Subgroups — #6345895

Order 512.

1638 conjugacy classes of subgroups.

The subgroup lattice has 981 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	#60311	C₂	1	2	yes	maximal, complemented
3	#18087	C₂	1	1	yes	maximal, characteristic, complemented
4	#18069	C₂	1	1	yes	maximal, characteristic, complemented
5	#18066	C₂	1	1	yes	maximal, characteristic, complemented
6	#18054	C₂	1	1	yes	maximal, characteristic, complemented
7	#18035	C₂	1	1	yes	maximal, characteristic, complemented
8	M₁₆×D₈	C₂	1	1	yes	maximal, characteristic, complemented
9	#18020	C₂	1	2	yes	maximal, complemented
10	#18007	C₂	1	2	yes	maximal, complemented
11	#18006	C₂	1	2	yes	maximal, complemented
12	#17973	C₂	1	1	yes	maximal, characteristic, complemented
13	#17970	C₂	1	1	yes	maximal, characteristic, complemented
14	#17959	C₂	1	1	yes	maximal, characteristic, complemented
15	#17920	C₂	1	2	yes	maximal, complemented
16	#17918	C₂	1	2	yes	maximal, complemented
17	#17914	C₂	1	2	yes	maximal, complemented
18	#17857	C₂	1	1	yes	maximal, characteristic, complemented
19	#17854	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×C₈×D₈	C₂	1	1	yes	maximal, characteristic, complemented
21	#17836	C₂	1	1	yes	maximal, characteristic, complemented
22	#17521	C₂	1	2	yes	maximal, complemented
23	#17328	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	#2994	C₂²	1	2	yes	complemented
44	#2993	C₂²	1	2	yes	complemented
45	#2992	—	2	2	no	—
46	#2990	C₂²	1	2	yes	—
47	#2988	C₂²	1	2	yes	complemented
48	#2981	C₂²	1	2	yes	complemented
49	#2977	—	2	2	no	—
50	#2976	—	2	2	no	—
51	#2974	—	2	2	no	—
52	#2974	C₂²	1	2	yes	complemented
53	#2972	C₂²	1	2	yes	complemented
54	#2970	C₂²	1	2	yes	complemented
55	#2969	C₂²	1	2	yes	complemented
56	#2968	—	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	C₂²	1	2	yes	complemented
65	#2933	—	2	2	no	—
66	#2929	—	2	2	no	—
67	C₂×#435	—	2	2	no	—
68	C₂×C₈×D₄	C₂²	1	2	yes	complemented
69	#2922	C₂²	1	1	yes	characteristic
70	#1594	C₂²	1	2	yes	complemented
71	#1592	C₂²	1	2	yes	complemented
72	#1591	C₂²	1	1	yes	characteristic, complemented
73	#1591	C₂²	1	1	yes	characteristic, complemented
74	#1590	C₂²	1	2	yes	complemented
75	#1589	C₂²	1	1	yes	characteristic, complemented
76	#1589	C₂²	1	1	yes	characteristic, complemented
77	#1589	C₂²	1	1	yes	characteristic, complemented
78	#1589	C₂²	1	1	yes	characteristic, complemented
79	#1588	C₂²	1	2	yes	complemented
80	#1586	C₂²	1	2	yes	complemented
81	#1586	C₂²	1	2	yes	complemented
82	#1585	C₂²	1	2	yes	complemented
83	#1583	C₂²	1	2	yes	complemented
84	#1582	C₂²	1	2	yes	complemented
85	#1582	C₂²	1	2	yes	complemented
86	#1582	C₂²	1	2	yes	complemented
87	#1581	C₂²	1	2	yes	complemented
88	#1581	C₂²	1	2	yes	complemented
89	#1581	C₂²	1	2	yes	complemented
90	#1581	C₂²	1	2	yes	complemented
91	#1580	C₂²	1	2	yes	complemented
92	#1580	C₂²	1	2	yes	complemented
93	#1580	C₂²	1	2	yes	complemented
94	SD₁₆⋊C₈	C₂²	1	2	yes	complemented
95	SD₁₆⋊C₈	C₂²	1	2	yes	complemented
96	SD₁₆⋊C₈	C₂²	1	2	yes	complemented
97	C₈×Q₁₆	C₂²	1	1	yes	characteristic, complemented
98	C₈×Q₁₆	C₂²	1	1	yes	characteristic, complemented
99	C₈×SD₁₆	C₂²	1	2	yes	complemented
100	C₈×D₈	C₂²	1	1	yes	characteristic
101	C₈×D₈	C₂²	1	1	yes	characteristic
102	C₈×D₈	C₂²	1	1	yes	characteristic
103	C₈×D₈	C₂²	1	1	yes	characteristic
104	C₈×D₈	C₂²	1	2	yes	complemented
