Subgroups — #6345970

Order 512.

1510 conjugacy classes of subgroups.

The subgroup lattice has 923 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#61427	C₂	1	1	yes	maximal, characteristic
2	#60300	C₂	1	2	yes	maximal, complemented
3	#18093	C₂	1	1	yes	maximal, characteristic, complemented
4	#18090	C₂	1	1	yes	maximal, characteristic, complemented
5	#18075	C₂	1	1	yes	maximal, characteristic, complemented
6	#18064	C₂	1	1	yes	maximal, characteristic, complemented
7	#18063	C₂	1	1	yes	maximal, characteristic, complemented
8	#18043	C₂	1	1	yes	maximal, characteristic, complemented
9	#18033	C₂	1	2	yes	maximal, complemented
10	#18028	C₂	1	2	yes	maximal, complemented
11	#17999	C₂	1	2	yes	maximal, complemented
12	#17974	C₂	1	1	yes	maximal, characteristic, complemented
13	#17972	C₂	1	1	yes	maximal, characteristic, complemented
14	#17963	C₂	1	1	yes	maximal, characteristic, complemented
15	#17954	C₂	1	2	yes	maximal, complemented
16	#17952	C₂	1	2	yes	maximal, complemented
17	#17932	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	#17890	C₂	1	1	yes	maximal, characteristic, complemented
21	#17827	C₂	1	1	yes	maximal, characteristic, complemented
22	#17513	C₂	1	2	yes	maximal, complemented
23	#17330	C₂	1	1	yes	maximal, characteristic, complemented
24	#3475	C₂²	1	2	yes	—
25	#3393	C₄	1	1	yes	characteristic
26	#3380	C₄	1	1	yes	characteristic
27	#3360	C₄	1	2	yes	—
28	#3341	C₄	1	1	yes	characteristic
29	#3336	C₄	1	1	yes	characteristic
30	#3336	C₄	1	1	yes	characteristic
31	#3303	C₄	1	2	yes	—
32	#3296	C₄	1	2	yes	—
33	#3296	C₄	1	2	yes	—
34	#3283	C₄	1	1	yes	characteristic
35	#3280	C₄	1	1	yes	characteristic
36	#3280	C₄	1	1	yes	characteristic
37	#3170	C₂²	1	1	yes	characteristic
38	#3168	C₂²	1	1	yes	characteristic
39	#3168	C₂²	1	1	yes	characteristic
40	#3102	C₂²	1	2	yes	—
41	#3102	C₂²	1	2	yes	—
42	#3101	C₂²	1	2	yes	—
43	#2995	—	2	2	no	—
44	#2994	C₂²	1	2	yes	complemented
45	#2993	—	2	2	no	—
46	#2993	C₂²	1	2	yes	complemented
47	#2991	C₂²	1	2	yes	complemented
48	#2989	C₂²	1	2	yes	complemented
49	#2986	C₂²	1	2	yes	—
50	#2985	C₂²	1	2	yes	—
51	#2978	—	2	2	no	—
52	#2976	—	2	2	no	—
53	#2975	C₂²	1	2	yes	—
54	#2974	C₂²	1	2	yes	—
55	#2971	C₂²	1	2	yes	complemented
56	#2969	—	2	2	no	—
57	#2969	C₂²	1	2	yes	complemented
58	#2967	—	2	2	no	—
59	#2966	C₂²	1	2	yes	complemented
60	#2965	C₂²	1	1	yes	characteristic
61	#2965	C₂²	1	2	yes	complemented
62	C₈×#41	C₂²	1	1	yes	characteristic
63	C₄×#135	C₂²	1	1	yes	characteristic
