Subgroups — #6346026

Order 512.

1592 conjugacy classes of subgroups.

The subgroup lattice has 950 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#61431	C₂	1	1	yes	maximal, characteristic
2	#60324	C₂	1	2	yes	maximal, complemented
3	#18093	C₂	1	1	yes	maximal, characteristic, complemented
4	#18075	C₂	1	1	yes	maximal, characteristic, complemented
5	#18073	C₂	1	1	yes	maximal, characteristic, complemented
6	#18064	C₂	1	1	yes	maximal, characteristic, complemented
7	#18044	C₂	1	1	yes	maximal, characteristic, complemented
8	#18043	C₂	1	1	yes	maximal, characteristic, complemented
9	#18014	C₂	1	2	yes	maximal, complemented
10	#18011	C₂	1	2	yes	maximal, complemented
11	#18006	C₂	1	2	yes	maximal, complemented
12	#17974	C₂	1	1	yes	maximal, characteristic, complemented
13	#17970	C₂	1	1	yes	maximal, characteristic, complemented
14	#17963	C₂	1	1	yes	maximal, characteristic, complemented
15	#17948	C₂	1	2	yes	maximal, complemented
16	#17946	C₂	1	2	yes	maximal, complemented
17	#17942	C₂	1	2	yes	maximal, complemented
18	#17899	C₂	1	1	yes	maximal, characteristic, complemented
19	#17895	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#1594	C₂	1	1	yes	maximal, characteristic, complemented
21	#17834	C₂	1	1	yes	maximal, characteristic, complemented
22	#17521	C₂	1	2	yes	maximal, complemented
23	#17330	C₂	1	1	yes	maximal, characteristic, complemented
24	#3481	C₂²	1	2	yes	—
25	#3396	C₄	1	1	yes	characteristic
26	#3380	C₄	1	1	yes	characteristic
27	#3361	C₄	1	2	yes	—
28	#3339	C₄	1	1	yes	characteristic
29	#3339	C₄	1	1	yes	characteristic
30	#3338	C₄	1	1	yes	characteristic
31	#3297	C₄	1	2	yes	—
32	#3297	C₄	1	2	yes	—
33	#3295	C₄	1	2	yes	—
34	#3280	C₄	1	1	yes	characteristic
35	#3280	C₄	1	1	yes	characteristic
36	D₄×D₈	C₄	1	1	yes	characteristic
37	#3169	C₂²	1	1	yes	characteristic
38	#3168	C₂²	1	1	yes	characteristic
39	#3168	C₂²	1	1	yes	characteristic
40	#3106	C₂²	1	2	yes	—
41	#3105	C₂²	1	2	yes	—
42	#3105	C₂²	1	2	yes	—
43	#2995	—	2	2	no	—
44	#2994	C₂²	1	2	yes	complemented
45	#2993	C₂²	1	2	yes	complemented
46	#2990	C₂²	1	2	yes	—
47	#2989	C₂²	1	2	yes	complemented
48	#2981	C₂²	1	2	yes	complemented
49	#2978	—	2	2	no	—
50	#2976	—	2	2	no	—
51	#2975	C₂²	1	2	yes	complemented
52	#2974	C₂²	1	2	yes	complemented
53	#2973	—	2	2	no	—
54	#2971	C₂²	1	2	yes	complemented
55	#2969	C₂²	1	2	yes	complemented
56	#2967	—	2	2	no	—
57	#2966	C₂²	1	2	yes	complemented
58	#2965	C₂²	1	1	yes	characteristic
59	C₈×#41	C₂²	1	1	yes	characteristic
60	C₄×#135	C₂²	1	1	yes	characteristic
61	C₂×C₄×D₈	C₂²	1	1	yes	characteristic
62	C₂×C₄×D₈	C₂²	1	1	yes	characteristic
63	#2935	C₂²	1	2	yes	complemented
64	D₄×M₁₆	—	2	2	no	—
65	D₄×M₁₆	C₂²	1	2	yes	complemented
66	#2933	—	2	2	no	—
67	#2930	—	2	2	no	—
68	C₂×#436	C₂²	1	2	yes	complemented
69	#2922	C₂²	1	1	yes	characteristic
70	#1594	C₂²	1	1	yes	characteristic
71	#1594	C₂²	1	1	yes	characteristic
72	#1594	C₂²	1	1	yes	characteristic
73	#1594	C₂²	1	1	yes	characteristic
74	#1594	C₂²	1	2	yes	complemented
75	#1594	C₂²	1	1	yes	characteristic, complemented
76	#1594	C₂²	1	1	yes	characteristic, complemented
77	#1594	C₂²	1	2	yes	complemented
78	#1594	C₂²	1	1	yes	characteristic, complemented
79	#1594	C₂²	1	1	yes	characteristic, complemented
80	#1593	C₂²	1	1	yes	characteristic, complemented
81	#1593	C₂²	1	1	yes	characteristic, complemented
82	#1592	C₂²	1	2	yes	complemented
83	#1590	C₂²	1	2	yes	complemented
84	#1590	C₂²	1	2	yes	complemented
85	#1590	C₂²	1	2	yes	complemented
86	#1589	C₂²	1	2	yes	complemented
87	#1589	C₂²	1	2	yes	complemented
88	#1589	C₂²	1	2	yes	complemented
89	#1588	C₂²	1	2	yes	complemented
90	#1588	C₂²	1	2	yes	complemented
91	#1588	C₂²	1	2	yes	complemented
92	#1586	C₂²	1	2	yes	complemented
93	#1586	C₂²	1	2	yes	complemented
94	#1586	C₂²	1	2	yes	complemented
95	#1586	C₂²	1	2	yes	complemented
96	#1585	C₂²	1	2	yes	complemented