105	C₈×D₈	C₂²	1	1	yes	characteristic, complemented
106	C₈×D₈	C₂²	1	1	yes	characteristic, complemented
107	C₈×D₈	C₂²	1	2	yes	complemented
108	C₈×D₈	C₂²	1	1	yes	characteristic, complemented
109	C₈×D₈	C₂²	1	1	yes	characteristic, 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	#1567	C₂²	1	1	yes	characteristic, complemented
116	#1564	C₂²	1	1	yes	characteristic, complemented
117	C₂×#335	C₂²	1	1	yes	characteristic, complemented
118	C₂×#335	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	#1452	C₂²	1	1	yes	characteristic, complemented
136	#1451	C₂²	1	1	yes	characteristic, complemented
137	#1450	C₂²	1	1	yes	characteristic, complemented
138	#1450	C₂²	1	1	yes	characteristic, complemented
139	C₈×M₁₆	C₂²	1	1	yes	characteristic, complemented
140	C₈×M₁₆	C₂²	1	1	yes	characteristic, complemented
141	C₈×M₁₆	C₂²	1	1	yes	characteristic, complemented
142	C₂×C₈²	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	C₂³×C₈	—	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	1	yes	characteristic
216	#446	D₄	1	1	yes	characteristic
217	#446	C₂³	1	2	yes	—
218	#446	C₂³	1	2	yes	—
219	C₈×Q₈	C₂×C₄	1	1	yes	characteristic
220	C₈×Q₈	C₂×C₄	1	1	yes	characteristic
221	C₈×Q₈	C₂³	1	2	yes	—
222	C₈×Q₈	C₂³	1	2	yes	—
223	C₄×Q₁₆	C₂×C₄	1	1	yes	characteristic
224	C₄×Q₁₆	C₂³	1	1	yes	characteristic
225	C₄×SD₁₆	C₂×C₄	1	2	yes	—
226	C₄×SD₁₆	C₂³	1	2	yes	—
227	C₄×SD₁₆	C₂³	1	2	yes	—
228	C₄×SD₁₆	C₂³	1	2	yes	—
229	C₄×D₈	C₂×C₄	1	1	yes	characteristic
230	C₄×D₈	C₂×C₄	1	1	yes	characteristic
231	C₄×D₈	C₂×C₄	1	2	yes	—
232	C₄×D₈	C₂×C₄	1	2	yes	—
233	C₄×D₈	C₂×C₄	1	1	yes	characteristic
234	C₄×D₈	C₂×C₄	1	1	yes	characteristic
235	C₄×D₈	C₂×C₄	1	1	yes	characteristic
236	C₄×D₈	C₂³	1	2	yes	—
237	C₄×D₈	C₂³	1	2	yes	—
238	C₄×D₈	C₂³	1	2	yes	—
239	C₄×D₈	C₂³	1	1	yes	characteristic
240	C₄×D₈	C₂³	1	1	yes	characteristic
241	C₄×D₈	C₂³	1	1	yes	characteristic
242	#436	—	2	2	no	—
243	#436	—	2	2	no	—
244	#436	D₄	1	1	yes	characteristic
245	#436	D₄	1	1	yes	characteristic
246	#436	C₂³	1	2	yes	—
247	#436	C₂³	1	2	yes	—
248	#436	C₂³	1	2	yes	—
249	#436	C₂³	1	2	yes	—
250	#435	—	2	2	no	—
251	#435	—	2	2	no	—
252	#435	—	2	2	no	—
253	#435	—	2	2	no	—
254	#435	—	2	2	no	—
255	#435	—	2	2	no	—
256	#435	—	2	2	no	—
257	#435	—	2	2	no	—
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	D₄	1	1	yes	characteristic
267	#435	D₄	1	1	yes	characteristic
268	#435	D₄	1	1	yes	characteristic
269	#435	D₄	1	1	yes	characteristic
270	C₈×D₄	—	2	2	no	—
271	C₈×D₄	—	2	2	no	—
272	C₈×D₄	—	2	2	no	—
273	C₈×D₄	—	2	2	no	—
274	C₈×D₄	—	2	2	no	—
275	C₈×D₄	—	2	2	no	—
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	C₈×D₄	C₂³	1	2	yes	—
290	C₈×D₄	C₂³	1	2	yes	—
291	C₈×D₄	C₂³	1	2	yes	—
292	C₈×D₄	C₂³	1	2	yes	—
293	#433	—	2	1	no	—
294	#433	—	2	1	no	—
295	#433	—	2	2	no	—
296	#433	—	2	2	no	—
297	#433	—	2	2	no	—
298	#433	—	2	2	no	—
299	#432	—	2	2	no	—
300	#432	C₂³	1	2	yes	—
301	#432	C₂³	1	2	yes	—
302	#431	—	2	2	no	—
303	#431	C₂³	1	2	yes	—
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	#431	C₂³	1	1	yes	characteristic
311	#431	C₂³	1	1	yes	characteristic
312	#431	C₂³	1	1	yes	characteristic
313	#431	C₂³	1	1	yes	characteristic
314	#427	C₂×C₄	1	1	yes	characteristic
315	C₂×#107	C₂×C₄	1	1	yes	characteristic
316	C₂×#107	C₂×C₄	1	1	yes	characteristic
317	#424	—	2	1	no	—
318	#424	—	2	2	no	—
319	#424	—	2	2	no	—
320	#423	C₂³	1	2	yes	—
