂²×C₃×C₄	—	2	1	no	—
691	C₂²×C₃×C₄	—	2	1	no	—
692	C₂²×C₃×C₄	—	2	1	no	—
693	C₂²×C₃×C₄	—	2	1	no	—
694	C₂×#67	—	2	1	no	—
695	C₂×#67	—	2	1	no	—
696	C₂²×Dic₃	—	2	1	no	—
697	C₂²×Dic₃	—	2	1	no	—
698	C₂²×Dic₃	—	2	1	no	—
699	C₂²×Dic₃	—	2	1	no	—
700	C₂²×Dic₃	—	2	1	no	—
701	C₂²×Dic₃	—	2	1	no	—
702	C₂²×Dic₃	—	2	1	no	—
703	D₃×Q₈	—	8	2	no	—
704	D₃×Q₈	—	8	2	no	—
705	#237	—	2	2	no	—
706	#237	C₂×Q₈	1	4	yes	complemented
707	D₃×D₄	—	2	2	no	—
708	D₃×D₄	C₂×Q₈	1	4	yes	complemented
709	C₂×D₁₂	C₂⁴	1	1	yes	characteristic
710	C₂×C₄×D₃	—	2	1	no	—
711	C₂×C₄×D₃	—	2	1	no	—
712	C₂×C₄×D₃	—	2	1	no	—
713	C₂×C₄×D₃	—	2	1	no	—
714	C₂×C₄×D₃	—	2	1	no	—
715	C₂×C₄×D₃	—	2	1	no	—
716	C₂×C₄×D₃	—	2	1	no	—
717	C₂×C₄×D₃	—	2	1	no	—
718	C₂×C₄×D₃	—	2	1	no	—
719	C₂×C₄×D₃	—	8	2	no	—
720	C₂×C₄×D₃	C₂×D₄	1	1	yes	characteristic
721	C₂×C₄×D₃	C₂×D₄	1	1	yes	characteristic
722	C₂×C₄×D₃	C₂⁴	1	1	yes	characteristic
723	C₂×Dic₆	—	2	1	no	—
724	C₂×Dic₆	—	2	1	no	—
725	C₂×Dic₆	—	2	1	no	—
726	C₂×Dic₆	—	2	1	no	—
727	C₂×Dic₆	—	2	1	no	—
728	C₂×Dic₆	—	2	1	no	—
729	C₂×Dic₆	—	2	1	no	—
730	C₂×Dic₆	—	2	1	no	—
731	C₂×Dic₆	—	2	1	no	—
732	C₂×Dic₆	—	2	1	no	—
733	C₂×Dic₆	—	2	1	no	—
734	C₂×Dic₆	—	2	1	no	—
735	C₂×Dic₆	—	8	2	no	—
736	C₂×Dic₆	—	8	2	no	—
737	C₂×Dic₆	—	8	2	no	—
738	C₂×Dic₆	C₂×D₄	1	1	yes	characteristic
739	C₂×Dic₆	C₂×D₄	1	1	yes	characteristic
740	C₂×Dic₆	C₂×D₄	1	1	yes	characteristic
741	C₂×Dic₆	C₂⁴	1	1	yes	characteristic
742	C₃×D₈	C₂×Q₈	1	4	yes	complemented
743	C₂×C₃×C₈	C₂⁴	1	1	yes	characteristic
744	C₂×C₃×C₈	C₂⁴	1	1	yes	characteristic
745	C₂×C₃×C₈	C₂⁴	1	1	yes	characteristic
746	C₂×C₃×C₈	C₂⁴	1	1	yes	characteristic
747	C₃×C₄⋊C₄	—	2	1	no	—
748	C₃×C₄⋊C₄	—	2	1	no	—
749	C₃×C₄⋊C₄	—	2	1	no	—
750	C₃×C₄⋊C₄	—	2	1	no	—
751	C₃×C₄⋊C₄	—	2	1	no	—
752	C₃×C₄⋊C₄	—	2	1	no	—
753	C₃×C₄⋊C₄	—	2	1	no	—
754	C₃×C₄⋊C₄	—	2	1	no	—
755	C₃×C₄⋊C₄	—	2	1	no	—
756	C₃×C₄⋊C₄	—	2	1	no	—
757	C₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
758	C₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
759	C₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
760	C₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
761	C₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
762	C₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
763	C₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
764	C₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
765	C₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
766	C₃×C₂²⋊C₄	—	2	1	no	—
767	C₃×C₂²⋊C₄	—	2	1	no	—
768	C₃×C₂²⋊C₄	—	2	1	no	—
769	C₃×C₂²⋊C₄	—	2	1	no	—
770	C₃×C₂²⋊C₄	—	2	1	no	—
771	C₃×C₂²⋊C₄	—	2	1	no	—
772	C₃×C₄²	C₂⁴	1	1	yes	characteristic
773	C₃×C₄²	C₂⁴	1	1	yes	characteristic
774	C₃×C₄²	C₂⁴	1	1	yes	characteristic
775	#217	—	2	1	no	—
776	#217	—	2	1	no	—
777	#217	—	2	1	no	—
778	#217	—	2	1	no	—
779	#217	—	2	1	no	—
780	#217	—	2	1	no	—
781	#214	C₂×Q₈	1	4	yes	complemented
782	#213	C₂×Q₈	1	4	yes	complemented
783	(C₂×D₃)⋊C₄	—	2	1	no	—
784	(C₂×D₃)⋊C₄	—	2	1	no	—
785	(C₂×D₃)⋊C₄	—	2	1	no	—
786	(C₂×D₃)⋊C₄	—	2	1	no	—
787	(C₂×D₃)⋊C₄	—	2	1	no	—
788	(C₂×D₃)⋊C₄	—	2	1	no	—
789	(C₂×D₃)⋊C₄	—	2	1	no	—
790	(C₂×D₃)⋊C₄	—	2	1	no	—
791	(C₂×D₃)⋊C₄	—	2	1	no	—
792	(C₂×D₃)⋊C₄	C₂×D₄	1	1	yes	characteristic
793	(C₂×D₃)⋊C₄	C₂×D₄	1	1	yes	characteristic
794	(C₂×D₃)⋊C₄	C₂×D₄	1	1	yes	characteristic
795	(C₂×D₃)⋊C₄	C₂×D₄	1	1	yes	characteristic
796	C₄⋊Dic₃	—	2	1	no	—
797	C₄⋊Dic₃	—	2	1	no	—
798	C₄⋊Dic₃	—	2	1	no	—
799	C₄⋊Dic₃	—	2	1	no	—
800	C₄⋊Dic₃	—	2	1	no	—
801	C₄⋊Dic₃	—	2	1	no	—
802	C₄⋊Dic₃	—	2	1	no	—
803	C₄⋊Dic₃	—	2	1	no	—
804	C₄⋊Dic₃	C₂×D₄	1	1	yes	characteristic