97	#1583	C₂²	1	2	yes	complemented
98	#1582	C₂²	1	2	yes	complemented
99	#1581	C₂²	1	2	yes	complemented
100	#1581	C₂²	1	2	yes	complemented
101	#1580	C₂²	1	1	yes	characteristic, complemented
102	#1580	C₂²	1	1	yes	characteristic, complemented
103	#1580	C₂²	1	1	yes	characteristic, complemented
104	#1580	C₂²	1	1	yes	characteristic, complemented
105	#1579	C₂²	1	1	yes	characteristic, complemented
106	#1579	C₂²	1	1	yes	characteristic, complemented
107	SD₁₆⋊C₈	C₂²	1	2	yes	complemented
108	C₈×SD₁₆	C₂²	1	2	yes	complemented
109	C₈×D₈	C₂²	1	2	yes	complemented
110	#1574	C₂²	1	2	yes	complemented
111	#1573	C₂²	1	2	yes	complemented
112	#1573	C₂²	1	2	yes	complemented
113	#1568	C₂²	1	1	yes	characteristic, complemented
114	#1568	C₂²	1	1	yes	characteristic, complemented
115	#1566	C₂²	1	1	yes	characteristic, complemented
116	#1564	C₂²	1	1	yes	characteristic, complemented
117	C₂×#334	C₂²	1	1	yes	characteristic, complemented
118	C₂×#334	C₂²	1	1	yes	characteristic, complemented
119	#1496	C₂²	1	2	yes	complemented
120	#1495	C₂²	1	2	yes	complemented
121	#1494	C₂²	1	2	yes	complemented
122	#1490	C₂²	1	2	yes	complemented
123	#1488	C₂²	1	2	yes	complemented
124	#1486	C₂²	1	2	yes	complemented
125	#1483	C₂²	1	2	yes	complemented
126	#1482	C₂²	1	2	yes	complemented
127	#1480	C₂²	1	2	yes	complemented
128	#1478	C₂²	1	2	yes	complemented
129	#1477	C₂²	1	2	yes	complemented
130	C₂×D₄⋊C₈	C₂²	1	2	yes	complemented
131	#1454	C₂²	1	1	yes	characteristic, complemented
132	#1454	C₂²	1	1	yes	characteristic, complemented
133	#1453	C₂²	1	1	yes	characteristic, complemented
134	#1453	C₂²	1	1	yes	characteristic, complemented
135	#1451	C₂²	1	1	yes	characteristic, complemented
136	#1451	C₂²	1	1	yes	characteristic, complemented
137	#1451	C₂²	1	1	yes	characteristic, complemented
138	#1450	C₂²	1	1	yes	characteristic, complemented
139	#1450	C₂²	1	1	yes	characteristic, complemented
140	#1450	C₂²	1	1	yes	characteristic, complemented
141	C₈×M₁₆	C₂²	1	1	yes	characteristic, complemented
142	C₂×#322	C₂²	1	1	yes	characteristic, complemented
143	C₂×#135	C₂×C₄	1	1	yes	characteristic
144	C₂²×D₈	C₂×C₄	1	1	yes	characteristic
145	C₂²×D₈	C₂×C₄	1	1	yes	characteristic
146	C₂×#131	—	2	2	no	—
147	C₂²×M₁₆	—	2	2	no	—
148	C₂²×M₁₆	—	2	2	no	—
149	#559	C₂×C₄	1	2	yes	—
150	#554	C₂×C₄	1	2	yes	—
151	#554	C₂×C₄	1	2	yes	—
152	#553	—	2	2	no	—
153	#553	C₂×C₄	1	2	yes	—
154	#553	C₂×C₄	1	2	yes	—
155	#551	—	2	2	no	—
156	#551	—	2	2	no	—
157	#546	—	2	2	no	—
158	#546	C₂×C₄	1	2	yes	—
159	#546	C₂×C₄	1	2	yes	—
160	D₄²	C₂×C₄	1	2	yes	—
161	#532	C₂³	1	2	yes	—
162	#529	—	2	2	no	—
163	#529	C₂³	1	2	yes	—
164	#529	C₂³	1	2	yes	—
165	#525	—	2	2	no	—
166	#525	—	2	2	no	—
167	C₄×#41	C₂³	1	2	yes	—
168	C₄×#41	C₂³	1	1	yes	characteristic
169	C₂×C₄×D₄	—	2	2	no	—
170	C₂×C₄×D₄	C₂³	1	2	yes	—
171	C₂×C₄×D₄	C₂³	1	2	yes	—
172	#500	C₂×C₄	1	1	yes	characteristic
173	#499	C₂×C₄	1	1	yes	characteristic
174	#499	C₂×C₄	1	1	yes	characteristic
175	#495	C₂×C₄	1	1	yes	characteristic
176	#495	C₂×C₄	1	1	yes	characteristic
177	#493	C₂×C₄	1	1	yes	characteristic
178	#488	C₂×C₄	1	2	yes	—
179	#488	C₂×C₄	1	2	yes	—
180	#486	C₂×C₄	1	2	yes	—
181	#484	C₂×C₄	1	2	yes	—
182	#484	C₂×C₄	1	2	yes	—
183	#482	C₂×C₄	1	2	yes	—
184	#482	C₂×C₄	1	2	yes	—
185	#481	C₂×C₄	1	2	yes	—
186	#481	C₂×C₄	1	2	yes	—
187	#478	C₂×C₄	1	2	yes	—
188	#478	C₂×C₄	1	2	yes	—
189	#478	C₂×C₄	1	2	yes	—
190	#478	C₂×C₄	1	2	yes	—
191	#477	C₂×C₄	1	2	yes	—
192	#476	C₂×C₄	1	2	yes	—
193	#467	C₂×C₄	1	1	yes	characteristic
194	#467	C₂×C₄	1	1	yes	characteristic
195	#466	C₂×C₄	1	1	yes	characteristic
196	#466	C₂×C₄	1	1	yes	characteristic
197	#466	C₂×C₄	1	1	yes	characteristic
198	#466	C₂×C₄	1	1	yes	characteristic
199	#466	C₂×C₄	1	2	yes	—
200	#465	C₂×C₄	1	2	yes	—
201	#465	C₂×C₄	1	2	yes	—
202	#463	C₂×C₄	1	2	yes	—
203	#463	C₂×C₄	1	2	yes	—
204	#463	C₂×C₄	1	2	yes	—
205	#463	C₂×C₄	1	2	yes	—
206	#460	C₂×C₄	1	2	yes	—
207	#459	C₂×C₄	1	2	yes	—