64	C₄×#135	C₂²	1	1	yes	characteristic
65	C₂×C₄×D₈	C₂²	1	1	yes	characteristic
66	#2925	C₂²	1	2	yes	—
67	#2924	—	2	2	no	—
68	#2922	C₂²	1	1	yes	characteristic
69	#2921	—	2	2	no	—
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	1	yes	characteristic
75	#1594	C₂²	1	1	yes	characteristic
76	#1593	C₂²	1	1	yes	characteristic, complemented
77	#1593	C₂²	1	1	yes	characteristic, complemented
78	#1593	C₂²	1	1	yes	characteristic, complemented
79	#1593	C₂²	1	1	yes	characteristic, complemented
80	#1592	C₂²	1	2	yes	complemented
81	#1592	C₂²	1	2	yes	complemented
82	#1592	C₂²	1	2	yes	complemented
83	#1591	C₂²	1	2	yes	complemented
84	#1590	C₂²	1	2	yes	complemented
85	#1590	C₂²	1	2	yes	complemented
86	#1590	C₂²	1	2	yes	complemented
87	#1589	C₂²	1	2	yes	—
88	#1589	C₂²	1	2	yes	—
89	#1588	C₂²	1	2	yes	complemented
90	#1588	C₂²	1	2	yes	complemented
91	#1588	C₂²	1	2	yes	complemented
92	#1585	C₂²	1	2	yes	complemented
93	#1584	C₂²	1	2	yes	complemented
94	#1584	C₂²	1	2	yes	complemented
95	#1583	C₂²	1	2	yes	complemented
96	#1583	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	—
100	#1581	C₂²	1	2	yes	—
101	#1580	C₂²	1	1	yes	characteristic
102	#1580	C₂²	1	1	yes	characteristic
103	#1579	C₂²	1	1	yes	characteristic, complemented
104	#1579	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×Q₁₆	C₂²	1	2	yes	complemented
109	C₈×SD₁₆	C₂²	1	2	yes	complemented
110	#1572	C₂²	1	2	yes	—
111	#1572	C₂²	1	2	yes	complemented
112	#1571	C₂²	1	2	yes	complemented
113	#1568	C₂²	1	1	yes	characteristic
114	#1568	C₂²	1	1	yes	characteristic, complemented
115	#1566	C₂²	1	1	yes	characteristic, complemented
116	#1564	C₂²	1	1	yes	characteristic
117	#1564	C₂²	1	1	yes	characteristic, complemented
118	C₂×#334	C₂²	1	1	yes	characteristic, complemented
119	#1497	C₂²	1	2	yes	—
120	#1495	C₂²	1	2	yes	complemented
121	#1494	C₂²	1	2	yes	complemented
122	#1490	C₂²	1	2	yes	—
123	#1489	C₂²	1	2	yes	complemented
124	#1488	C₂²	1	2	yes	complemented
125	#1485	C₂²	1	2	yes	—
126	#1483	C₂²	1	2	yes	complemented
127	#1482	C₂²	1	2	yes	complemented
128	#1478	C₂²	1	2	yes	—
129	#1477	C₂²	1	2	yes	complemented
130	#1476	C₂²	1	2	yes	complemented
131	#1454	C₂²	1	1	yes	characteristic
132	#1454	C₂²	1	1	yes	characteristic, complemented
133	#1453	C₂²	1	1	yes	characteristic
134	#1453	C₂²	1	1	yes	characteristic, complemented
135	#1451	C₂²	1	1	yes	characteristic
136	#1451	C₂²	1	1	yes	characteristic, complemented
137	#1451	C₂²	1	1	yes	characteristic, complemented
138	#1450	C₂²	1	1	yes	characteristic