321	C₂×C₄⋊C₈	—	2	2	no	—
322	C₂×C₄⋊C₈	C₂³	1	2	yes	—
323	C₂×C₄⋊C₈	C₂³	1	2	yes	—
324	#416	C₂×C₄	1	2	yes	—
325	C₂×#102	C₂×C₄	1	2	yes	—
326	C₂×#102	C₂×C₄	1	2	yes	—
327	#408	—	2	1	no	—
328	#408	—	2	2	no	—
329	#408	—	2	2	no	—
330	#408	—	2	2	no	—
331	#407	—	2	2	no	—
332	#407	—	2	2	no	—
333	C₂×C₂²⋊C₈	—	2	2	no	—
334	C₂×C₂²⋊C₈	—	2	2	no	—
335	C₂×C₂²⋊C₈	—	2	2	no	—
336	C₂×C₂²⋊C₈	—	2	2	no	—
337	#405	—	2	2	no	—
338	#405	—	2	2	no	—
339	C₄×M₁₆	C₂³	1	1	yes	characteristic
340	C₄×M₁₆	C₂³	1	1	yes	characteristic
341	C₄×M₁₆	C₂³	1	1	yes	characteristic
342	C₂×#97	—	2	2	no	—
343	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
344	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
345	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
346	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
347	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
348	#335	C₂³	1	1	yes	characteristic
349	#335	C₂³	1	1	yes	characteristic
350	#335	C₂³	1	1	yes	characteristic
351	#335	C₂³	1	2	yes	—
352	#335	C₂³	1	2	yes	—
353	#335	C₂³	1	1	yes	characteristic
354	#335	C₂³	1	2	yes	—
355	#334	C₂³	1	2	yes	—
356	#334	C₂³	1	2	yes	—
357	#334	C₂³	1	2	yes	—
358	Q₈⋊C₈	C₂³	1	2	yes	—
359	Q₈⋊C₈	C₂³	1	2	yes	—
360	Q₈⋊C₈	C₂³	1	2	yes	—
361	Q₈⋊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	D₄⋊C₈	C₂³	1	2	yes	—
371	D₄⋊C₈	C₂³	1	2	yes	—
372	D₄⋊C₈	C₂³	1	2	yes	—
373	D₄⋊C₈	C₂³	1	2	yes	—
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	#322	C₂³	1	1	yes	characteristic
383	#322	C₂³	1	1	yes	characteristic
384	C₈²	C₂³	1	1	yes	characteristic
385	C₈²	C₂³	1	1	yes	characteristic
386	C₈²	C₂³	1	1	yes	characteristic
387	C₈²	C₂³	1	1	yes	characteristic
388	C₈²	C₂³	1	1	yes	characteristic
389	C₈²	C₂³	1	1	yes	characteristic
390	C₂×#41	—	2	2	no	—
391	C₂×#41	C₂²×C₄	1	2	yes	—
392	C₂×#41	#41	1	1	yes	characteristic
393	C₂²×D₄	—	2	2	no	—
394	C₂²×D₄	C₂²×C₄	1	2	yes	—
395	C₂²×D₄	C₂²×C₄	1	2	yes	—
396	C₂³×C₄	—	2	2	no	—
397	C₂³×C₄	—	2	2	no	—
398	#135	—	2	4	no	—
399	C₂×Q₁₆	C₂²×C₄	1	1	yes	characteristic
400	C₂×SD₁₆	C₂²×C₄	1	2	yes	—
401	C₂×SD₁₆	C₂²×C₄	1	2	yes	—
402	C₂×SD₁₆	C₂²×C₄	1	2	yes	—
403	C₂×D₈	—	2	4	no	—
404	C₂×D₈	—	2	4	no	—
405	C₂×D₈	C₂²×C₄	1	2	yes	—
406	C₂×D₈	C₂²×C₄	1	2	yes	—
407	C₂×D₈	C₂²×C₄	1	1	yes	characteristic
408	C₂×D₈	C₂²×C₄	1	1	yes	characteristic
409	C₂×D₈	C₂²×C₄	1	2	yes	—
410	C₂×D₈	C₂²×C₄	1	1	yes	characteristic
411	#131	—	8	4	no	—
412	C₂×M₁₆	—	2	1	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	C₂×D₄	1	1	yes	characteristic
420	C₂×M₁₆	C₂×D₄	1	1	yes	characteristic
421	C₂×M₁₆	C₂×D₄	1	1	yes	characteristic
422	C₂×M₁₆	C₂×D₄	1	1	yes	characteristic
423	C₂²×C₈	—	2	1	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	—	2	2	no	—
430	C₂²×C₈	—	2	2	no	—
431	C₂²×C₈	—	2	2	no	—
432	C₂²×C₈	—	2	2	no	—
433	C₂²×C₈	—	2	2	no	—
434	C₂²×C₈	—	8	4	no	—
435	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
436	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
437	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
438	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
439	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
440	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
441	C₂²×C₈	C₂×D₄	1	1	yes	characteristic
442	C₂²×C₈	C₂×D₄	1	1	yes	characteristic
443	C₄⋊Q₈	C₂²×C₄	1	2	yes	—
444	#127	C₂²×C₄	1	2	yes	—
445	#126	—	2	2	no	—
446	#126	—	2	2	no	—