805	C₄⋊Dic₃	C₂×D₄	1	1	yes	characteristic
806	C₄⋊Dic₃	C₂×D₄	1	1	yes	characteristic
807	C₄⋊Dic₃	C₂⁴	1	1	yes	characteristic
808	C₄⋊Dic₃	C₂⁴	1	1	yes	characteristic
809	C₄⋊Dic₃	C₂⁴	1	1	yes	characteristic
810	C₄⋊Dic₃	C₂⁴	1	1	yes	characteristic
811	C₄⋊Dic₃	C₂⁴	1	1	yes	characteristic
812	C₄⋊Dic₃	C₂⁴	1	1	yes	characteristic
813	Dic₃⋊C₄	—	2	1	no	—
814	Dic₃⋊C₄	—	2	1	no	—
815	Dic₃⋊C₄	—	2	1	no	—
816	Dic₃⋊C₄	—	2	1	no	—
817	Dic₃⋊C₄	—	2	1	no	—
818	Dic₃⋊C₄	—	2	1	no	—
819	Dic₃⋊C₄	—	2	1	no	—
820	Dic₃⋊C₄	—	2	1	no	—
821	Dic₃⋊C₄	—	2	1	no	—
822	Dic₃⋊C₄	—	2	1	no	—
823	Dic₃⋊C₄	—	2	1	no	—
824	Dic₃⋊C₄	—	2	1	no	—
825	Dic₃⋊C₄	—	2	1	no	—
826	Dic₃⋊C₄	—	2	1	no	—
827	Dic₃⋊C₄	—	2	1	no	—
828	Dic₃⋊C₄	—	2	1	no	—
829	Dic₃⋊C₄	—	2	1	no	—
830	Dic₃⋊C₄	—	2	1	no	—
831	Dic₃⋊C₄	—	2	1	no	—
832	Dic₃⋊C₄	—	2	1	no	—
833	Dic₃⋊C₄	—	2	1	no	—
834	Dic₃⋊C₄	—	2	1	no	—
835	Dic₃⋊C₄	—	2	1	no	—
836	Dic₃⋊C₄	—	2	1	no	—
837	Dic₃⋊C₄	—	2	1	no	—
838	Dic₃⋊C₄	C₂×D₄	1	1	yes	characteristic
839	Dic₃⋊C₄	C₂×D₄	1	1	yes	characteristic
840	Dic₃⋊C₄	C₂×D₄	1	1	yes	characteristic
841	Dic₃⋊C₄	C₂×D₄	1	1	yes	characteristic
842	Dic₃⋊C₄	C₂×D₄	1	1	yes	characteristic
843	Dic₃⋊C₄	C₂×D₄	1	1	yes	characteristic
844	Dic₃⋊C₄	C₂×D₄	1	1	yes	characteristic
845	Dic₃⋊C₄	C₂×D₄	1	1	yes	characteristic
846	Dic₃⋊C₄	C₂×D₄	1	1	yes	characteristic
847	Dic₃⋊C₄	C₂×D₄	1	1	yes	characteristic
848	C₄×Dic₃	—	2	1	no	—
849	C₄×Dic₃	—	2	1	no	—
850	C₄×Dic₃	—	2	1	no	—
851	C₄×Dic₃	—	2	1	no	—
852	C₄×Dic₃	—	2	1	no	—
853	C₄×Dic₃	—	2	1	no	—
854	C₄×Dic₃	—	2	1	no	—
855	C₄×Dic₃	—	2	1	no	—
856	C₄×Dic₃	—	2	1	no	—
857	C₄×Dic₃	C₂×D₄	1	1	yes	characteristic
858	C₄×Dic₃	C₂×D₄	1	1	yes	characteristic
859	C₄×Dic₃	C₂⁴	1	1	yes	characteristic
860	C₄×Dic₃	C₂⁴	1	1	yes	characteristic
861	C₄×Dic₃	C₂⁴	1	1	yes	characteristic
862	C₂×C₃⋊C₈	C₂⁴	1	1	yes	characteristic
863	C₂×C₃⋊C₈	C₂⁴	1	1	yes	characteristic
864	C₂×C₃⋊C₈	C₂⁴	1	1	yes	characteristic
865	C₂×C₃⋊C₈	C₂⁴	1	1	yes	characteristic
866	#204	C₂×Q₈	1	4	yes	complemented
867	ΓL(1,𝔽₂₅)	—	2	2	no	—
868	ΓL(1,𝔽₂₅)	C₂×Q₈	1	4	yes	complemented
869	D₃×C₈	—	2	2	no	—
870	D₃×C₈	—	2	2	no	—
871	C₂×#41	—	3	1	no	—
872	C₂²×Q₈	—	6	1	no	—
873	C₂²×Q₈	—	6	1	no	—
874	C₂²×Q₈	—	6	1	no	—
875	C₂²×Q₈	—	6	1	no	—
876	C₂²×Q₈	—	6	1	no	—
877	C₂²×D₄	—	3	1	no	—
878	C₂³×C₄	—	6	1	no	—
879	AGL(1,ℤ/8)	—	3	8	no	—
880	C₂×SD₁₆	—	3	1	no	—
881	C₂×SD₁₆	—	3	1	no	—
882	C₂×D₈	—	3	1	no	—
883	C₂×D₈	C₂²×D₃	1	1	yes	characteristic
884	C₂×M₁₆	—	3	1	no	—
885	C₂×M₁₆	—	3	1	no	—
886	C₂²×C₈	—	3	1	no	—
887	C₂²×C₈	—	3	1	no	—
888	C₄⋊Q₈	—	3	1	no	—
889	C₄⋊Q₈	—	3	1	no	—
890	C₄⋊Q₈	—	3	1	no	—
891	C₄⋊Q₈	—	3	1	no	—
892	C₄⋊Q₈	—	3	1	no	—
893	C₄⋊Q₈	—	3	1	no	—
894	C₄⋊Q₈	—	3	1	no	—
895	C₄⋊Q₈	—	3	1	no	—
896	C₄⋊Q₈	—	3	1	no	—
897	C₄⋊Q₈	—	3	1	no	—
898	C₄⋊Q₈	—	3	1	no	—
899	C₄⋊Q₈	—	3	1	no	—
900	C₄⋊Q₈	—	3	1	no	—
901	C₄⋊Q₈	—	3	1	no	—
902	C₄⋊Q₈	—	6	1	no	—
903	C₄⋊Q₈	—	6	1	no	—
904	C₄⋊Q₈	—	6	1	no	—
905	C₄⋊Q₈	—	6	1	no	—
906	C₄⋊Q₈	—	6	1	no	—
907	C₄⋊Q₈	—	6	1	no	—
908	C₄⋊Q₈	—	6	1	no	—
909	C₄⋊Q₈	—	6	1	no	—
910	C₄⋊Q₈	—	6	1	no	—
911	C₄⋊Q₈	—	6	1	no	—
912	C₄⋊Q₈	—	6	1	no	—
913	C₄⋊Q₈	—	6	1	no	—
914	C₄⋊Q₈	—	6	1	no	—
915	C₄⋊Q₈	—	6	1	no	—
916	C₄⋊Q₈	C₂²×D₃	1	1	yes	characteristic
917	C₄⋊Q₈	C₂²×D₃	1	1	yes	characteristic
918	#125	—	3	1	no	—
919	#125	—	3	1	no	—
920	#125	—	3	1	no	—
921	#125	—	3	1	no	—
922	#125	—	3	1	no	—
923	#125	—	3	1	no	—
924	#125	—	3	1	no	—
925	#125	—	3	1	no	—
926	#125	—	6	1	no	—
927	#125	—	6	1	no	—
928	#125	—	6	1	no	—
929	#125	—	6	1	no	—
930	#125	—	6	1	no	—
931	#125	—	6	1	no	—
932	#125	—	6	1	no	—
933	#125	—	6	1	no	—