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	C₂×#135	C₂×C₄	1	1	yes	characteristic
145	C₂²×D₈	C₂×C₄	1	1	yes	characteristic
146	#556	C₂×C₄	1	2	yes	—
147	#555	C₂×C₄	1	2	yes	—
148	#554	C₂×C₄	1	2	yes	—
149	#553	—	2	2	no	—
150	#552	—	2	2	no	—
151	#552	C₂×C₄	1	2	yes	—
152	#552	C₂×C₄	1	2	yes	—
153	#551	—	2	2	no	—
154	#551	—	2	2	no	—
155	#547	C₂×C₄	1	2	yes	—
156	#546	C₂×C₄	1	2	yes	—
157	#546	C₂×C₄	1	2	yes	—
158	#533	C₂³	1	2	yes	—
159	#529	—	2	2	no	—
160	#529	—	2	2	no	—
161	#529	C₂³	1	2	yes	—
162	#529	C₂³	1	2	yes	—
163	#525	—	2	2	no	—
164	C₄×#41	C₂³	1	2	yes	—
165	C₄×#41	C₂³	1	2	yes	—
166	C₄×#41	C₂³	1	1	yes	characteristic
167	C₂×C₄×D₄	C₂³	1	2	yes	—
168	C₂×#117	—	2	2	no	—
169	#500	C₂×C₄	1	1	yes	characteristic
170	#499	C₂×C₄	1	1	yes	characteristic
171	#499	C₂×C₄	1	1	yes	characteristic
172	#495	C₂×C₄	1	1	yes	characteristic
173	#495	C₂×C₄	1	1	yes	characteristic
174	#494	C₂×C₄	1	1	yes	characteristic
175	#488	C₂×C₄	1	2	yes	—
176	#488	C₂×C₄	1	2	yes	—
177	#487	C₂×C₄	1	2	yes	—
178	#485	C₂×C₄	1	2	yes	—
179	#485	C₂×C₄	1	2	yes	—
180	#483	C₂×C₄	1	2	yes	—
181	#483	C₂×C₄	1	2	yes	—
182	#482	C₂×C₄	1	2	yes	—
183	#482	C₂×C₄	1	2	yes	—
184	#479	C₂×C₄	1	2	yes	—
185	#479	C₂×C₄	1	2	yes	—
186	#478	C₂×C₄	1	2	yes	—
187	#478	C₂×C₄	1	2	yes	—
188	#476	C₂×C₄	1	2	yes	—
189	#476	C₂×C₄	1	2	yes	—
190	#467	C₂×C₄	1	1	yes	characteristic
191	#467	C₂×C₄	1	1	yes	characteristic
192	#467	C₂×C₄	1	1	yes	characteristic
193	#467	C₂×C₄	1	1	yes	characteristic
194	#467	C₂×C₄	1	2	yes	—
195	#466	C₂×C₄	1	1	yes	characteristic
196	#466	C₂×C₄	1	1	yes	characteristic
197	#465	C₂×C₄	1	2	yes	—
198	#465	C₂×C₄	1	2	yes	—
199	#464	C₂×C₄	1	2	yes	—
200	#464	C₂×C₄	1	2	yes	—
201	#463	C₂×C₄	1	2	yes	—
202	#463	C₂×C₄	1	2	yes	—
203	#461	C₂×C₄	1	2	yes	—
204	#461	C₂×C₄	1	2	yes	—
205	#452	C₂×C₄	1	2	yes	—
206	#452	C₂×C₄	1	2	yes	—
207	#450	C₂×C₄	1	2	yes	—
208	#450	C₂×C₄	1	2	yes	—
209	#449	C₂×C₄	1	2	yes	—
210	#449	C₂×C₄	1	2	yes	—
211	#446	—	2	1	no	—
212	#446	—	2	2	no	—
213	#446	—	2	2	no	—
214	#446	—	2	2	no	—
215	#446	C₂³	1	2	yes	—
216	#446	C₂³	1	2	yes	—
217	#446	C₂³	1	2	yes	—
218	#446	C₂³	1	2	yes	—
219	C₈×Q₈	—	2	2	no	—
220	C₈×Q₈	C₂×C₄	1	1	yes	characteristic
221	C₈×Q₈	C₂×C₄	1	1	yes	characteristic
222	C₈×Q₈	C₂³	1	2	yes	—
223	C₈×Q₈	C₂³	1	2	yes	—
224	C₈×Q₈	C₂³	1	2	yes	—
225	C₈×Q₈	C₂³	1	2	yes	—
226	C₄×Q₁₆	C₂×C₄	1	1	yes	characteristic
227	C₄×Q₁₆	C₂×C₄	1	1	yes	characteristic
228	C₄×Q₁₆	C₂³	1	2	yes	—
229	C₄×Q₁₆	C₂³	1	1	yes	characteristic
230	C₄×Q₁₆	C₂³	1	1	yes	characteristic