447	#126	—	2	2	no	—
448	#126	—	2	2	no	—
449	#125	—	2	2	no	—
450	#125	C₂²×C₄	1	2	yes	—
451	#125	C₂²×C₄	1	2	yes	—
452	#124	—	2	2	no	—
453	#124	—	2	2	no	—
454	#124	C₂²×C₄	1	2	yes	—
455	#124	C₂²×C₄	1	2	yes	—
456	#123	—	2	2	no	—
457	#123	—	2	2	no	—
458	#123	—	2	2	no	—
459	#123	—	2	2	no	—
460	#123	—	2	2	no	—
461	#123	—	2	2	no	—
462	#123	—	2	2	no	—
463	#123	—	2	2	no	—
464	C₂²⋊Q₈	—	2	2	no	—
465	C₂²⋊Q₈	—	2	2	no	—
466	C₂²⋊Q₈	—	2	2	no	—
467	C₂²⋊Q₈	—	2	2	no	—
468	C₂²⋊Q₈	—	2	2	no	—
469	C₂²⋊Q₈	C₂²×C₄	1	2	yes	—
470	C₂²⋊Q₈	C₂²×C₄	1	2	yes	—
471	#121	—	2	2	no	—
472	#121	—	2	2	no	—
473	#121	—	2	2	no	—
474	#121	—	2	2	no	—
475	#121	—	2	2	no	—
476	#121	—	2	2	no	—
477	#121	C₂²×C₄	1	2	yes	—
478	#121	C₂²×C₄	1	2	yes	—
479	#121	C₂²×C₄	1	2	yes	—
480	#121	C₂²×C₄	1	2	yes	—
481	#120	—	2	2	no	—
482	#120	—	2	2	no	—
483	#120	—	2	2	no	—
484	#120	—	2	2	no	—
485	C₄×Q₈	C₂²×C₄	1	2	yes	—
486	C₄×Q₈	C₂²×C₄	1	1	yes	characteristic
487	C₄×Q₈	C₂×D₄	1	1	yes	characteristic
488	C₄×Q₈	C₂⁴	1	2	yes	—
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	—	2	2	no	—
496	C₄×D₄	—	2	2	no	—
497	C₄×D₄	—	2	2	no	—
498	C₄×D₄	—	2	2	no	—
499	C₄×D₄	—	2	2	no	—
500	C₄×D₄	—	2	2	no	—
501	C₄×D₄	—	2	2	no	—
502	C₄×D₄	C₂²×C₄	1	2	yes	—
503	C₄×D₄	C₂²×C₄	1	2	yes	—
504	C₄×D₄	C₂²×C₄	1	2	yes	—
505	C₄×D₄	C₂²×C₄	1	2	yes	—
506	C₄×D₄	C₂²×C₄	1	2	yes	—
507	C₄×D₄	C₂²×C₄	1	1	yes	characteristic
508	C₄×D₄	C₂²×C₄	1	1	yes	characteristic
509	C₄×D₄	C₂²×C₄	1	1	yes	characteristic
510	C₄×D₄	C₂×D₄	1	1	yes	characteristic
511	C₄×D₄	C₂×D₄	1	1	yes	characteristic
512	C₄×D₄	C₂×D₄	1	1	yes	characteristic
513	C₄×D₄	C₂⁴	1	2	yes	—
514	C₄×D₄	C₂⁴	1	2	yes	—
515	C₄×D₄	C₂⁴	1	2	yes	—
516	#117	—	2	2	no	—
517	#117	—	2	2	no	—
518	#117	—	2	2	no	—
519	#117	C₂²×C₄	1	2	yes	—
520	#117	#41	1	1	yes	characteristic
521	#117	#41	1	1	yes	characteristic
522	#117	#41	1	1	yes	characteristic
523	C₂×C₄⋊C₄	—	2	2	no	—
524	C₂×C₄⋊C₄	C₂²×C₄	1	2	yes	—
525	C₂×C₄⋊C₄	C₂²×C₄	1	2	yes	—
526	C₂×C₂²⋊C₄	—	2	2	no	—
527	C₂×C₂²⋊C₄	—	2	2	no	—
528	C₂×C₂²⋊C₄	—	2	2	no	—
529	C₂×C₂²⋊C₄	—	2	2	no	—
530	C₂×C₄²	—	2	2	no	—
531	C₂×C₄²	C₂⁴	1	1	yes	characteristic
532	C₂×C₄²	C₂⁴	1	1	yes	characteristic
533	C₂×C₄²	C₂⁴	1	1	yes	characteristic
534	#107	C₂²×C₄	1	1	yes	characteristic
535	#107	C₂²×C₄	1	1	yes	characteristic
536	#107	C₂²×C₄	1	1	yes	characteristic
537	#107	C₂²×C₄	1	2	yes	—
538	#107	C₂²×C₄	1	2	yes	—
539	#107	C₂²×C₄	1	1	yes	characteristic
540	#107	C₂²×C₄	1	2	yes	—
541	#106	C₂²×C₄	1	2	yes	—
542	#106	C₂²×C₄	1	2	yes	—
543	#106	C₂²×C₄	1	2	yes	—
544	C₄⋊C₈	—	2	2	no	—
545	C₄⋊C₈	—	2	2	no	—
546	C₄⋊C₈	—	2	2	no	—
547	C₄⋊C₈	—	2	2	no	—
548	C₄⋊C₈	—	2	2	no	—
549	C₄⋊C₈	—	2	2	no	—
550	C₄⋊C₈	—	2	2	no	—
551	C₄⋊C₈	—	2	1	no	—
552	C₄⋊C₈	—	2	1	no	—
553	C₄⋊C₈	—	2	1	no	—
554	C₄⋊C₈	—	2	1	no	—
555	C₄⋊C₈	C₂²×C₄	1	1	yes	characteristic
556	C₄⋊C₈	C₂²×C₄	1	1	yes	characteristic
557	C₄⋊C₈	C₂²×C₄	1	1	yes	characteristic
558	C₄⋊C₈	C₂²×C₄	1	1	yes	characteristic
559	C₄⋊C₈	C₂²×C₄	1	1	yes	characteristic
560	C₄⋊C₈	C₂²×C₄	1	1	yes	characteristic
561	C₄⋊C₈	C₂×D₄	1	1	yes	characteristic
562	C₄⋊C₈	C₂×D₄	1	1	yes	characteristic
563	C₄⋊C₈	C₂×D₄	1	1	yes	characteristic
564	C₄⋊C₈	C₂×D₄	1	1	yes	characteristic
565	C₄⋊C₈	C₂×D₄	1	1	yes	characteristic
566	C₄⋊C₈	C₂×D₄	1	1	yes	characteristic
567	C₄⋊C₈	C₂⁴	1	2	yes	—
568	C₄⋊C₈	C₂⁴	1	2	yes	—
569	C₄⋊C₈	C₂⁴	1	2	yes	—
570	C₄⋊C₈	C₂⁴	1	2	yes	—
571	#103	C₂²×C₄	1	2	yes	—
572	#103	C₂²×C₄	1	2	yes	—