208	#450	C₂×C₄	1	2	yes	—
209	#450	C₂×C₄	1	2	yes	—
210	#449	C₂×C₄	1	2	yes	—
211	#449	C₂×C₄	1	2	yes	—
212	#447	C₂×C₄	1	2	yes	—
213	#447	C₂×C₄	1	2	yes	—
214	#446	—	2	2	no	—
215	#446	D₄	1	2	yes	—
216	#446	C₂³	1	2	yes	—
217	#446	C₂³	1	2	yes	—
218	C₈×Q₈	C₂×C₄	1	1	yes	characteristic
219	C₈×Q₈	C₂×C₄	1	1	yes	characteristic
220	C₈×Q₈	C₂³	1	2	yes	—
221	C₈×Q₈	C₂³	1	2	yes	—
222	C₄×Q₁₆	C₂×C₄	1	1	yes	characteristic
223	C₄×Q₁₆	C₂³	1	1	yes	characteristic
224	C₄×SD₁₆	C₂×C₄	1	2	yes	—
225	C₄×SD₁₆	C₂³	1	2	yes	—
226	C₄×SD₁₆	C₂³	1	2	yes	—
227	C₄×SD₁₆	C₂³	1	2	yes	—
228	C₄×D₈	C₂×C₄	1	1	yes	characteristic
229	C₄×D₈	C₂×C₄	1	1	yes	characteristic
230	C₄×D₈	C₂×C₄	1	2	yes	—
231	C₄×D₈	C₂×C₄	1	2	yes	—
232	C₄×D₈	C₂×C₄	1	1	yes	characteristic
233	C₄×D₈	C₂×C₄	1	1	yes	characteristic
234	C₄×D₈	C₂×C₄	1	1	yes	characteristic
235	C₄×D₈	C₂³	1	2	yes	—
236	C₄×D₈	C₂³	1	2	yes	—
237	C₄×D₈	C₂³	1	2	yes	—
238	C₄×D₈	C₂³	1	1	yes	characteristic
239	C₄×D₈	C₂³	1	1	yes	characteristic
240	C₄×D₈	C₂³	1	1	yes	characteristic
241	#436	—	2	2	no	—
242	#436	—	2	2	no	—
243	#436	—	2	2	no	—
244	#436	—	2	2	no	—
245	#436	—	2	2	no	—
246	#436	—	2	2	no	—
247	#436	—	2	2	no	—
248	#436	—	2	2	no	—
249	#436	D₄	1	2	yes	—
250	#436	C₂³	1	2	yes	—
251	#436	C₂³	1	2	yes	—
252	#436	C₂³	1	2	yes	—
253	#436	C₂³	1	2	yes	—
254	#436	C₂³	1	2	yes	—
255	#436	C₂³	1	2	yes	—
256	#436	C₂³	1	2	yes	—
257	#436	C₂³	1	2	yes	—
258	#435	—	2	2	no	—
259	#435	—	2	2	no	—
260	#435	—	2	2	no	—
261	#435	—	2	2	no	—
262	#435	—	2	2	no	—
263	#435	—	2	2	no	—
264	#435	—	2	2	no	—
265	#435	—	2	2	no	—
266	#435	—	2	2	no	—
267	#435	—	2	2	no	—
268	#435	—	2	2	no	—
269	#435	—	2	2	no	—
270	#435	—	2	2	no	—
271	#435	—	2	2	no	—
272	#435	—	2	2	no	—
273	#435	—	2	2	no	—
274	#435	D₄	1	2	yes	—
275	#435	D₄	1	2	yes	—
276	C₈×D₄	—	2	2	no	—
277	C₈×D₄	—	2	2	no	—
278	C₈×D₄	—	2	2	no	—
279	C₈×D₄	C₂×C₄	1	1	yes	characteristic
280	C₈×D₄	C₂×C₄	1	1	yes	characteristic
281	C₈×D₄	C₂×C₄	1	1	yes	characteristic
282	C₈×D₄	C₂×C₄	1	1	yes	characteristic
283	C₈×D₄	C₂×C₄	1	1	yes	characteristic
284	C₈×D₄	C₂×C₄	1	1	yes	characteristic
285	C₈×D₄	C₂³	1	2	yes	—
286	C₈×D₄	C₂³	1	2	yes	—
287	C₈×D₄	C₂³	1	2	yes	—
288	C₈×D₄	C₂³	1	2	yes	—
289	#433	—	2	1	no	—
290	#433	—	2	1	no	—
291	#433	—	2	2	no	—
292	#433	—	2	2	no	—
293	#433	—	2	2	no	—
294	#433	—	2	2	no	—
295	#432	—	2	2	no	—
296	#432	—	2	2	no	—
297	#432	C₂³	1	2	yes	—
298	#432	C₂³	1	2	yes	—
299	#431	C₂³	1	2	yes	—
300	#431	C₂³	1	1	yes	characteristic
301	#431	C₂³	1	1	yes	characteristic
302	#431	C₂³	1	1	yes	characteristic
303	#431	C₂³	1	1	yes	characteristic
304	#431	C₂³	1	1	yes	characteristic
305	#431	C₂³	1	1	yes	characteristic
306	#431	C₂³	1	1	yes	characteristic
307	#431	C₂³	1	1	yes	characteristic
308	#431	C₂³	1	1	yes	characteristic
309	#431	C₂³	1	1	yes	characteristic
310	#427	C₂×C₄	1	1	yes	characteristic
311	C₂×#107	C₂×C₄	1	1	yes	characteristic
312	C₂×#107	C₂×C₄	1	1	yes	characteristic
313	#424	—	2	1	no	—
314	#424	—	2	2	no	—
315	#424	—	2	2	no	—
316	#423	—	2	2	no	—
317	#423	C₂³	1	2	yes	—
318	C₂×C₄⋊C₈	C₂³	1	2	yes	—
319	C₂×C₄⋊C₈	C₂³	1	2	yes	—
320	#416	C₂×C₄	1	2	yes	—
321	C₂×#102	C₂×C₄	1	2	yes	—
322	C₂×#102	C₂×C₄	1	2	yes	—
323	#408	—	2	1	no	—
324	#408	—	2	2	no	—
325	#408	—	2	2	no	—
326	#408	—	2	2	no	—
327	#407	—	2	2	no	—
328	#407	—	2	2	no	—
329	#407	—	2	2	no	—
330	#407	—	2	2	no	—
331	C₂×C₂²⋊C₈	—	2	2	no	—
332	C₂×C₂²⋊C₈	—	2	2	no	—
333	#405	—	2	2	no	—
334	#405	—	2	2	no	—
335	C₄×M₁₆	—	2	2	no	—
336	C₄×M₁₆	C₂³	1	1	yes	characteristic
337	C₄×M₁₆	C₂³	1	1	yes	characteristic
338	C₄×M₁₆	C₂³	1	1	yes	characteristic
339	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
340	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
341	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
342	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
343	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
344	#335	C₂³	1	2	yes	—
345	#335	C₂³	1	2	yes	—
346	#335	C₂³	1	2	yes	—