934	#125	C₂²×D₃	1	1	yes	characteristic
935	#125	C₂²×D₃	1	1	yes	characteristic
936	#125	C₂²×D₃	1	1	yes	characteristic
937	#125	C₂²×D₃	1	1	yes	characteristic
938	C₂²⋊Q₈	—	2	1	no	—
939	C₂²⋊Q₈	—	2	1	no	—
940	C₂²⋊Q₈	—	2	1	no	—
941	C₂²⋊Q₈	—	2	1	no	—
942	C₂²⋊Q₈	—	2	1	no	—
943	C₂²⋊Q₈	—	2	1	no	—
944	C₂²⋊Q₈	—	3	1	no	—
945	C₂²⋊Q₈	—	3	1	no	—
946	C₂²⋊Q₈	—	3	1	no	—
947	C₂²⋊Q₈	—	3	1	no	—
948	C₂²⋊Q₈	—	6	1	no	—
949	C₂²⋊Q₈	—	6	1	no	—
950	C₂²⋊Q₈	—	6	1	no	—
951	C₂²⋊Q₈	—	6	1	no	—
952	C₂²⋊Q₈	—	6	1	no	—
953	C₂²⋊Q₈	—	6	1	no	—
954	C₂²⋊Q₈	—	6	1	no	—
955	C₂²⋊Q₈	—	6	1	no	—
956	C₂²⋊Q₈	—	6	1	no	—
957	C₂²⋊Q₈	—	6	1	no	—
958	C₂²⋊Q₈	—	6	1	no	—
959	C₂²⋊Q₈	—	6	1	no	—
960	C₂²⋊Q₈	—	6	1	no	—
961	C₂²⋊Q₈	—	6	1	no	—
962	C₂²⋊Q₈	—	6	1	no	—
963	C₂²⋊Q₈	—	6	1	no	—
964	C₂²⋊Q₈	—	6	1	no	—
965	C₂²⋊Q₈	—	6	1	no	—
966	C₂²⋊Q₈	—	6	1	no	—
967	C₂²⋊Q₈	—	6	1	no	—
968	C₂²⋊Q₈	—	6	1	no	—
969	C₂²⋊Q₈	—	6	1	no	—
970	C₂²⋊Q₈	—	6	1	no	—
971	C₂²⋊Q₈	—	6	1	no	—
972	C₂²⋊Q₈	—	6	1	no	—
973	C₂²⋊Q₈	—	6	1	no	—
974	C₂²⋊Q₈	—	6	1	no	—
975	C₂²⋊Q₈	—	6	1	no	—
976	C₂²⋊Q₈	—	6	1	no	—
977	C₂²⋊Q₈	—	6	1	no	—
978	C₂²⋊Q₈	—	6	1	no	—
979	C₂²⋊Q₈	—	6	1	no	—
980	C₂²⋊Q₈	—	6	1	no	—
981	C₂²⋊Q₈	—	6	1	no	—
982	C₂²⋊Q₈	—	6	1	no	—
983	C₂²⋊Q₈	—	6	1	no	—
984	C₂²⋊Q₈	—	6	1	no	—
985	C₂²⋊Q₈	—	6	1	no	—
986	C₂²⋊Q₈	—	6	1	no	—
987	C₂²⋊Q₈	—	6	1	no	—
988	C₄×Q₈	—	3	1	no	—
989	C₄×Q₈	—	3	1	no	—
990	C₄×Q₈	—	3	1	no	—
991	C₄×Q₈	—	3	1	no	—
992	C₄×Q₈	—	3	1	no	—
993	C₄×Q₈	—	3	1	no	—
994	C₄×Q₈	—	3	1	no	—
995	C₄×Q₈	—	3	1	no	—
996	C₄×Q₈	—	3	1	no	—
997	C₄×Q₈	—	6	1	no	—
998	C₄×Q₈	—	6	1	no	—
999	C₄×Q₈	—	6	1	no	—
1000	C₄×Q₈	—	6	1	no	—
1001	C₄×Q₈	—	6	1	no	—
1002	C₄×Q₈	—	6	1	no	—
1003	C₄×Q₈	C₂²×D₃	1	1	yes	characteristic
1004	C₄×D₄	—	3	1	no	—
1005	C₄×D₄	—	3	1	no	—
1006	C₄×D₄	—	3	1	no	—
1007	C₄×D₄	—	3	1	no	—
1008	C₄×D₄	—	3	1	no	—
1009	C₄×D₄	—	3	1	no	—
1010	C₄×D₄	—	3	1	no	—
1011	C₄×D₄	—	3	1	no	—
1012	C₄×D₄	—	3	1	no	—
1013	C₄×D₄	—	3	1	no	—
1014	C₄×D₄	—	3	1	no	—
1015	C₄×D₄	—	3	1	no	—
1016	C₄×D₄	—	6	1	no	—
1017	C₄×D₄	—	6	1	no	—
1018	C₄×D₄	—	6	1	no	—
1019	C₄×D₄	—	6	1	no	—
1020	C₄×D₄	—	6	1	no	—
1021	C₄×D₄	—	6	1	no	—
1022	C₄×D₄	—	6	1	no	—
1023	C₄×D₄	—	6	1	no	—
1024	C₄×D₄	—	6	1	no	—
1025	C₄×D₄	—	6	1	no	—
1026	C₄×D₄	—	6	1	no	—
1027	C₄×D₄	—	6	1	no	—
1028	C₄×D₄	C₂²×D₃	1	1	yes	characteristic
1029	C₄×D₄	C₂²×D₃	1	1	yes	characteristic
1030	C₄×D₄	C₂²×D₃	1	1	yes	characteristic
1031	C₄×D₄	C₂²×D₃	1	1	yes	characteristic
1032	C₄×D₄	C₂²×D₃	1	1	yes	characteristic
1033	C₄×D₄	C₂²×D₃	1	1	yes	characteristic
1034	#117	—	3	1	no	—
1035	#117	—	3	1	no	—
1036	#117	—	3	1	no	—
1037	#117	—	3	1	no	—
1038	#117	—	3	1	no	—
1039	#117	—	6	1	no	—
1040	#117	—	6	1	no	—
1041	#117	—	6	1	no	—
1042	C₂×C₄⋊C₄	—	2	1	no	—
1043	C₂×C₄⋊C₄	—	2	1	no	—
1044	C₂×C₄⋊C₄	—	3	1	no	—
1045	C₂×C₄⋊C₄	—	3	1	no	—
1046	C₂×C₄⋊C₄	—	3	1	no	—
1047	C₂×C₄⋊C₄	—	6	1	no	—
1048	C₂×C₄⋊C₄	—	6	1	no	—
1049	C₂×C₄⋊C₄	—	6	1	no	—
1050	C₂×C₄⋊C₄	—	6	1	no	—
1051	C₂×C₄⋊C₄	—	6	1	no	—
1052	C₂×C₄⋊C₄	—	6	1	no	—
1053	C₂×C₄⋊C₄	—	6	1	no	—
1054	C₂×C₄⋊C₄	—	6	1	no	—
1055	C₂×C₄⋊C₄	—	6	1	no	—
1056	C₂×C₂²⋊C₄	—	6	1	no	—
1057	C₂×C₂²⋊C₄	—	6	1	no	—
1058	C₂×C₂²⋊C₄	—	6	1	no	—
1059	C₂×C₂²⋊C₄	—	6	1	no	—
1060	C₂×C₂²⋊C₄	—	6	1	no	—
1061	C₂×C₄²	—	3	1	no	—
1062	C₂×C₄²	—	6	1	no	—
1063	#107	—	3	1	no	—
1064	#107	—	3	1	no	—
1065	#107	—	3	1	no	—
1066	#107	—	3	1	no	—
1067	#107	—	3	1	no	—
1068	#107	—	3	1	no	—
1069	#107	—	3	1	no	—
1070	#107	—	3	1	no	—
1071	#107	—	3	1	no	—
1072	#107	—	3	1	no	—
1073	#107	—	3	1	no	—
1074	#107	—	3	1	no	—
1075	#107	—	3	1	no	—
1076	#107	—	3	1	no	—
1077	#107	—	3	1	no	—
1078	#107	—	3	1	no	—
1079	#107	—	3	1	no	—