573	#103	C₂²×C₄	1	2	yes	—
574	#103	C₂²×C₄	1	2	yes	—
575	#102	C₂²×C₄	1	2	yes	—
576	#102	C₂²×C₄	1	2	yes	—
577	#102	C₂²×C₄	1	2	yes	—
578	#102	C₂²×C₄	1	2	yes	—
579	#102	C₂²×C₄	1	2	yes	—
580	#102	C₂²×C₄	1	2	yes	—
581	#102	C₂²×C₄	1	2	yes	—
582	#102	C₂²×C₄	1	2	yes	—
583	#102	C₂²×C₄	1	2	yes	—
584	#102	C₂²×C₄	1	2	yes	—
585	#102	C₂²×C₄	1	2	yes	—
586	#102	C₂²×C₄	1	2	yes	—
587	C₂²⋊C₈	—	2	2	no	—
588	C₂²⋊C₈	—	2	2	no	—
589	C₂²⋊C₈	—	2	2	no	—
590	C₂²⋊C₈	—	2	1	no	—
591	C₂²⋊C₈	—	2	1	no	—
592	C₂²⋊C₈	—	2	1	no	—
593	C₂²⋊C₈	—	2	1	no	—
594	C₂²⋊C₈	—	2	2	no	—
595	C₂²⋊C₈	—	2	2	no	—
596	C₂²⋊C₈	—	2	2	no	—
597	C₂²⋊C₈	—	2	2	no	—
598	C₂²⋊C₈	—	2	2	no	—
599	C₂²⋊C₈	—	2	2	no	—
600	C₂²⋊C₈	—	2	2	no	—
601	C₂²⋊C₈	—	2	2	no	—
602	C₂²⋊C₈	—	2	2	no	—
603	C₂²⋊C₈	—	2	2	no	—
604	C₂²⋊C₈	—	2	2	no	—
605	C₂²⋊C₈	—	2	2	no	—
606	C₂²⋊C₈	C₂²×C₄	1	1	yes	characteristic
607	C₂²⋊C₈	C₂²×C₄	1	1	yes	characteristic
608	C₂²⋊C₈	C₂²×C₄	1	1	yes	characteristic
609	C₂²⋊C₈	C₂²×C₄	1	1	yes	characteristic
610	C₂²⋊C₈	C₂²×C₄	1	1	yes	characteristic
611	C₂²⋊C₈	C₂²×C₄	1	1	yes	characteristic
612	C₂²⋊C₈	C₂×D₄	1	1	yes	characteristic
613	C₂²⋊C₈	C₂×D₄	1	1	yes	characteristic
614	C₂²⋊C₈	C₂×D₄	1	1	yes	characteristic
615	C₂²⋊C₈	C₂×D₄	1	1	yes	characteristic
616	C₂²⋊C₈	C₂×D₄	1	1	yes	characteristic
617	C₂²⋊C₈	C₂×D₄	1	1	yes	characteristic
618	#97	—	2	2	no	—
619	#97	—	2	2	no	—
620	#97	—	2	2	no	—
621	#97	—	2	2	no	—
622	#97	—	2	1	no	—
623	#97	C₂×D₄	1	1	yes	characteristic
624	#97	C₂×D₄	1	1	yes	characteristic
625	#97	C₂×D₄	1	1	yes	characteristic
626	#97	C₂×D₄	1	1	yes	characteristic
627	C₄×C₈	—	2	2	no	—
628	C₄×C₈	—	2	2	no	—
629	C₄×C₈	—	2	2	no	—
630	C₄×C₈	—	2	1	no	—
631	C₄×C₈	C₂²×C₄	1	1	yes	characteristic
632	C₄×C₈	C₂²×C₄	1	1	yes	characteristic
633	C₄×C₈	C₂²×C₄	1	1	yes	characteristic
634	C₄×C₈	C₂²×C₄	1	1	yes	characteristic
635	C₄×C₈	C₂²×C₄	1	1	yes	characteristic
636	C₄×C₈	C₂²×C₄	1	1	yes	characteristic
637	C₄×C₈	C₂×D₄	1	1	yes	characteristic
638	C₄×C₈	C₂×D₄	1	1	yes	characteristic
639	C₄×C₈	C₂⁴	1	1	yes	characteristic
640	C₄×C₈	C₂⁴	1	1	yes	characteristic
641	C₄×C₈	C₂⁴	1	1	yes	characteristic
642	C₄×C₈	C₂⁴	1	1	yes	characteristic
643	C₄×C₈	C₂⁴	1	1	yes	characteristic
644	C₄×C₈	C₂⁴	1	1	yes	characteristic
645	C₄×C₈	C₂⁴	1	1	yes	characteristic
646	C₄×C₈	C₂⁴	1	1	yes	characteristic
647	C₄×C₈	C₂⁴	1	1	yes	characteristic
648	C₄×C₈	C₂⁴	1	1	yes	characteristic
649	C₄×C₈	C₂⁴	1	1	yes	characteristic
650	C₄×C₈	C₂⁴	1	1	yes	characteristic
651	C₂⁴	—	2	2	no	—
652	C₂⁴	—	2	2	no	—
653	#41	—	2	4	no	—
654	#41	—	4	2	no	—
655	#41	—	4	2	no	—
656	#41	—	8	2	no	—
657	#41	—	8	2	no	—
658	C₂×Q₈	—	2	2	no	—
659	C₂×Q₈	C₄×D₄	1	1	yes	characteristic
660	C₂×Q₈	C₂³×C₄	1	2	yes	—
661	C₂×D₄	—	2	4	no	—
662	C₂×D₄	—	2	4	no	—
663	C₂×D₄	—	2	2	no	—
664	C₂×D₄	—	2	2	no	—
665	C₂×D₄	—	2	2	no	—
666	C₂×D₄	—	2	2	no	—
667	C₂×D₄	—	2	2	no	—
668	C₂×D₄	—	2	2	no	—
669	C₂×D₄	—	2	2	no	—
670	C₂×D₄	—	2	2	no	—
671	C₂×D₄	—	2	2	no	—
672	C₂×D₄	—	4	2	no	—
673	C₂×D₄	—	4	2	no	—
674	C₂×D₄	—	8	4	no	—
675	C₂×D₄	C₄×D₄	1	1	yes	characteristic
676	C₂×D₄	C₄×D₄	1	1	yes	characteristic
677	C₂×D₄	C₄×D₄	1	1	yes	characteristic
678	C₂×D₄	C₂³×C₄	1	2	yes	—
679	C₂×D₄	C₂³×C₄	1	2	yes	—
680	C₂×D₄	C₂³×C₄	1	2	yes	—
681	C₂²×C₄	—	2	2	no	—
682	C₂²×C₄	—	2	2	no	—
683	C₂²×C₄	—	2	2	no	—
684	C₂²×C₄	—	2	2	no	—
685	C₂²×C₄	—	2	2	no	—
686	C₂²×C₄	—	2	2	no	—
687	C₂²×C₄	—	2	2	no	—
688	C₂²×C₄	—	2	2	no	—