347	#334	C₂³	1	1	yes	characteristic
348	#334	C₂³	1	1	yes	characteristic
349	#334	C₂³	1	1	yes	characteristic
350	#334	C₂³	1	2	yes	—
351	#334	C₂³	1	2	yes	—
352	#334	C₂³	1	1	yes	characteristic
353	#334	C₂³	1	2	yes	—
354	Q₈⋊C₈	C₂³	1	2	yes	—
355	Q₈⋊C₈	C₂³	1	2	yes	—
356	Q₈⋊C₈	C₂³	1	2	yes	—
357	Q₈⋊C₈	C₂³	1	2	yes	—
358	D₄⋊C₈	C₂³	1	2	yes	—
359	D₄⋊C₈	C₂³	1	2	yes	—
360	D₄⋊C₈	C₂³	1	2	yes	—
361	D₄⋊C₈	C₂³	1	2	yes	—
362	D₄⋊C₈	C₂³	1	2	yes	—
363	D₄⋊C₈	C₂³	1	2	yes	—
364	D₄⋊C₈	C₂³	1	2	yes	—
365	D₄⋊C₈	C₂³	1	2	yes	—
366	D₄⋊C₈	C₂³	1	2	yes	—
367	D₄⋊C₈	C₂³	1	2	yes	—
368	D₄⋊C₈	C₂³	1	2	yes	—
369	D₄⋊C₈	C₂³	1	2	yes	—
370	#322	C₂³	1	1	yes	characteristic
371	#322	C₂³	1	1	yes	characteristic
372	#322	C₂³	1	1	yes	characteristic
373	#322	C₂³	1	1	yes	characteristic
374	#322	C₂³	1	1	yes	characteristic
375	#322	C₂³	1	1	yes	characteristic
376	#322	C₂³	1	1	yes	characteristic
377	#322	C₂³	1	1	yes	characteristic
378	#322	C₂³	1	1	yes	characteristic
379	#322	C₂³	1	1	yes	characteristic
380	#322	C₂³	1	1	yes	characteristic
381	#322	C₂³	1	1	yes	characteristic
382	C₈²	C₂³	1	1	yes	characteristic
383	C₈²	C₂³	1	1	yes	characteristic
384	C₈²	C₂³	1	1	yes	characteristic
385	C₈²	C₂³	1	1	yes	characteristic
386	C₂×#41	—	2	2	no	—
387	C₂×#41	C₂²×C₄	1	2	yes	—
388	C₂×#41	#41	1	1	yes	characteristic
389	C₂²×D₄	—	2	2	no	—
390	C₂²×D₄	C₂²×C₄	1	2	yes	—
391	C₂²×D₄	C₂²×C₄	1	2	yes	—
392	C₂³×C₄	—	2	2	no	—
393	C₂³×C₄	—	2	2	no	—
394	#135	—	4	2	no	—
395	C₂×Q₁₆	C₂²×C₄	1	1	yes	characteristic
396	C₂×SD₁₆	C₂²×C₄	1	2	yes	—
397	C₂×SD₁₆	C₂²×C₄	1	2	yes	—
398	C₂×SD₁₆	C₂²×C₄	1	2	yes	—
399	C₂×D₈	—	4	2	no	—
400	C₂×D₈	—	4	2	no	—
401	C₂×D₈	C₂²×C₄	1	1	yes	characteristic
402	C₂×D₈	C₂²×C₄	1	1	yes	characteristic
403	C₂×D₈	C₂²×C₄	1	1	yes	characteristic
404	C₂×D₈	C₂²×C₄	1	2	yes	—
405	C₂×D₈	C₂²×C₄	1	2	yes	—
406	C₂×D₈	C₂²×C₄	1	2	yes	—
407	#131	—	8	4	no	—
408	C₂×M₁₆	—	2	1	no	—
409	C₂×M₁₆	—	2	2	no	—
410	C₂×M₁₆	—	2	2	no	—
411	C₂×M₁₆	—	2	2	no	—
412	C₂×M₁₆	—	2	2	no	—
413	C₂×M₁₆	—	2	2	no	—
414	C₂×M₁₆	—	2	2	no	—
415	C₂×M₁₆	—	2	2	no	—
416	C₂×M₁₆	—	2	2	no	—
417	C₂×M₁₆	—	2	2	no	—
418	C₂×M₁₆	—	8	4	no	—
419	C₂×M₁₆	—	8	4	no	—
420	C₂×M₁₆	C₂×D₄	1	2	yes	—
421	C₂×M₁₆	C₂×D₄	1	2	yes	—
422	C₂²×C₈	—	2	1	no	—
423	C₂²×C₈	—	2	2	no	—
424	C₂²×C₈	—	2	2	no	—
425	C₂²×C₈	—	2	2	no	—
426	C₂²×C₈	—	2	2	no	—
427	C₂²×C₈	—	2	2	no	—
428	C₂²×C₈	—	2	2	no	—
429	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
430	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
431	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
432	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
433	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
434	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
435	C₂²×C₈	C₂×D₄	1	2	yes	—
436	C₄⋊Q₈	C₂²×C₄	1	2	yes	—
437	#127	C₂²×C₄	1	2	yes	—
438	#126	—	2	2	no	—
439	#126	—	2	2	no	—
440	#126	—	2	2	no	—
441	#126	—	2	2	no	—
442	#125	—	2	2	no	—
443	#125	C₂²×C₄	1	2	yes	—
444	#125	C₂²×C₄	1	2	yes	—
445	#124	—	2	2	no	—
446	#124	—	2	2	no	—
447	#124	C₂²×C₄	1	2	yes	—
448	#124	C₂²×C₄	1	2	yes	—
449	#123	—	2	2	no	—
450	#123	—	2	2	no	—
451	#123	—	2	2	no	—
452	#123	—	2	2	no	—
453	#123	—	2	2	no	—
454	#123	—	2	2	no	—
455	#123	—	2	2	no	—
456	#123	—	2	2	no	—
457	C₂²⋊Q₈	—	2	2	no	—
458	C₂²⋊Q₈	—	2	2	no	—
459	C₂²⋊Q₈	—	2	2	no	—
460	C₂²⋊Q₈	—	2	2	no	—
461	C₂²⋊Q₈	—	2	2	no	—
462	C₂²⋊Q₈	C₂²×C₄	1	2	yes	—
463	C₂²⋊Q₈	C₂²×C₄	1	2	yes	—
464	#121	—	2	2	no	—
465	#121	—	2	2	no	—
466	#121	—	2	2	no	—
467	#121	—	2	2	no	—
468	#121	—	2	2	no	—
469	#121	—	2	2	no	—
470	#121	C₂²×C₄	1	2	yes	—
471	#121	C₂²×C₄	1	2	yes	—
472	#121	C₂²×C₄	1	2	yes	—
473	#121	C₂²×C₄	1	2	yes	—
474	#120	—	2	2	no	—
475	#120	—	2	2	no	—
476	#120	—	2	2	no	—
477	#120	—	2	2	no	—
478	C₄×Q₈	C₂²×C₄	1	2	yes	—
479	C₄×Q₈	C₂²×C₄	1	1	yes	characteristic
480	C₄×Q₈	C₂×D₄	1	1	yes	characteristic
481	C₄×Q₈	C₂⁴	1	2	yes	—
482	C₄×D₄	—	2	2	no	—
483	C₄×D₄	—	2	2	no	—
484	C₄×D₄	—	2	2	no	—
485	C₄×D₄	—	2	2	no	—