1080	#107	C₂²×D₃	1	1	yes	characteristic
1081	#107	C₂²×D₃	1	1	yes	characteristic
1082	#107	C₂²×D₃	1	1	yes	characteristic
1083	#107	C₂²×D₃	1	1	yes	characteristic
1084	#107	C₂²×D₃	1	1	yes	characteristic
1085	#106	—	3	1	no	—
1086	#106	—	3	1	no	—
1087	#106	—	3	1	no	—
1088	#106	—	3	1	no	—
1089	#106	—	3	1	no	—
1090	#106	—	3	1	no	—
1091	#106	—	3	1	no	—
1092	#106	—	3	1	no	—
1093	#106	—	3	1	no	—
1094	#106	—	3	1	no	—
1095	#106	C₂²×D₃	1	1	yes	characteristic
1096	#106	C₂²×D₃	1	1	yes	characteristic
1097	#106	C₂²×D₃	1	1	yes	characteristic
1098	#106	C₂²×D₃	1	1	yes	characteristic
1099	C₄⋊C₈	—	3	1	no	—
1100	C₄⋊C₈	—	3	1	no	—
1101	C₄⋊C₈	—	3	1	no	—
1102	C₄⋊C₈	—	3	1	no	—
1103	C₄⋊C₈	—	3	1	no	—
1104	C₄⋊C₈	—	3	1	no	—
1105	C₄⋊C₈	—	3	1	no	—
1106	C₄⋊C₈	—	3	1	no	—
1107	C₄⋊C₈	—	3	1	no	—
1108	C₄⋊C₈	C₂²×D₃	1	1	yes	characteristic
1109	C₄⋊C₈	C₂²×D₃	1	1	yes	characteristic
1110	C₄⋊C₈	C₂²×D₃	1	1	yes	characteristic
1111	#103	—	3	1	no	—
1112	#103	—	3	1	no	—
1113	#103	—	3	1	no	—
1114	#103	—	3	1	no	—
1115	#103	—	3	1	no	—
1116	#103	—	3	1	no	—
1117	#102	—	3	1	no	—
1118	#102	—	3	1	no	—
1119	#102	—	3	1	no	—
1120	#102	—	3	1	no	—
1121	#102	—	3	1	no	—
1122	#102	—	3	1	no	—
1123	#102	—	3	1	no	—
1124	#102	—	3	1	no	—
1125	#102	—	3	1	no	—
1126	#102	—	3	1	no	—
1127	#102	—	3	1	no	—
1128	#102	—	3	1	no	—
1129	#102	C₂²×D₃	1	1	yes	characteristic
1130	#102	C₂²×D₃	1	1	yes	characteristic
1131	#102	C₂²×D₃	1	1	yes	characteristic
1132	#102	C₂²×D₃	1	1	yes	characteristic
1133	#102	C₂²×D₃	1	1	yes	characteristic
1134	#102	C₂²×D₃	1	1	yes	characteristic
1135	#97	—	3	1	no	—
1136	#97	—	3	1	no	—
1137	#97	—	3	1	no	—
1138	#97	—	3	1	no	—
1139	#97	C₂²×D₃	1	1	yes	characteristic
1140	#97	C₂²×D₃	1	1	yes	characteristic
1141	C₄×C₈	—	3	1	no	—
1142	C₄×C₈	—	3	1	no	—
1143	C₄×C₈	—	3	1	no	—
1144	C₄×C₈	—	3	1	no	—
1145	C₄×C₈	—	3	1	no	—
1146	C₄×C₈	C₂²×D₃	1	1	yes	characteristic
1147	C₂³×C₃	—	2	1	no	—
1148	C₂³×C₃	—	2	1	no	—
1149	C₂²×D₃	—	2	1	no	—
1150	C₂²×D₃	—	2	4	no	—
1151	C₂²×D₃	—	8	1	no	—
1152	C₂²×D₃	—	8	1	no	—
1153	C₂²×D₃	C₂²×D₄	1	1	yes	characteristic
1154	C₃×Q₈	—	4	1	no	—
1155	C₃×Q₈	—	8	1	no	—
1156	C₃×Q₈	—	8	1	no	—
1157	C₃×D₄	—	2	1	no	—
1158	C₃×D₄	—	2	1	no	—
1159	C₃×D₄	C₂²×Q₈	1	2	yes	—
1160	C₃×D₄	C₂²×Q₈	1	2	yes	—
1161	C₂×C₃×C₄	—	2	1	no	—
1162	C₂×C₃×C₄	—	2	1	no	—
1163	C₂×C₃×C₄	—	2	1	no	—
1164	C₂×C₃×C₄	—	2	1	no	—
1165	C₂×C₃×C₄	—	2	1	no	—
1166	C₂×C₃×C₄	—	2	1	no	—
1167	C₂×C₃×C₄	—	4	2	no	—
1168	C₂×C₃×C₄	—	8	1	no	—
1169	C₂×C₃×C₄	—	8	1	no	—
1170	C₂×C₃×C₄	—	8	1	no	—
1171	C₂×C₃×C₄	—	8	1	no	—
1172	C₂×C₃×C₄	—	8	1	no	—
1173	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
1174	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
1175	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
1176	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
1177	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
1178	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
1179	C₂×C₃×C₄	C₂⁵	1	1	yes	characteristic
1180	#67	—	2	4	no	—
1181	#67	—	2	4	no	—
1182	C₂×Dic₃	—	2	1	no	—
1183	C₂×Dic₃	—	2	4	no	—
1184	C₂×Dic₃	—	2	1	no	—
1185	C₂×Dic₃	—	2	1	no	—
1186	C₂×Dic₃	—	2	1	no	—
1187	C₂×Dic₃	—	2	1	no	—
1188	C₂×Dic₃	—	2	1	no	—
1189	C₂×Dic₃	—	2	1	no	—
1190	C₂×Dic₃	—	4	2	no	—
1191	C₂×Dic₃	—	4	2	no	—
1192	C₂×Dic₃	—	8	1	no	—
1193	C₂×Dic₃	—	8	1	no	—
1194	C₂×Dic₃	—	8	1	no	—
1195	C₂×Dic₃	—	8	1	no	—
1196	C₂×Dic₃	C₂²×D₄	1	1	yes	characteristic
1197	C₂×Dic₃	C₂²×D₄	1	1	yes	characteristic
1198	C₂×Dic₃	C₂²×D₄	1	1	yes	characteristic
1199	C₂×Dic₃	C₂²×D₄	1	1	yes	characteristic
1200	C₂×Dic₃	C₂²×D₄	1	1	yes	characteristic