689	C₂²×C₄	—	2	2	no	—
690	C₂²×C₄	—	2	2	no	—
691	C₂²×C₄	—	2	2	no	—
692	C₂²×C₄	—	8	2	no	—
693	C₂²×C₄	—	8	2	no	—
694	C₂²×C₄	—	8	2	no	—
695	C₂²×C₄	—	8	2	no	—
696	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
697	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
698	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
699	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
700	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
701	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
702	C₂²×C₄	C₂×#41	1	1	yes	characteristic
703	C₂²×C₄	C₂×#41	1	1	yes	characteristic
704	C₂²×C₄	C₂×#41	1	1	yes	characteristic
705	Q₁₆	—	2	2	no	—
706	SD₁₆	—	2	4	no	—
707	SD₁₆	—	4	2	no	—
708	SD₁₆	—	4	2	no	—
709	D₈	—	2	4	no	—
710	D₈	—	2	4	no	—
711	D₈	—	2	2	no	—
712	D₈	—	2	2	no	—
713	D₈	—	4	2	no	—
714	D₈	#131	1	4	yes	complemented
715	M₁₆	—	2	2	no	—
716	M₁₆	—	2	2	no	—
717	M₁₆	—	4	1	no	—
718	M₁₆	—	4	1	no	—
719	M₁₆	—	4	2	no	—
720	M₁₆	—	4	4	no	—
721	M₁₆	—	8	2	no	—
722	M₁₆	—	8	2	no	—
723	M₁₆	—	8	2	no	—
724	M₁₆	—	8	2	no	—
725	C₂×C₈	—	2	2	no	—
726	C₂×C₈	—	2	2	no	—
727	C₂×C₈	—	2	2	no	—
728	C₂×C₈	—	2	2	no	—
729	C₂×C₈	—	2	2	no	—
730	C₂×C₈	—	2	2	no	—
731	C₂×C₈	—	2	2	no	—
732	C₂×C₈	—	2	2	no	—
733	C₂×C₈	—	2	1	no	—
734	C₂×C₈	—	2	1	no	—
735	C₂×C₈	—	2	1	no	—
736	C₂×C₈	—	2	1	no	—
737	C₂×C₈	—	4	1	no	—
738	C₂×C₈	—	4	1	no	—
739	C₂×C₈	—	4	1	no	—
740	C₂×C₈	—	4	1	no	—
741	C₂×C₈	—	4	2	no	—
742	C₂×C₈	—	4	4	no	—
743	C₂×C₈	—	4	4	no	—
744	C₂×C₈	—	8	2	no	—
745	C₂×C₈	—	8	2	no	—
746	C₂×C₈	—	8	2	no	—
747	C₂×C₈	—	8	2	no	—
748	C₂×C₈	—	8	2	no	—
749	C₂×C₈	—	8	2	no	—
750	C₂×C₈	—	8	2	no	—
751	C₂×C₈	—	8	2	no	—
752	C₂×C₈	C₂³×C₄	1	1	yes	characteristic
753	C₂×C₈	C₂³×C₄	1	1	yes	characteristic
754	C₂×C₈	C₂³×C₄	1	1	yes	characteristic
755	C₂×C₈	C₂³×C₄	1	1	yes	characteristic
756	C₂×C₈	C₂³×C₄	1	1	yes	characteristic
757	C₂×C₈	C₂³×C₄	1	1	yes	characteristic
758	C₂×C₈	C₂³×C₄	1	1	yes	characteristic
759	C₂×C₈	C₂³×C₄	1	1	yes	characteristic
760	C₂×C₈	C₂²×D₄	1	1	yes	characteristic
761	C₂×C₈	C₂²×D₄	1	1	yes	characteristic
762	C₂×C₈	C₂²×D₄	1	1	yes	characteristic
763	C₂×C₈	C₂²×D₄	1	1	yes	characteristic
764	C₂×C₈	C₂²×D₄	1	1	yes	characteristic
765	C₂×C₈	C₂²×D₄	1	1	yes	characteristic
766	C₂×C₈	C₂²×D₄	1	1	yes	characteristic
767	C₂×C₈	C₂²×D₄	1	1	yes	characteristic
768	C₄⋊C₄	—	2	2	no	—
769	C₄⋊C₄	—	2	2	no	—
770	C₄⋊C₄	—	2	2	no	—
771	C₄⋊C₄	—	2	2	no	—
772	C₄⋊C₄	—	2	2	no	—
773	C₄⋊C₄	—	2	2	no	—
774	C₄⋊C₄	—	2	2	no	—
775	C₄⋊C₄	—	2	2	no	—
776	C₄⋊C₄	—	2	2	no	—
777	C₄⋊C₄	—	2	2	no	—
778	C₄⋊C₄	—	2	2	no	—
779	C₄⋊C₄	C₄×D₄	1	1	yes	characteristic
780	C₄⋊C₄	C₄×D₄	1	1	yes	characteristic
781	C₄⋊C₄	C₄×D₄	1	1	yes	characteristic
782	C₄⋊C₄	C₄×D₄	1	1	yes	characteristic
783	C₄⋊C₄	C₄×D₄	1	1	yes	characteristic
784	C₄⋊C₄	C₄×D₄	1	1	yes	characteristic
785	C₄⋊C₄	C₂³×C₄	1	2	yes	—
786	C₄⋊C₄	C₂³×C₄	1	2	yes	—
787	C₄⋊C₄	C₂³×C₄	1	2	yes	—
788	C₄⋊C₄	C₂³×C₄	1	2	yes	—
789	C₂²⋊C₄	—	2	2	no	—
790	C₂²⋊C₄	—	2	2	no	—
791	C₂²⋊C₄	—	2	2	no	—
792	C₂²⋊C₄	—	2	2	no	—
793	C₂²⋊C₄	—	2	2	no	—
794	C₂²⋊C₄	—	2	2	no	—
795	C₂²⋊C₄	—	2	2	no	—
796	C₂²⋊C₄	—	2	2	no	—
797	C₂²⋊C₄	—	2	2	no	—
798	C₂²⋊C₄	—	2	2	no	—
799	C₂²⋊C₄	—	2	2	no	—
800	C₂²⋊C₄	—	2	2	no	—
801	C₂²⋊C₄	—	2	2	no	—
802	C₂²⋊C₄	—	2	2	no	—
803	C₂²⋊C₄	—	2	2	no	—
804	C₂²⋊C₄	—	2	2	no	—
805	C₂²⋊C₄	—	2	2	no	—
806	C₂²⋊C₄	—	2	2	no	—
807	C₂²⋊C₄	—	2	2	no	—
808	C₂²⋊C₄	C₄×D₄	1	1	yes	characteristic