486	C₄×D₄	—	2	2	no	—
487	C₄×D₄	—	2	2	no	—
488	C₄×D₄	—	2	2	no	—
489	C₄×D₄	—	2	2	no	—
490	C₄×D₄	—	2	2	no	—
491	C₄×D₄	—	2	2	no	—
492	C₄×D₄	—	2	2	no	—
493	C₄×D₄	—	2	2	no	—
494	C₄×D₄	—	2	2	no	—
495	C₄×D₄	C₂²×C₄	1	2	yes	—
496	C₄×D₄	C₂²×C₄	1	2	yes	—
497	C₄×D₄	C₂²×C₄	1	2	yes	—
498	C₄×D₄	C₂²×C₄	1	2	yes	—
499	C₄×D₄	C₂²×C₄	1	2	yes	—
500	C₄×D₄	C₂²×C₄	1	1	yes	characteristic
501	C₄×D₄	C₂²×C₄	1	1	yes	characteristic
502	C₄×D₄	C₂²×C₄	1	1	yes	characteristic
503	C₄×D₄	C₂×D₄	1	1	yes	characteristic
504	C₄×D₄	C₂×D₄	1	1	yes	characteristic
505	C₄×D₄	C₂×D₄	1	1	yes	characteristic
506	C₄×D₄	C₂⁴	1	2	yes	—
507	C₄×D₄	C₂⁴	1	2	yes	—
508	C₄×D₄	C₂⁴	1	2	yes	—
509	#117	—	2	2	no	—
510	#117	—	2	2	no	—
511	#117	—	2	2	no	—
512	#117	C₂²×C₄	1	2	yes	—
513	#117	#41	1	1	yes	characteristic
514	#117	#41	1	1	yes	characteristic
515	#117	#41	1	1	yes	characteristic
516	C₂×C₄⋊C₄	—	2	2	no	—
517	C₂×C₄⋊C₄	C₂²×C₄	1	2	yes	—
518	C₂×C₄⋊C₄	C₂²×C₄	1	2	yes	—
519	C₂×C₂²⋊C₄	—	2	2	no	—
520	C₂×C₂²⋊C₄	—	2	2	no	—
521	C₂×C₂²⋊C₄	—	2	2	no	—
522	C₂×C₂²⋊C₄	—	2	2	no	—
523	C₂×C₄²	—	2	2	no	—
524	C₂×C₄²	C₂⁴	1	1	yes	characteristic
525	C₂×C₄²	C₂⁴	1	1	yes	characteristic
526	C₂×C₄²	C₂⁴	1	1	yes	characteristic
527	#107	C₂²×C₄	1	1	yes	characteristic
528	#107	C₂²×C₄	1	1	yes	characteristic
529	#107	C₂²×C₄	1	1	yes	characteristic
530	#107	C₂²×C₄	1	2	yes	—
531	#107	C₂²×C₄	1	2	yes	—
532	#107	C₂²×C₄	1	1	yes	characteristic
533	#107	C₂²×C₄	1	2	yes	—
534	#106	C₂²×C₄	1	2	yes	—
535	#106	C₂²×C₄	1	2	yes	—
536	#106	C₂²×C₄	1	2	yes	—
537	C₄⋊C₈	—	2	2	no	—
538	C₄⋊C₈	—	2	2	no	—
539	C₄⋊C₈	—	2	2	no	—
540	C₄⋊C₈	—	2	2	no	—
541	C₄⋊C₈	—	2	2	no	—
542	C₄⋊C₈	—	2	2	no	—
543	C₄⋊C₈	—	2	2	no	—
544	C₄⋊C₈	—	2	1	no	—
545	C₄⋊C₈	—	2	1	no	—
546	C₄⋊C₈	—	2	1	no	—
547	C₄⋊C₈	—	2	1	no	—
548	C₄⋊C₈	C₂²×C₄	1	1	yes	characteristic
549	C₄⋊C₈	C₂²×C₄	1	1	yes	characteristic
550	C₄⋊C₈	C₂²×C₄	1	1	yes	characteristic
551	C₄⋊C₈	C₂²×C₄	1	1	yes	characteristic
552	C₄⋊C₈	C₂²×C₄	1	1	yes	characteristic
553	C₄⋊C₈	C₂²×C₄	1	1	yes	characteristic
554	C₄⋊C₈	C₂×D₄	1	2	yes	—
555	C₄⋊C₈	C₂×D₄	1	2	yes	—
556	C₄⋊C₈	C₂×D₄	1	2	yes	—
557	C₄⋊C₈	C₂⁴	1	2	yes	—
558	C₄⋊C₈	C₂⁴	1	2	yes	—
559	C₄⋊C₈	C₂⁴	1	2	yes	—
560	C₄⋊C₈	C₂⁴	1	2	yes	—
561	#103	C₂²×C₄	1	2	yes	—
562	#103	C₂²×C₄	1	2	yes	—
563	#103	C₂²×C₄	1	2	yes	—
564	#103	C₂²×C₄	1	2	yes	—
565	#102	C₂²×C₄	1	2	yes	—
566	#102	C₂²×C₄	1	2	yes	—
567	#102	C₂²×C₄	1	2	yes	—
568	#102	C₂²×C₄	1	2	yes	—
569	#102	C₂²×C₄	1	2	yes	—
570	#102	C₂²×C₄	1	2	yes	—
571	#102	C₂²×C₄	1	2	yes	—
572	#102	C₂²×C₄	1	2	yes	—
573	#102	C₂²×C₄	1	2	yes	—
574	#102	C₂²×C₄	1	2	yes	—
575	#102	C₂²×C₄	1	2	yes	—
576	#102	C₂²×C₄	1	2	yes	—
577	C₂²⋊C₈	—	2	2	no	—
578	C₂²⋊C₈	—	2	2	no	—
579	C₂²⋊C₈	—	2	2	no	—
580	C₂²⋊C₈	—	2	1	no	—
581	C₂²⋊C₈	—	2	1	no	—
582	C₂²⋊C₈	—	2	1	no	—
583	C₂²⋊C₈	—	2	1	no	—
584	C₂²⋊C₈	—	2	2	no	—
585	C₂²⋊C₈	—	2	2	no	—
586	C₂²⋊C₈	—	2	2	no	—
587	C₂²⋊C₈	—	2	2	no	—
588	C₂²⋊C₈	—	2	2	no	—
589	C₂²⋊C₈	—	2	2	no	—
590	C₂²⋊C₈	—	2	2	no	—
591	C₂²⋊C₈	—	2	2	no	—
592	C₂²⋊C₈	—	2	2	no	—
593	C₂²⋊C₈	—	2	2	no	—
594	C₂²⋊C₈	—	2	2	no	—
595	C₂²⋊C₈	—	2	2	no	—
596	C₂²⋊C₈	C₂²×C₄	1	1	yes	characteristic
597	C₂²⋊C₈	C₂²×C₄	1	1	yes	characteristic
598	C₂²⋊C₈	C₂²×C₄	1	1	yes	characteristic
599	C₂²⋊C₈	C₂²×C₄	1	1	yes	characteristic
600	C₂²⋊C₈	C₂²×C₄	1	1	yes	characteristic
601	C₂²⋊C₈	C₂²×C₄	1	1	yes	characteristic
602	C₂²⋊C₈	C₂×D₄	1	2	yes	—
603	C₂²⋊C₈	C₂×D₄	1	2	yes	—
604	C₂²⋊C₈	C₂×D₄	1	2	yes	—
605	#97	—	2	2	no	—
606	#97	—	2	2	no	—
607	#97	—	2	2	no	—
608	#97	—	2	2	no	—
609	#97	—	2	1	no	—
610	#97	C₂×D₄	1	2	yes	—
611	#97	C₂×D₄	1	2	yes	—
612	C₄×C₈	—	2	2	no	—
613	C₄×C₈	—	2	2	no	—
614	C₄×C₈	—	2	2	no	—
615	C₄×C₈	—	2	1	no	—
616	C₄×C₈	C₂²×C₄	1	1	yes	characteristic
617	C₄×C₈	C₂²×C₄	1	1	yes	characteristic
618	C₄×C₈	C₂²×C₄	1	1	yes	characteristic
619	C₄×C₈	C₂²×C₄	1	1	yes	characteristic
620	C₄×C₈	C₂²×C₄	1	1	yes	characteristic
621	C₄×C₈	C₂²×C₄	1	1	yes	characteristic
622	C₄×C₈	C₂×D₄	1	2	yes	—
623	C₄×C₈	C₂⁴	1	1	yes	characteristic