1201	C₂×Dic₃	C₂²×D₄	1	1	yes	characteristic
1202	C₂×Dic₃	C₂²×D₄	1	1	yes	characteristic
1203	D₁₂	—	2	1	no	—
1204	D₁₂	C₂²×Q₈	1	2	yes	—
1205	C₄×D₃	—	2	2	no	—
1206	C₄×D₃	—	4	1	no	—
1207	C₄×D₃	—	4	2	no	—
1208	C₄×D₃	—	8	1	no	—
1209	C₄×D₃	—	8	1	no	—
1210	C₄×D₃	—	8	1	no	—
1211	C₄×D₃	—	8	1	no	—
1212	C₄×D₃	—	8	1	no	—
1213	C₄×D₃	—	8	1	no	—
1214	C₄×D₃	—	8	1	no	—
1215	C₄×D₃	—	8	1	no	—
1216	C₄×D₃	C₂²×Q₈	1	2	yes	—
1217	C₄×D₃	2₋¹⁺⁴	1	2	yes	—
1218	Dic₆	—	2	1	no	—
1219	Dic₆	—	2	2	no	—
1220	Dic₆	—	2	2	no	—
1221	Dic₆	—	4	1	no	—
1222	Dic₆	—	4	2	no	—
1223	Dic₆	—	4	2	no	—
1224	Dic₆	—	4	2	no	—
1225	Dic₆	—	8	1	no	—
1226	Dic₆	—	8	1	no	—
1227	Dic₆	—	8	1	no	—
1228	Dic₆	—	8	1	no	—
1229	Dic₆	—	8	1	no	—
1230	Dic₆	—	8	1	no	—
1231	Dic₆	—	8	1	no	—
1232	Dic₆	—	8	1	no	—
1233	Dic₆	—	8	1	no	—
1234	Dic₆	C₂²×Q₈	1	2	yes	—
1235	C₃×C₈	—	2	1	no	—
1236	C₃×C₈	—	2	1	no	—
1237	C₃×C₈	—	2	1	no	—
1238	C₃×C₈	C₂²×Q₈	1	2	yes	—
1239	C₃⋊C₈	—	2	1	no	—
1240	C₃⋊C₈	—	2	1	no	—
1241	C₃⋊C₈	—	2	1	no	—
1242	C₃⋊C₈	C₂²×Q₈	1	2	yes	—
1243	C₂⁴	—	6	1	no	—
1244	#41	—	3	4	no	—
1245	#41	—	6	2	no	—
1246	C₂×Q₈	—	2	1	no	—
1247	C₂×Q₈	—	2	1	no	—
1248	C₂×Q₈	—	3	1	no	—
1249	C₂×Q₈	—	3	1	no	—
1250	C₂×Q₈	—	3	1	no	—
1251	C₂×Q₈	—	3	1	no	—
1252	C₂×Q₈	—	6	1	no	—
1253	C₂×Q₈	—	6	1	no	—
1254	C₂×Q₈	—	6	1	no	—
1255	C₂×Q₈	—	6	1	no	—
1256	C₂×Q₈	—	6	1	no	—
1257	C₂×Q₈	—	6	1	no	—
1258	C₂×Q₈	—	6	1	no	—
1259	C₂×Q₈	—	6	1	no	—
1260	C₂×Q₈	—	6	1	no	—
1261	C₂×Q₈	—	6	1	no	—
1262	C₂×Q₈	—	6	1	no	—
1263	C₂×Q₈	—	6	1	no	—
1264	C₂×Q₈	—	24	2	no	—
1265	C₂×Q₈	—	24	2	no	—
1266	C₂×Q₈	—	24	2	no	—
1267	C₂×Q₈	—	24	2	no	—
1268	C₂×Q₈	—	24	2	no	—
1269	C₂×Q₈	D₃×D₄	1	1	yes	characteristic
1270	C₂×D₄	—	3	4	no	—
1271	C₂×D₄	—	3	1	no	—
1272	C₂×D₄	—	6	2	no	—
1273	C₂×D₄	—	6	1	no	—
1274	C₂×D₄	—	6	1	no	—
1275	C₂×D₄	C₂³×D₃	1	1	yes	characteristic
1276	C₂×D₄	C₂³×D₃	1	1	yes	characteristic
1277	C₂²×C₄	—	2	1	no	—
1278	C₂²×C₄	—	2	1	no	—
1279	C₂²×C₄	—	2	1	no	—
1280	C₂²×C₄	—	2	1	no	—
1281	C₂²×C₄	—	2	1	no	—
1282	C₂²×C₄	—	2	1	no	—
1283	C₂²×C₄	—	3	1	no	—
1284	C₂²×C₄	—	3	1	no	—
1285	C₂²×C₄	—	3	1	no	—
1286	C₂²×C₄	—	6	1	no	—
1287	C₂²×C₄	—	6	1	no	—
1288	C₂²×C₄	—	6	1	no	—
1289	C₂²×C₄	—	6	1	no	—
1290	C₂²×C₄	—	6	1	no	—
1291	C₂²×C₄	—	6	1	no	—
1292	C₂²×C₄	—	6	1	no	—
1293	C₂²×C₄	—	6	1	no	—
1294	C₂²×C₄	—	6	1	no	—
1295	C₂²×C₄	—	6	1	no	—
1296	C₂²×C₄	—	6	1	no	—
1297	C₂²×C₄	—	6	1	no	—
1298	C₂²×C₄	—	6	1	no	—
1299	C₂²×C₄	—	6	1	no	—
1300	C₂²×C₄	—	6	1	no	—
1301	C₂²×C₄	—	6	1	no	—
1302	C₂²×C₄	—	24	2	no	—
1303	SD₁₆	—	3	4	no	—
1304	SD₁₆	—	3	4	no	—
1305	D₈	—	3	4	no	—
1306	D₈	D₃×Q₈	1	4	yes	complemented
1307	M₁₆	—	3	4	no	—
1308	M₁₆	—	6	2	no	—
1309	C₂×C₈	—	3	1	no	—
1310	C₂×C₈	—	3	1	no	—
1311	C₂×C₈	—	3	1	no	—
1312	C₂×C₈	—	3	1	no	—
1313	C₂×C₈	—	6	2	no	—
1314	C₂×C₈	—	6	2	no	—
1315	C₂×C₈	C₂³×D₃	1	1	yes	characteristic
1316	C₂×C₈	C₂³×D₃	1	1	yes	characteristic
1317	C₂×C₈	C₂³×D₃	1	1	yes	characteristic
1318	C₂×C₈	C₂³×D₃	1	1	yes	characteristic
1319	C₄⋊C₄	—	2	1	no	—
1320	C₄⋊C₄	—	2	1	no	—
1321	C₄⋊C₄	—	2	1	no	—
1322	C₄⋊C₄	—	2	1	no	—
1323	C₄⋊C₄	—	2	1	no	—
1324	C₄⋊C₄	—	2	1	no	—
1325	C₄⋊C₄	—	2	1	no	—
1326	C₄⋊C₄	—	2	1	no	—
1327	C₄⋊C₄	—	2	1	no	—
1328	C₄⋊C₄	—	2	1	no	—
1329	C₄⋊C₄	—	3	1	no	—
1330	C₄⋊C₄	—	3	1	no	—
1331	C₄⋊C₄	—	3	1	no	—
1332	C₄⋊C₄	—	3	1	no	—
1333	C₄⋊C₄	—	3	1	no	—
1334	C₄⋊C₄	—	3	1	no	—
1335	C₄⋊C₄	—	3	1	no	—
1336	C₄⋊C₄	—	3	1	no	—
1337	C₄⋊C₄	—	3	1	no	—
1338	C₄⋊C₄	—	3	1	no	—
1339	C₄⋊C₄	—	3	1	no	—
1340	C₄⋊C₄	—	3	1	no	—
1341	C₄⋊C₄	—	3	1	no	—
1342	C₄⋊C₄	—	3	1	no	—
1343	C₄⋊C₄	—	3	1	no	—
1344	C₄⋊C₄	—	3	1	no	—
1345	C₄⋊C₄	—	3	1	no	—