809	C₂²⋊C₄	C₄×D₄	1	1	yes	characteristic
810	C₂²⋊C₄	C₄×D₄	1	1	yes	characteristic
811	C₂²⋊C₄	C₄×D₄	1	1	yes	characteristic
812	C₂²⋊C₄	C₄×D₄	1	1	yes	characteristic
813	C₂²⋊C₄	C₄×D₄	1	1	yes	characteristic
814	C₄²	—	2	2	no	—
815	C₄²	—	2	2	no	—
816	C₄²	—	2	2	no	—
817	C₄²	C₂³×C₄	1	1	yes	characteristic
818	C₄²	C₂³×C₄	1	1	yes	characteristic
819	C₄²	C₂³×C₄	1	1	yes	characteristic
820	C₄²	C₂²×D₄	1	1	yes	characteristic
821	C₄²	C₂²×D₄	1	1	yes	characteristic
822	C₄²	C₂²×D₄	1	1	yes	characteristic
823	C₄²	C₂×#41	1	1	yes	characteristic
824	C₄²	C₂×#41	1	1	yes	characteristic
825	C₄²	C₂×#41	1	1	yes	characteristic
826	C₄²	C₂⁵	1	1	yes	characteristic
827	C₂³	—	2	2	no	—
828	C₂³	—	2	2	no	—
829	C₂³	—	2	2	no	—
830	C₂³	—	4	4	no	—
831	C₂³	—	4	4	no	—
832	C₂³	—	4	4	no	—
833	C₂³	—	8	2	no	—
834	C₂³	—	8	2	no	—
835	C₂³	—	8	2	no	—
836	C₂³	C₂×C₄×D₄	1	1	yes	characteristic
837	C₂³	C₂×C₄×D₄	1	1	yes	characteristic
838	C₂³	C₂×C₄×D₄	1	1	yes	characteristic
839	Q₈	—	2	2	no	—
840	Q₈	—	2	2	no	—
841	Q₈	—	4	1	no	—
842	Q₈	—	8	2	no	—
843	D₄	—	2	2	no	—
844	D₄	—	2	2	no	—
845	D₄	—	2	2	no	—
846	D₄	—	2	2	no	—
847	D₄	—	2	2	no	—
848	D₄	—	2	2	no	—
849	D₄	—	2	2	no	—
850	D₄	—	4	1	no	—
851	D₄	—	4	4	no	—
852	D₄	—	4	4	no	—
853	D₄	—	4	4	no	—
854	D₄	—	4	4	no	—
855	D₄	—	8	2	no	—
856	D₄	—	8	2	no	—
857	D₄	—	8	2	no	—
858	D₄	—	8	2	no	—
859	D₄	—	8	2	no	—
860	D₄	C₂×#131	1	4	yes	—
861	C₂×C₄	—	2	2	no	—
862	C₂×C₄	—	2	1	no	—
863	C₂×C₄	—	2	1	no	—
864	C₂×C₄	—	2	1	no	—
865	C₂×C₄	—	2	1	no	—
866	C₂×C₄	—	2	1	no	—
867	C₂×C₄	—	2	1	no	—
868	C₂×C₄	—	2	1	no	—
869	C₂×C₄	—	2	1	no	—
870	C₂×C₄	—	2	1	no	—
871	C₂×C₄	—	2	1	no	—
872	C₂×C₄	—	2	1	no	—
873	C₂×C₄	—	2	1	no	—
874	C₂×C₄	—	2	2	no	—
875	C₂×C₄	—	2	2	no	—
876	C₂×C₄	—	2	2	no	—
877	C₂×C₄	—	2	2	no	—
878	C₂×C₄	—	2	2	no	—
879	C₂×C₄	—	4	1	no	—
880	C₂×C₄	—	4	1	no	—
881	C₂×C₄	—	4	4	no	—
882	C₂×C₄	—	4	2	no	—
883	C₂×C₄	—	4	2	no	—
884	C₂×C₄	—	4	2	no	—
885	C₂×C₄	—	4	2	no	—
886	C₂×C₄	—	4	2	no	—
887	C₂×C₄	—	4	2	no	—
888	C₂×C₄	—	8	2	no	—
889	C₂×C₄	—	8	2	no	—
890	C₂×C₄	—	8	2	no	—
891	C₂×C₄	—	8	2	no	—
892	C₂×C₄	—	8	2	no	—
893	C₂×C₄	—	8	2	no	—
894	C₂×C₄	—	8	2	no	—
895	C₂×C₄	C₂×C₄×D₄	1	1	yes	characteristic
896	C₂×C₄	C₂×C₄×D₄	1	1	yes	characteristic
897	C₂×C₄	C₂×C₄×D₄	1	1	yes	characteristic
898	C₂×C₄	C₂×C₄×D₄	1	1	yes	characteristic
899	C₂×C₄	C₂×C₄×D₄	1	1	yes	characteristic
900	C₂×C₄	C₂×C₄×D₄	1	1	yes	characteristic
901	C₂×C₄	C₂×C₄×D₄	1	1	yes	characteristic
902	C₂×C₄	C₂×C₄×D₄	1	1	yes	characteristic
903	C₂×C₄	C₂×C₄×D₄	1	1	yes	characteristic
904	C₂×C₄	C₂⁴×C₄	1	1	yes	characteristic
905	C₂×C₄	C₂³×D₄	1	1	yes	characteristic
906	C₂×C₄	C₂²×#41	1	1	yes	characteristic
907	C₈	—	2	1	no	—
908	C₈	—	2	1	no	—
909	C₈	—	2	1	no	—
910	C₈	—	2	1	no	—
911	C₈	—	2	1	no	—
912	C₈	—	2	1	no	—
913	C₈	—	2	1	no	—
914	C₈	—	2	1	no	—
915	C₈	—	2	1	no	—
916	C₈	—	2	1	no	—
917	C₈	—	2	1	no	—
918	C₈	—	2	1	no	—
919	C₈	—	2	1	no	—
920	C₈	—	2	1	no	—
921	C₈	—	4	1	no	—
922	C₈	—	4	1	no	—
923	C₈	—	4	1	no	—
924	C₈	—	4	1	no	—
925	C₈	—	4	2	no	—
926	C₈	—	4	2	no	—
927	C₈	—	4	2	no	—
928	C₈	—	4	2	no	—
929	C₈	C₂×#131	1	2	yes	—
930	C₈	#576	1	2	yes	—
931	C₂²	—	2	1	no	—
932	C₂²	—	2	1	no	—
933	C₂²	—	2	1	no	—
934	C₂²	—	2	1	no	—
935	C₂²	—	2	1	no	—
936	C₂²	—	2	1	no	—
937	C₂²	—	2	1	no	—
938	C₂²	—	2	1	no	—
939	C₂²	—	2	4	no	—
940	C₂²	—	4	2	no	—
941	C₂²	—	4	2	no	—
942	C₂²	—	4	2	no	—
943	C₂²	—	4	2	no	—
944	C₂²	—	4	2	no	—
945	C₂²	—	4	2	no	—