624	C₄×C₈	C₂⁴	1	1	yes	characteristic
625	C₄×C₈	C₂⁴	1	1	yes	characteristic
626	C₄×C₈	C₂⁴	1	1	yes	characteristic
627	C₄×C₈	C₂⁴	1	1	yes	characteristic
628	C₄×C₈	C₂⁴	1	1	yes	characteristic
629	C₄×C₈	C₂⁴	1	1	yes	characteristic
630	C₄×C₈	C₂⁴	1	1	yes	characteristic
631	C₄×C₈	C₂⁴	1	1	yes	characteristic
632	C₄×C₈	C₂⁴	1	1	yes	characteristic
633	C₄×C₈	C₂⁴	1	1	yes	characteristic
634	C₄×C₈	C₂⁴	1	1	yes	characteristic
635	C₂⁴	—	2	2	no	—
636	C₂⁴	—	2	2	no	—
637	#41	—	4	2	no	—
638	#41	—	4	2	no	—
639	#41	—	4	2	no	—
640	#41	—	8	2	no	—
641	#41	—	8	2	no	—
642	C₂×Q₈	—	2	2	no	—
643	C₂×Q₈	C₄×D₄	1	1	yes	characteristic
644	C₂×Q₈	C₂³×C₄	1	2	yes	—
645	C₂×D₄	—	2	2	no	—
646	C₂×D₄	—	2	2	no	—
647	C₂×D₄	—	2	2	no	—
648	C₂×D₄	—	2	2	no	—
649	C₂×D₄	—	2	2	no	—
650	C₂×D₄	—	2	2	no	—
651	C₂×D₄	—	2	2	no	—
652	C₂×D₄	—	2	2	no	—
653	C₂×D₄	—	2	2	no	—
654	C₂×D₄	—	4	2	no	—
655	C₂×D₄	—	4	2	no	—
656	C₂×D₄	—	4	2	no	—
657	C₂×D₄	—	4	2	no	—
658	C₂×D₄	—	8	4	no	—
659	C₂×D₄	C₄×D₄	1	1	yes	characteristic
660	C₂×D₄	C₄×D₄	1	1	yes	characteristic
661	C₂×D₄	C₄×D₄	1	1	yes	characteristic
662	C₂×D₄	C₂³×C₄	1	2	yes	—
663	C₂×D₄	C₂³×C₄	1	2	yes	—
664	C₂×D₄	C₂³×C₄	1	2	yes	—
665	C₂²×C₄	—	2	2	no	—
666	C₂²×C₄	—	2	2	no	—
667	C₂²×C₄	—	2	2	no	—
668	C₂²×C₄	—	2	2	no	—
669	C₂²×C₄	—	2	2	no	—
670	C₂²×C₄	—	2	2	no	—
671	C₂²×C₄	—	2	2	no	—
672	C₂²×C₄	—	2	2	no	—
673	C₂²×C₄	—	2	2	no	—
674	C₂²×C₄	—	2	2	no	—
675	C₂²×C₄	—	2	2	no	—
676	C₂²×C₄	—	8	2	no	—
677	C₂²×C₄	—	8	2	no	—
678	C₂²×C₄	—	8	2	no	—
679	C₂²×C₄	—	8	2	no	—
680	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
681	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
682	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
683	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
684	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
685	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
686	C₂²×C₄	C₂×#41	1	1	yes	characteristic
687	C₂²×C₄	C₂×#41	1	1	yes	characteristic
688	C₂²×C₄	C₂×#41	1	1	yes	characteristic
689	Q₁₆	—	2	2	no	—
690	SD₁₆	—	4	2	no	—
691	SD₁₆	—	4	2	no	—
692	SD₁₆	—	4	2	no	—
693	D₈	—	2	2	no	—
694	D₈	—	2	2	no	—
695	D₈	—	2	2	no	—
696	D₈	—	4	2	no	—
697	D₈	—	4	2	no	—
698	D₈	—	4	2	no	—
699	M₁₆	—	4	2	no	—
700	M₁₆	—	4	2	no	—
701	M₁₆	—	4	4	no	—
702	M₁₆	—	4	4	no	—
703	M₁₆	—	4	2	no	—
704	M₁₆	—	8	2	no	—
705	M₁₆	—	8	2	no	—
706	M₁₆	—	8	2	no	—
707	M₁₆	—	8	2	no	—
708	M₁₆	—	8	2	no	—
709	M₁₆	—	8	2	no	—
710	M₁₆	—	8	2	no	—
711	C₂×C₈	—	2	2	no	—
712	C₂×C₈	—	2	2	no	—
713	C₂×C₈	—	2	2	no	—
714	C₂×C₈	—	2	2	no	—
715	C₂×C₈	—	2	2	no	—
716	C₂×C₈	—	2	2	no	—
717	C₂×C₈	—	2	2	no	—
718	C₂×C₈	—	2	1	no	—
719	C₂×C₈	—	2	1	no	—
720	C₂×C₈	—	2	1	no	—
721	C₂×C₈	—	2	1	no	—
722	C₂×C₈	—	4	1	no	—
723	C₂×C₈	—	4	1	no	—
724	C₂×C₈	—	4	1	no	—
725	C₂×C₈	—	4	2	no	—
726	C₂×C₈	—	4	4	no	—
727	C₂×C₈	—	4	2	no	—
728	C₂×C₈	—	8	2	no	—
729	C₂×C₈	—	8	2	no	—
730	C₂×C₈	—	8	2	no	—
731	C₂×C₈	—	8	2	no	—
732	C₂×C₈	—	8	2	no	—
733	C₂×C₈	C₂³×C₄	1	1	yes	characteristic
734	C₂×C₈	C₂³×C₄	1	1	yes	characteristic
735	C₂×C₈	C₂³×C₄	1	1	yes	characteristic
736	C₂×C₈	C₂³×C₄	1	1	yes	characteristic
737	C₂×C₈	C₂³×C₄	1	1	yes	characteristic
738	C₂×C₈	C₂³×C₄	1	1	yes	characteristic
739	C₂×C₈	C₂³×C₄	1	1	yes	characteristic
740	C₂×C₈	C₂³×C₄	1	1	yes	characteristic
741	C₂×C₈	C₂²×D₄	1	2	yes	—
742	C₂×C₈	C₂²×D₄	1	2	yes	—
743	C₂×C₈	C₂²×D₄	1	2	yes	—
744	C₂×C₈	C₂²×D₄	1	2	yes	—
745	C₄⋊C₄	—	2	2	no	—
746	C₄⋊C₄	—	2	2	no	—
747	C₄⋊C₄	—	2	2	no	—
748	C₄⋊C₄	—	2	2	no	—
749	C₄⋊C₄	—	2	2	no	—
750	C₄⋊C₄	—	2	2	no	—
751	C₄⋊C₄	—	2	2	no	—
752	C₄⋊C₄	—	2	2	no	—
753	C₄⋊C₄	—	2	2	no	—
754	C₄⋊C₄	—	2	2	no	—
755	C₄⋊C₄	—	2	2	no	—
756	C₄⋊C₄	C₄×D₄	1	1	yes	characteristic
757	C₄⋊C₄	C₄×D₄	1	1	yes	characteristic
758	C₄⋊C₄	C₄×D₄	1	1	yes	characteristic
759	C₄⋊C₄	C₄×D₄	1	1	yes	characteristic
760	C₄⋊C₄	C₄×D₄	1	1	yes	characteristic
761	C₄⋊C₄	C₄×D₄	1	1	yes	characteristic
762	C₄⋊C₄	C₂³×C₄	1	2	yes	—
763	C₄⋊C₄	C₂³×C₄	1	2	yes	—
764	C₄⋊C₄	C₂³×C₄	1	2	yes	—