1346	C₄⋊C₄	—	3	1	no	—
1347	C₄⋊C₄	—	3	1	no	—
1348	C₄⋊C₄	—	6	1	no	—
1349	C₄⋊C₄	—	6	1	no	—
1350	C₄⋊C₄	—	6	1	no	—
1351	C₄⋊C₄	—	6	1	no	—
1352	C₄⋊C₄	—	6	1	no	—
1353	C₄⋊C₄	—	6	1	no	—
1354	C₄⋊C₄	—	6	1	no	—
1355	C₄⋊C₄	—	6	1	no	—
1356	C₄⋊C₄	—	6	1	no	—
1357	C₄⋊C₄	—	6	1	no	—
1358	C₄⋊C₄	—	6	1	no	—
1359	C₄⋊C₄	—	6	1	no	—
1360	C₄⋊C₄	—	6	1	no	—
1361	C₄⋊C₄	—	6	1	no	—
1362	C₄⋊C₄	—	6	1	no	—
1363	C₄⋊C₄	—	6	1	no	—
1364	C₄⋊C₄	—	6	1	no	—
1365	C₄⋊C₄	—	6	1	no	—
1366	C₄⋊C₄	—	6	1	no	—
1367	C₄⋊C₄	—	6	1	no	—
1368	C₄⋊C₄	—	6	1	no	—
1369	C₄⋊C₄	—	6	1	no	—
1370	C₄⋊C₄	—	6	1	no	—
1371	C₄⋊C₄	—	6	1	no	—
1372	C₄⋊C₄	—	6	1	no	—
1373	C₄⋊C₄	—	6	1	no	—
1374	C₄⋊C₄	—	6	1	no	—
1375	C₄⋊C₄	—	6	1	no	—
1376	C₄⋊C₄	—	6	1	no	—
1377	C₄⋊C₄	—	6	1	no	—
1378	C₄⋊C₄	—	6	1	no	—
1379	C₄⋊C₄	—	6	1	no	—
1380	C₄⋊C₄	—	6	1	no	—
1381	C₄⋊C₄	D₃×D₄	1	1	yes	characteristic
1382	C₄⋊C₄	D₃×D₄	1	1	yes	characteristic
1383	C₄⋊C₄	D₃×D₄	1	1	yes	characteristic
1384	C₄⋊C₄	C₂³×D₃	1	1	yes	characteristic
1385	C₄⋊C₄	C₂³×D₃	1	1	yes	characteristic
1386	C₄⋊C₄	C₂³×D₃	1	1	yes	characteristic
1387	C₄⋊C₄	C₂³×D₃	1	1	yes	characteristic
1388	C₄⋊C₄	C₂³×D₃	1	1	yes	characteristic
1389	C₄⋊C₄	C₂³×D₃	1	1	yes	characteristic
1390	C₂²⋊C₄	—	2	1	no	—
1391	C₂²⋊C₄	—	2	1	no	—
1392	C₂²⋊C₄	—	2	1	no	—
1393	C₂²⋊C₄	—	2	1	no	—
1394	C₂²⋊C₄	—	2	1	no	—
1395	C₂²⋊C₄	—	2	1	no	—
1396	C₂²⋊C₄	—	3	1	no	—
1397	C₂²⋊C₄	—	3	1	no	—
1398	C₂²⋊C₄	—	3	1	no	—
1399	C₂²⋊C₄	—	3	1	no	—
1400	C₂²⋊C₄	—	6	1	no	—
1401	C₂²⋊C₄	—	6	1	no	—
1402	C₂²⋊C₄	—	6	1	no	—
1403	C₂²⋊C₄	—	6	1	no	—
1404	C₂²⋊C₄	—	6	1	no	—
1405	C₂²⋊C₄	—	6	1	no	—
1406	C₂²⋊C₄	—	6	1	no	—
1407	C₂²⋊C₄	—	6	1	no	—
1408	C₂²⋊C₄	—	6	1	no	—
1409	C₂²⋊C₄	—	6	1	no	—
1410	C₂²⋊C₄	—	6	1	no	—
1411	C₂²⋊C₄	—	6	1	no	—
1412	C₂²⋊C₄	—	6	1	no	—
1413	C₂²⋊C₄	—	6	1	no	—
1414	C₂²⋊C₄	—	6	1	no	—
1415	C₄²	—	3	1	no	—
1416	C₄²	—	3	1	no	—
1417	C₄²	—	3	1	no	—
1418	C₄²	—	3	1	no	—
1419	C₄²	—	3	1	no	—
1420	C₄²	—	6	1	no	—
1421	C₄²	—	6	1	no	—
1422	C₄²	—	6	1	no	—
1423	C₄²	—	6	1	no	—
1424	C₄²	—	6	1	no	—
1425	C₄²	—	6	1	no	—
1426	C₄²	—	6	1	no	—
1427	C₄²	—	6	1	no	—
1428	C₄²	—	6	1	no	—
1429	C₄²	C₂³×D₃	1	1	yes	characteristic
1430	C₄²	C₂³×D₃	1	1	yes	characteristic
1431	C₄²	C₂³×D₃	1	1	yes	characteristic
1432	C₂²×C₃	—	2	2	no	—
1433	C₂²×C₃	—	2	2	no	—
1434	C₂²×C₃	—	4	1	no	—
1435	C₂²×C₃	—	4	1	no	—
1436	C₂²×C₃	—	4	1	no	—
1437	C₂²×C₃	—	4	1	no	—
1438	C₂²×C₃	C₂³×D₄	1	1	yes	characteristic
1439	C₂×D₃	—	2	1	no	—
1440	C₂×D₃	—	2	1	no	—
1441	C₂×D₃	—	2	2	no	—
1442	C₂×D₃	—	4	1	no	—
1443	C₂×D₃	—	4	1	no	—
1444	C₂×D₃	—	8	4	no	—
1445	C₂×D₃	D₄×Q₈	1	2	yes	—
1446	C₃×C₄	—	2	1	no	—
1447	C₃×C₄	—	2	1	no	—
1448	C₃×C₄	—	2	1	no	—
1449	C₃×C₄	—	2	1	no	—
1450	C₃×C₄	—	2	1	no	—
1451	C₃×C₄	—	2	1	no	—
1452	C₃×C₄	—	4	1	no	—
1453	C₃×C₄	—	4	1	no	—
1454	C₃×C₄	—	4	1	no	—
1455	C₃×C₄	—	4	1	no	—
1456	C₃×C₄	—	4	1	no	—
1457	C₃×C₄	—	4	1	no	—
1458	C₃×C₄	C₂³×Q₈	1	1	yes	characteristic
1459	C₃×C₄	C₂×2₋¹⁺⁴	1	1	yes	characteristic
1460	Dic₃	—	2	1	no	—
1461	Dic₃	—	2	1	no	—
1462	Dic₃	—	2	1	no	—
1463	Dic₃	—	2	2	no	—
1464	Dic₃	—	2	1	no	—
1465	Dic₃	—	2	1	no	—
1466	Dic₃	—	4	1	no	—
1467	Dic₃	—	4	1	no	—
1468	Dic₃	—	4	1	no	—
1469	Dic₃	—	4	1	no	—
1470	Dic₃	—	4	1	no	—
1471	Dic₃	—	4	1	no	—
1472	Dic₃	D₄×Q₈	1	2	yes	—
1473	Dic₃	#576	1	2	yes	—
1474	C₂³	—	2	1	no	—
1475	C₂³	—	2	1	no	—
1476	C₂³	—	3	1	no	—
1477	C₂³	—	6	4	no	—
1478	C₂³	—	6	1	no	—
1479	C₂³	—	24	1	no	—
1480	C₂³	—	24	1	no	—
1481	Q₈	—	3	2	no	—
1482	Q₈	—	4	1	no	—
1483	Q₈	—	6	2	no	—
1484	Q₈	—	6	2	no	—
1485	Q₈	—	6	1	no	—
1486	Q₈	—	8	1	no	—
1487	Q₈	—	8	1	no	—
1488	Q₈	—	12	1	no	—
1489	Q₈	—	12	2	no	—
1490	Q₈	—	12	2	no	—