946	C₂²	—	4	2	no	—
947	C₂²	—	4	2	no	—
948	C₂²	—	8	8	no	—
949	C₂²	—	16	4	no	—
950	C₂²	#2957	1	2	yes	—
951	C₂²	C₂²×C₄×D₄	1	1	yes	characteristic
952	C₄	—	2	1	no	—
953	C₄	—	2	1	no	—
954	C₄	—	2	1	no	—
955	C₄	—	2	1	no	—
956	C₄	—	2	1	no	—
957	C₄	—	2	1	no	—
958	C₄	—	2	1	no	—
959	C₄	—	2	1	no	—
960	C₄	—	2	1	no	—
961	C₄	—	2	1	no	—
962	C₄	—	4	2	no	—
963	C₄	—	4	2	no	—
964	C₄	—	4	2	no	—
965	C₄	—	4	2	no	—
966	C₄	—	4	2	no	—
967	C₄	C₂²×#131	1	1	yes	characteristic
968	C₄	#3573	1	1	yes	characteristic
969	C₄	C₂×#576	1	1	yes	characteristic
970	C₄	#3584	1	1	yes	characteristic
971	C₂	—	2	2	no	—
972	C₂	—	4	1	no	—
973	C₂	—	4	1	no	—
974	C₂	—	4	4	no	—
975	C₂	—	8	2	no	—
976	C₂	—	8	2	no	—
977	C₂	D₄×#131	1	1	yes	characteristic
978	C₂	C₄×#576	1	1	yes	characteristic
979	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. #60311	C₂	semidirect
3. #18087	C₂	semidirect
4. #18069	C₂	semidirect
5. #18066	C₂	semidirect
6. #18054	C₂	semidirect
7. #18035	C₂	semidirect
8. M₁₆×D₈	C₂	semidirect
9. #18020	C₂	semidirect
10. #18007	C₂	semidirect
11. #18006	C₂	semidirect
12. #17973	C₂	semidirect
13. #17970	C₂	semidirect
14. #17959	C₂	semidirect
15. #17920	C₂	semidirect
16. #17918	C₂	semidirect
17. #17914	C₂	semidirect
18. #17857	C₂	semidirect
19. #17854	C₂	semidirect
20. C₂×C₈×D₈	C₂	semidirect
21. #17836	C₂	semidirect
22. #17521	C₂	semidirect
23. #17328	C₂	semidirect
43. #2994	C₂²	semidirect
44. #2993	C₂²	semidirect
47. #2988	C₂²	semidirect
48. #2981	C₂²	semidirect
52. #2974	C₂²	semidirect
53. #2972	C₂²	semidirect
54. #2970	C₂²	semidirect
55. #2969	C₂²	semidirect
57. #2966	C₂²	semidirect
63. #2935	C₂²	semidirect
64. D₄×M₁₆	C₂²	semidirect
68. C₂×C₈×D₄	C₂²	semidirect
70. #1594	C₂²	semidirect
71. #1592	C₂²	semidirect
72. #1591	C₂²	semidirect
73. #1591	C₂²	semidirect
74. #1590	C₂²	semidirect
75. #1589	C₂²	semidirect
76. #1589	C₂²	semidirect
77. #1589	C₂²	semidirect
78. #1589	C₂²	semidirect
79. #1588	C₂²	semidirect
80. #1586	C₂²	semidirect
81. #1586	C₂²	semidirect
82. #1585	C₂²	semidirect
83. #1583	C₂²	semidirect
84. #1582	C₂²	semidirect
85. #1582	C₂²	semidirect
86. #1582	C₂²	semidirect
87. #1581	C₂²	semidirect
88. #1581	C₂²	semidirect
89. #1581	C₂²	semidirect
90. #1581	C₂²	semidirect
91. #1580	C₂²	semidirect
92. #1580	C₂²	semidirect
93. #1580	C₂²	semidirect
94. SD₁₆⋊C₈	C₂²	semidirect
95. SD₁₆⋊C₈	C₂²	semidirect
96. SD₁₆⋊C₈	C₂²	semidirect
97. C₈×Q₁₆	C₂²	semidirect
98. C₈×Q₁₆	C₂²	semidirect
99. C₈×SD₁₆	C₂²	semidirect
104. C₈×D₈	C₂²	semidirect
105. C₈×D₈	C₂²	semidirect
106. C₈×D₈	C₂²	semidirect
107. C₈×D₈	C₂²	semidirect
108. C₈×D₈	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. #1567	C₂²	semidirect
116. #1564	C₂²	semidirect
117. C₂×#335	C₂²	semidirect
118. C₂×#335	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. #1452	C₂²	semidirect
136. #1451	C₂²	semidirect
137. #1450	C₂²	semidirect
138. #1450	C₂²	semidirect
139. C₈×M₁₆	C₂²	semidirect
140. C₈×M₁₆	C₂²	semidirect
141. C₈×M₁₆	C₂²	semidirect
142. C₂×C₈²	C₂²	semidirect
714. D₈	#131	semidirect

Maximal subgroups

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

subgroup	index
#61431	2
#60311	2
#18087	2
#18069	2
#18066	2
#18054	2
#18035	2
M₁₆×D₈	2
#18020	2
#18007	2
#18006	2
#17973	2
#17970	2
#17959	2
#17920	2
#17918	2
#17914	2
#17857	2
#17854	2
C₂×C₈×D₈	2
#17836	2
#17521	2
#17328	2