765	C₄⋊C₄	C₂³×C₄	1	2	yes	—
766	C₂²⋊C₄	—	2	2	no	—
767	C₂²⋊C₄	—	2	2	no	—
768	C₂²⋊C₄	—	2	2	no	—
769	C₂²⋊C₄	—	2	2	no	—
770	C₂²⋊C₄	—	2	2	no	—
771	C₂²⋊C₄	—	2	2	no	—
772	C₂²⋊C₄	—	2	2	no	—
773	C₂²⋊C₄	—	2	2	no	—
774	C₂²⋊C₄	—	2	2	no	—
775	C₂²⋊C₄	—	2	2	no	—
776	C₂²⋊C₄	—	2	2	no	—
777	C₂²⋊C₄	—	2	2	no	—
778	C₂²⋊C₄	—	2	2	no	—
779	C₂²⋊C₄	—	2	2	no	—
780	C₂²⋊C₄	—	2	2	no	—
781	C₂²⋊C₄	—	2	2	no	—
782	C₂²⋊C₄	—	2	2	no	—
783	C₂²⋊C₄	—	2	2	no	—
784	C₂²⋊C₄	—	2	2	no	—
785	C₂²⋊C₄	C₄×D₄	1	1	yes	characteristic
786	C₂²⋊C₄	C₄×D₄	1	1	yes	characteristic
787	C₂²⋊C₄	C₄×D₄	1	1	yes	characteristic
788	C₂²⋊C₄	C₄×D₄	1	1	yes	characteristic
789	C₂²⋊C₄	C₄×D₄	1	1	yes	characteristic
790	C₂²⋊C₄	C₄×D₄	1	1	yes	characteristic
791	C₄²	—	2	2	no	—
792	C₄²	—	2	2	no	—
793	C₄²	—	2	2	no	—
794	C₄²	C₂³×C₄	1	1	yes	characteristic
795	C₄²	C₂³×C₄	1	1	yes	characteristic
796	C₄²	C₂³×C₄	1	1	yes	characteristic
797	C₄²	C₂²×D₄	1	1	yes	characteristic
798	C₄²	C₂²×D₄	1	1	yes	characteristic
799	C₄²	C₂²×D₄	1	1	yes	characteristic
800	C₄²	C₂×#41	1	1	yes	characteristic
801	C₄²	C₂×#41	1	1	yes	characteristic
802	C₄²	C₂×#41	1	1	yes	characteristic
803	C₄²	C₂⁵	1	1	yes	characteristic
804	C₂³	—	2	2	no	—
805	C₂³	—	2	2	no	—
806	C₂³	—	2	2	no	—
807	C₂³	—	4	4	no	—
808	C₂³	—	8	2	no	—
809	C₂³	—	8	2	no	—
810	C₂³	—	8	2	no	—
811	C₂³	—	8	2	no	—
812	C₂³	—	8	2	no	—
813	C₂³	C₂×C₄×D₄	1	1	yes	characteristic
814	C₂³	C₂×C₄×D₄	1	1	yes	characteristic
815	C₂³	C₂×C₄×D₄	1	1	yes	characteristic
816	Q₈	—	2	2	no	—
817	Q₈	—	2	2	no	—
818	Q₈	—	4	1	no	—
819	Q₈	—	8	2	no	—
820	D₄	—	2	2	no	—
821	D₄	—	2	2	no	—
822	D₄	—	2	2	no	—
823	D₄	—	2	2	no	—
824	D₄	—	2	2	no	—
825	D₄	—	2	2	no	—
826	D₄	—	2	2	no	—
827	D₄	—	2	2	no	—
828	D₄	—	4	1	no	—
829	D₄	—	4	4	no	—
830	D₄	—	8	2	no	—
831	D₄	—	8	2	no	—
832	D₄	—	8	2	no	—
833	D₄	—	8	2	no	—
834	D₄	—	8	2	no	—
835	D₄	—	8	2	no	—
836	D₄	—	8	2	no	—
837	D₄	—	8	2	no	—
838	C₂×C₄	—	2	2	no	—
839	C₂×C₄	—	2	2	no	—
840	C₂×C₄	—	2	2	no	—
841	C₂×C₄	—	2	2	no	—
842	C₂×C₄	—	2	1	no	—
843	C₂×C₄	—	2	1	no	—
844	C₂×C₄	—	2	1	no	—
845	C₂×C₄	—	2	1	no	—
846	C₂×C₄	—	2	1	no	—
847	C₂×C₄	—	2	1	no	—
848	C₂×C₄	—	2	2	no	—
849	C₂×C₄	—	2	2	no	—
850	C₂×C₄	—	2	2	no	—
851	C₂×C₄	—	2	2	no	—
852	C₂×C₄	—	2	2	no	—
853	C₂×C₄	—	4	1	no	—
854	C₂×C₄	—	4	1	no	—
855	C₂×C₄	—	4	2	no	—
856	C₂×C₄	—	4	2	no	—
857	C₂×C₄	—	4	2	no	—
858	C₂×C₄	—	4	2	no	—
859	C₂×C₄	—	4	2	no	—
860	C₂×C₄	—	4	2	no	—
861	C₂×C₄	—	8	2	no	—
862	C₂×C₄	—	8	2	no	—
863	C₂×C₄	—	8	2	no	—
864	C₂×C₄	—	8	2	no	—
865	C₂×C₄	—	8	2	no	—
866	C₂×C₄	—	8	2	no	—
867	C₂×C₄	—	8	2	no	—
868	C₂×C₄	—	8	2	no	—
869	C₂×C₄	C₂×C₄×D₄	1	1	yes	characteristic
870	C₂×C₄	C₂×C₄×D₄	1	1	yes	characteristic
871	C₂×C₄	C₂×C₄×D₄	1	1	yes	characteristic
872	C₂×C₄	C₂×C₄×D₄	1	1	yes	characteristic
873	C₂×C₄	C₂×C₄×D₄	1	1	yes	characteristic
874	C₂×C₄	C₂×C₄×D₄	1	1	yes	characteristic
875	C₂×C₄	C₂×C₄×D₄	1	1	yes	characteristic
876	C₂×C₄	C₂×C₄×D₄	1	1	yes	characteristic
877	C₂×C₄	C₂×C₄×D₄	1	1	yes	characteristic
878	C₂×C₄	C₂⁴×C₄	1	1	yes	characteristic
879	C₂×C₄	C₂³×D₄	1	1	yes	characteristic
880	C₂×C₄	C₂²×#41	1	1	yes	characteristic
881	C₈	—	2	2	no	—
882	C₈	—	2	2	no	—
883	C₈	—	2	2	no	—
884	C₈	—	2	2	no	—
885	C₈	—	2	1	no	—
886	C₈	—	2	1	no	—
887	C₈	—	2	1	no	—
888	C₈	—	2	1	no	—
889	C₈	—	2	1	no	—
890	C₈	—	2	1	no	—
891	C₈	—	2	1	no	—
892	C₈	—	4	1	no	—
893	C₈	—	4	1	no	—
894	C₈	—	4	1	no	—
895	C₈	—	4	1	no	—
896	C₈	—	4	2	no	—
897	C₈	—	4	2	no	—
898	C₈	—	4	2	no	—
899	C₈	—	4	2	no	—
900	C₈	#568	1	2	yes	—
901	C₂²	—	2	1	no	—
902	C₂²	—	2	1	no	—
903	C₂²	—	2	1	no	—
904	C₂²	—	2	1	no	—
905	C₂²	—	2	1	no	—
906	C₂²	—	2	1	no	—
907	C₂²	—	2	1	no	—
908	C₂²	—	2	1	no	—
909	C₂²	—	4	2	no	—
910	C₂²	—	4	2	no	—
911	C₂²	—	4	2	no	—
912	C₂²	—	4	2	no	—
913	C₂²	—	4	2	no	—
914	C₂²	—	4	2	no	—
915	C₂²	—	4	2	no	—
916	C₂²	—	4	2	no	—
917	C₂²	—	4	2	no	—
918	C₂²	—	16	4	no	—
919	C₂²	—	16	4	no	—
920	C₂²	#2957	1	2	yes	—
921	C₂²	C₂²×C₄×D₄	1	1	yes	characteristic
922	C₄	—	2	1	no	—
923	C₄	—	2	1	no	—