1491	Q₈	—	12	2	no	—
1492	Q₈	—	24	1	no	—
1493	Q₈	—	24	1	no	—
1494	Q₈	—	24	1	no	—
1495	Q₈	—	24	1	no	—
1496	Q₈	—	24	1	no	—
1497	Q₈	—	24	1	no	—
1498	Q₈	—	24	1	no	—
1499	Q₈	—	24	1	no	—
1500	Q₈	—	24	1	no	—
1501	D₄	—	2	1	no	—
1502	D₄	—	2	1	no	—
1503	D₄	—	3	2	no	—
1504	D₄	—	6	4	no	—
1505	D₄	—	6	4	no	—
1506	D₄	—	6	1	no	—
1507	D₄	C₂×D₃×Q₈	1	2	yes	—
1508	D₄	C₂×D₃×Q₈	1	2	yes	—
1509	C₂×C₄	—	2	1	no	—
1510	C₂×C₄	—	2	1	no	—
1511	C₂×C₄	—	2	1	no	—
1512	C₂×C₄	—	2	1	no	—
1513	C₂×C₄	—	2	1	no	—
1514	C₂×C₄	—	2	1	no	—
1515	C₂×C₄	—	3	1	no	—
1516	C₂×C₄	—	3	1	no	—
1517	C₂×C₄	—	3	2	no	—
1518	C₂×C₄	—	3	2	no	—
1519	C₂×C₄	—	3	1	no	—
1520	C₂×C₄	—	3	1	no	—
1521	C₂×C₄	—	3	1	no	—
1522	C₂×C₄	—	3	1	no	—
1523	C₂×C₄	—	3	1	no	—
1524	C₂×C₄	—	4	2	no	—
1525	C₂×C₄	—	6	2	no	—
1526	C₂×C₄	—	6	4	no	—
1527	C₂×C₄	—	6	1	no	—
1528	C₂×C₄	—	6	1	no	—
1529	C₂×C₄	—	6	1	no	—
1530	C₂×C₄	—	6	1	no	—
1531	C₂×C₄	—	6	1	no	—
1532	C₂×C₄	—	6	1	no	—
1533	C₂×C₄	—	6	1	no	—
1534	C₂×C₄	—	8	1	no	—
1535	C₂×C₄	—	8	1	no	—
1536	C₂×C₄	—	8	1	no	—
1537	C₂×C₄	—	8	1	no	—
1538	C₂×C₄	—	8	1	no	—
1539	C₂×C₄	—	12	1	no	—
1540	C₂×C₄	—	12	2	no	—
1541	C₂×C₄	—	12	2	no	—
1542	C₂×C₄	—	12	2	no	—
1543	C₂×C₄	—	24	1	no	—
1544	C₂×C₄	—	24	1	no	—
1545	C₂×C₄	—	24	1	no	—
1546	C₂×C₄	—	24	1	no	—
1547	C₂×C₄	—	24	1	no	—
1548	C₂×C₄	—	24	1	no	—
1549	C₂×C₄	—	24	1	no	—
1550	C₂×C₄	—	24	1	no	—
1551	C₂×C₄	—	24	1	no	—
1552	C₂×C₄	—	24	1	no	—
1553	C₂×C₄	—	24	1	no	—
1554	C₂×C₄	—	24	1	no	—
1555	C₂×C₄	C₂×D₃×D₄	1	1	yes	characteristic
1556	C₂×C₄	C₂×D₃×D₄	1	1	yes	characteristic
1557	C₂×C₄	C₂×D₃×D₄	1	1	yes	characteristic
1558	C₂×C₄	C₂×D₃×D₄	1	1	yes	characteristic
1559	C₂×C₄	C₂×D₃×D₄	1	1	yes	characteristic
1560	C₂×C₄	C₂×D₃×D₄	1	1	yes	characteristic
1561	C₂×C₄	C₂⁴×D₃	1	1	yes	characteristic
1562	C₈	—	2	1	no	—
1563	C₈	—	2	1	no	—
1564	C₈	—	2	1	no	—
1565	C₈	—	3	2	no	—
1566	C₈	—	6	1	no	—
1567	C₈	—	6	1	no	—
1568	C₈	—	6	1	no	—
1569	C₈	C₂×D₃×Q₈	1	2	yes	—
1570	C₂×C₃	—	4	2	no	—
1571	C₂×C₃	—	4	2	no	—
1572	C₂×C₃	C₂×D₄×Q₈	1	1	yes	characteristic
1573	C₂×C₃	C₂×#576	1	1	yes	characteristic
1574	C₂×C₃	#3586	1	1	yes	characteristic
1575	D₃	—	2	2	no	—
1576	D₃	—	4	2	no	—
1577	C₂²	—	2	2	no	—
1578	C₂²	—	2	2	no	—
1579	C₂²	—	3	2	no	—
1580	C₂²	—	4	1	no	—
1581	C₂²	—	4	1	no	—
1582	C₂²	—	4	1	no	—
1583	C₂²	—	4	1	no	—
1584	C₂²	—	6	1	no	—
1585	C₂²	—	6	1	no	—
1586	C₂²	—	6	2	no	—
1587	C₂²	—	12	1	no	—
1588	C₂²	—	12	1	no	—
1589	C₂²	—	24	4	no	—
1590	C₂²	C₂²×D₃×D₄	1	1	yes	characteristic
1591	C₄	—	2	1	no	—
1592	C₄	—	2	1	no	—
1593	C₄	—	2	1	no	—
1594	C₄	—	2	1	no	—
1595	C₄	—	2	1	no	—
1596	C₄	—	2	1	no	—
1597	C₄	—	3	2	no	—
1598	C₄	—	3	2	no	—
1599	C₄	—	4	1	no	—
1600	C₄	—	4	1	no	—
1601	C₄	—	4	1	no	—
1602	C₄	—	4	1	no	—
1603	C₄	—	4	1	no	—
1604	C₄	—	4	1	no	—
1605	C₄	—	6	1	no	—
1606	C₄	—	6	1	no	—
1607	C₄	—	6	1	no	—
1608	C₄	—	6	1	no	—
1609	C₄	—	6	1	no	—
1610	C₄	—	6	2	no	—
1611	C₄	—	12	1	no	—
1612	C₄	—	12	1	no	—
1613	C₄	—	12	1	no	—
1614	C₄	—	12	1	no	—
1615	C₄	—	12	1	no	—
1616	C₄	—	12	1	no	—
1617	C₄	C₂²×D₃×Q₈	1	1	yes	characteristic
1618	C₄	D₃×2₋¹⁺⁴	1	1	yes	characteristic
1619	C₃	#61381	1	1	yes	characteristic, complemented, Sylow
1620	C₂	—	4	2	no	—
1621	C₂	—	4	2	no	—
1622	C₂	—	6	2	no	—
1623	C₂	—	12	2	no	—
1624	C₂	D₃×D₄×Q₈	1	1	yes	characteristic
1625	C₂	#87201	1	1	yes	characteristic
1626	C₂	D₃×#576	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×D₃×D₄
commutator, cosocle	C₂×C₃×C₄	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₃
Fitting	C₃×#3389	C₂
socle	C₂²×C₃	C₂³×D₄
prime radical	C₂×#911	C₂²
hypercenter	#3389	D₃