924	C₄	—	2	1	no	—
925	C₄	—	2	1	no	—
926	C₄	—	2	1	no	—
927	C₄	—	2	1	no	—
928	C₄	—	2	1	no	—
929	C₄	—	2	1	no	—
930	C₄	—	2	1	no	—
931	C₄	—	2	1	no	—
932	C₄	—	4	2	no	—
933	C₄	—	4	2	no	—
934	C₄	—	4	2	no	—
935	C₄	—	4	2	no	—
936	C₄	—	4	2	no	—
937	C₄	C₂×#568	1	1	yes	characteristic
938	C₄	#3573	1	1	yes	characteristic
939	C₄	#3585	1	2	yes	—
940	C₂	—	2	2	no	—
941	C₂	—	4	1	no	—
942	C₂	—	4	1	no	—
943	C₂	—	8	2	no	—
944	C₂	—	8	2	no	—
945	C₂	—	8	2	no	—
946	C₂	#60147	1	1	yes	characteristic
947	C₂	#60176	1	1	yes	characteristic
948	C₂	C₂×#2957	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂³×D₄
commutator	C₂×C₄	C₂⁴×C₄
Frattini, cosocle	C₄²	C₂⁵
socle	C₂²	C₂²×C₄×D₄
prime radical	#61431	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄ ◁ #2965 ◁ G
LECS	G ▷ C₄² ▷ C₂² ▷ C₁

Complements

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

N	H ≅ G/N	type
2. #60324	C₂	semidirect
3. #18093	C₂	semidirect
4. #18075	C₂	semidirect
5. #18073	C₂	semidirect
6. #18064	C₂	semidirect
7. #18044	C₂	semidirect
8. #18043	C₂	semidirect
9. #18014	C₂	semidirect
10. #18011	C₂	semidirect
11. #18006	C₂	semidirect
12. #17974	C₂	semidirect
13. #17970	C₂	semidirect
14. #17963	C₂	semidirect
15. #17948	C₂	semidirect
16. #17946	C₂	semidirect
17. #17942	C₂	semidirect
18. #17899	C₂	semidirect
19. #17895	C₂	semidirect
20. C₂×#1594	C₂	semidirect
21. #17834	C₂	semidirect
22. #17521	C₂	semidirect
23. #17330	C₂	semidirect
44. #2994	C₂²	semidirect
45. #2993	C₂²	semidirect
47. #2989	C₂²	semidirect
48. #2981	C₂²	semidirect
51. #2975	C₂²	semidirect
52. #2974	C₂²	semidirect
54. #2971	C₂²	semidirect
55. #2969	C₂²	semidirect
57. #2966	C₂²	semidirect
63. #2935	C₂²	semidirect
65. D₄×M₁₆	C₂²	semidirect
68. C₂×#436	C₂²	semidirect
74. #1594	C₂²	semidirect
75. #1594	C₂²	semidirect
76. #1594	C₂²	semidirect
77. #1594	C₂²	semidirect
78. #1594	C₂²	semidirect
79. #1594	C₂²	semidirect
80. #1593	C₂²	semidirect
81. #1593	C₂²	semidirect
82. #1592	C₂²	semidirect
83. #1590	C₂²	semidirect
84. #1590	C₂²	semidirect
85. #1590	C₂²	semidirect
86. #1589	C₂²	semidirect
87. #1589	C₂²	semidirect
88. #1589	C₂²	semidirect
89. #1588	C₂²	semidirect
90. #1588	C₂²	semidirect
91. #1588	C₂²	semidirect
92. #1586	C₂²	semidirect
93. #1586	C₂²	semidirect
94. #1586	C₂²	semidirect
95. #1586	C₂²	semidirect
96. #1585	C₂²	semidirect
97. #1583	C₂²	semidirect
98. #1582	C₂²	semidirect
99. #1581	C₂²	semidirect
100. #1581	C₂²	semidirect
101. #1580	C₂²	semidirect
102. #1580	C₂²	semidirect
103. #1580	C₂²	semidirect
104. #1580	C₂²	semidirect
105. #1579	C₂²	semidirect
106. #1579	C₂²	semidirect
107. SD₁₆⋊C₈	C₂²	semidirect
108. C₈×SD₁₆	C₂²	semidirect
109. C₈×D₈	C₂²	semidirect
110. #1574	C₂²	semidirect
111. #1573	C₂²	semidirect
112. #1573	C₂²	semidirect
113. #1568	C₂²	semidirect
114. #1568	C₂²	semidirect
115. #1566	C₂²	semidirect
116. #1564	C₂²	semidirect
117. C₂×#334	C₂²	semidirect
118. C₂×#334	C₂²	semidirect
119. #1496	C₂²	semidirect
120. #1495	C₂²	semidirect
121. #1494	C₂²	semidirect
122. #1490	C₂²	semidirect
123. #1488	C₂²	semidirect
124. #1486	C₂²	semidirect
125. #1483	C₂²	semidirect
126. #1482	C₂²	semidirect
127. #1480	C₂²	semidirect
128. #1478	C₂²	semidirect
129. #1477	C₂²	semidirect
130. C₂×D₄⋊C₈	C₂²	semidirect
131. #1454	C₂²	semidirect
132. #1454	C₂²	semidirect
133. #1453	C₂²	semidirect
134. #1453	C₂²	semidirect
135. #1451	C₂²	semidirect
136. #1451	C₂²	semidirect
137. #1451	C₂²	semidirect
138. #1450	C₂²	semidirect
139. #1450	C₂²	semidirect
140. #1450	C₂²	semidirect
141. C₈×M₁₆	C₂²	semidirect
142. C₂×#322	C₂²	semidirect

Maximal subgroups

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

subgroup	index
#61431	2
#60324	2
#18093	2
#18075	2
#18073	2
#18064	2
#18044	2
#18043	2
#18014	2
#18011	2
#18006	2
#17974	2
#17970	2
#17963	2
#17948	2
#17946	2
#17942	2
#17899	2
#17895	2
C₂×#1594	2
#17834	2
#17521	2
#17330	2