hypocenter	C₃	#61381
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂² ◁ C₄×Q₈ ◁ #3389

Complements

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

N	H ≅ G/N	type
1. #86949	C₂	semidirect
2. #86926	C₂	semidirect
3. C₃×#3389	C₂	semidirect
4. #83633	C₂	semidirect
5. #83631	C₂	semidirect
6. #81976	C₂	semidirect
7. #81975	C₂	semidirect
8. #81966	C₂	semidirect
9. #81965	C₂	semidirect
10. #81918	C₂	semidirect
11. #81913	C₂	semidirect
12. #81170	C₂	semidirect
13. #81169	C₂	semidirect
14. #81168	C₂	semidirect
15. #81165	C₂	semidirect
16. #81163	C₂	semidirect
17. #81159	C₂	semidirect
18. #81158	C₂	semidirect
19. #81157	C₂	semidirect
20. #80968	C₂	semidirect
21. D₃×#474	C₂	semidirect
22. #80960	C₂	semidirect
23. #80957	C₂	semidirect
24. #79976	C₂	semidirect
25. #79961	C₂	semidirect
28. #79856	C₂	semidirect
29. #79855	C₂	semidirect
31. D₈×Dic₆	C₂	semidirect
34. C₃×#554	C₂²	semidirect
39. #5722	C₂²	semidirect
46. #5685	C₂²	semidirect
47. #5685	C₂²	semidirect
62. Q₈×Dic₆	C₂²	semidirect
68. #5543	C₂²	semidirect
72. D₄×Dic₆	C₂²	semidirect
73. D₄×Dic₆	C₂²	semidirect
79. C₃×#501	C₂²	semidirect
80. C₃×#501	C₂²	semidirect
81. C₃×#499	C₂²	semidirect
84. C₃×#478	C₂²	semidirect
85. C₃×#478	C₂²	semidirect
87. C₃×#474	C₂²	semidirect
88. C₃×#446	C₂²	semidirect
95. #5091	C₂²	semidirect
97. #5081	C₂²	semidirect
98. #5078	C₂²	semidirect
101. #5065	C₂²	semidirect
102. #5064	C₂²	semidirect
103. #5064	C₂²	semidirect
104. #5064	C₂²	semidirect
105. #5063	C₂²	semidirect
106. #5063	C₂²	semidirect
107. #5024	C₂²	semidirect
114. #5009	C₂²	semidirect
115. #5009	C₂²	semidirect
119. #5007	C₂²	semidirect
130. #4878	C₂²	semidirect
131. #4877	C₂²	semidirect
132. #4876	C₂²	semidirect
133. #4875	C₂²	semidirect
134. #4875	C₂²	semidirect
135. #4875	C₂²	semidirect
136. #4874	C₂²	semidirect
137. #4874	C₂²	semidirect
138. #4874	C₂²	semidirect
139. #4874	C₂²	semidirect
146. #4858	C₂²	semidirect
147. #4857	C₂²	semidirect
148. #4856	C₂²	semidirect
149. #4856	C₂²	semidirect
150. #4856	C₂²	semidirect
151. #4855	C₂²	semidirect
152. #4855	C₂²	semidirect
153. #4854	C₂²	semidirect
156. #4850	C₂²	semidirect
163. #4830	C₂²	semidirect
164. #4829	C₂²	semidirect
165. #4829	C₂²	semidirect
166. #4828	C₂²	semidirect
167. #4828	C₂²	semidirect
176. #4766	C₂²	semidirect
178. #4763	C₂²	semidirect
180. #4761	C₂²	semidirect
184. #4759	C₂²	semidirect
185. #4759	C₂²	semidirect
186. #4759	C₂²	semidirect
196. #4702	C₂²	semidirect
197. #4702	C₂²	semidirect
198. #4701	C₂²	semidirect
199. #4701	C₂²	semidirect
202. #4682	C₂²	semidirect
203. C₈×Dic₆	C₂²	semidirect
209. #3389	D₃	semidirect
303. #911	Q₈	semidirect
528. #554	C₂×D₃	semidirect
567. #501	C₂×D₃	semidirect
568. #501	C₂×D₃	semidirect
578. #499	C₂×D₃	semidirect
599. #478	C₂×D₃	semidirect
600. #478	C₂×D₃	semidirect
628. #474	C₂×D₃	semidirect
634. #446	C₂×D₃	semidirect
706. #237	C₂×Q₈	semidirect
708. D₃×D₄	C₂×Q₈	semidirect
742. C₃×D₈	C₂×Q₈	semidirect
781. #214	C₂×Q₈	semidirect
782. #213	C₂×Q₈	semidirect
866. #204	C₂×Q₈	semidirect
868. ΓL(1,𝔽₂₅)	C₂×Q₈	semidirect
1306. D₈	D₃×Q₈	semidirect
1619. C₃	#61381	semidirect

Maximal subgroups

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

subgroup	index
#86949	2
#86926	2
C₃×#3389	2
#83633	2
#83631	2
#81976	2
#81975	2
#81966	2
#81965	2
#81918	2
#81913	2
#81170	2
#81169	2
#81168	2
#81165	2
#81163	2
#81159	2
#81158	2
#81157	2
#80968	2
D₃×#474	2
#80960	2
#80957	2
#79976	2
#79961	2
#79866	2
#79865	2
#79856	2
#79855	2
#79587	2
D₈×Dic₆	2
#61381	3