231	C₄×SD₁₆	C₂×C₄	1	2	yes	—
232	C₄×SD₁₆	C₂×C₄	1	2	yes	—
233	C₄×SD₁₆	C₂³	1	2	yes	—
234	C₄×SD₁₆	C₂³	1	2	yes	—
235	C₄×SD₁₆	C₂³	1	2	yes	—
236	C₄×SD₁₆	C₂³	1	2	yes	—
237	C₄×D₈	C₂×C₄	1	1	yes	characteristic
238	C₄×D₈	C₂×C₄	1	2	yes	—
239	C₄×D₈	C₂×C₄	1	1	yes	characteristic
240	C₄×D₈	C₂×C₄	1	1	yes	characteristic
241	C₄×D₈	C₂×C₄	1	1	yes	characteristic
242	C₄×D₈	C₂³	1	2	yes	—
243	C₄×D₈	C₂³	1	1	yes	characteristic
244	C₄×D₈	C₂³	1	1	yes	characteristic
245	#436	—	2	2	no	—
246	#436	—	2	2	no	—
247	#436	—	2	2	no	—
248	#436	—	2	1	no	—
249	#436	—	2	2	no	—
250	#436	—	2	2	no	—
251	#436	—	2	2	no	—
252	#436	—	2	2	no	—
253	#436	—	2	2	no	—
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	#436	C₂³	1	2	yes	—
259	#436	C₂³	1	2	yes	—
260	#435	—	2	2	no	—
261	#435	—	2	2	no	—
262	#435	—	2	2	no	—
263	#435	—	2	2	no	—
264	#435	—	2	1	no	—
265	#435	—	2	1	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	C₈×D₄	—	2	2	no	—
273	C₈×D₄	—	2	2	no	—
274	C₈×D₄	C₂×C₄	1	1	yes	characteristic
275	C₈×D₄	C₂×C₄	1	1	yes	characteristic
276	C₈×D₄	C₂×C₄	1	1	yes	characteristic
277	C₈×D₄	C₂×C₄	1	1	yes	characteristic
278	C₈×D₄	C₂×C₄	1	1	yes	characteristic
279	C₈×D₄	C₂×C₄	1	1	yes	characteristic
280	C₈×D₄	C₂³	1	2	yes	—
281	C₈×D₄	C₂³	1	2	yes	—
282	#433	—	2	2	no	—
283	#433	—	2	2	no	—
284	#433	—	2	2	no	—
285	#433	—	2	2	no	—
286	#433	—	2	2	no	—
287	#433	—	2	2	no	—
288	#433	—	2	2	no	—
289	#433	—	2	2	no	—
290	#433	—	2	2	no	—
291	#433	—	2	2	no	—
292	#433	D₄	1	2	yes	—
293	#433	D₄	1	2	yes	—
294	#432	—	2	2	no	—
295	#432	—	2	2	no	—
296	#432	C₂³	1	2	yes	—
297	#432	C₂³	1	2	yes	—
298	#431	—	2	2	no	—
299	#431	—	2	2	no	—
300	#431	C₂³	1	2	yes	—
301	#431	C₂³	1	2	yes	—
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	#431	C₂³	1	1	yes	characteristic
311	#431	C₂³	1	1	yes	characteristic
312	#427	C₂×C₄	1	1	yes	characteristic
313	#427	C₂×C₄	1	1	yes	characteristic
314	C₂×#107	C₂×C₄	1	1	yes	characteristic
315	#424	—	2	2	no	—
316	#424	—	2	2	no	—
317	#424	D₄	1	2	yes	—
318	#423	—	2	2	no	—
319	#423	—	2	2	no	—
320	#423	C₂³	1	2	yes	—
321	C₂×C₄⋊C₈	C₂³	1	2	yes	—
322	#416	C₂×C₄	1	2	yes	—
323	#416	C₂×C₄	1	2	yes	—
324	C₂×#102	C₂×C₄	1	2	yes	—
325	#408	—	2	2	no	—
326	#408	D₄	1	2	yes	—
327	#407	—	2	2	no	—
328	#407	—	2	2	no	—
329	#407	—	2	2	no	—
330	C₂×C₂²⋊C₈	—	2	2	no	—
331	#405	—	2	2	no	—
332	#405	—	2	2	no	—
333	#405	—	2	2	no	—
334	C₄×M₁₆	—	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	#335	C₂³	1	2	yes	—
348	#334	C₂³	1	1	yes	characteristic
349	#334	C₂³	1	1	yes	characteristic
350	#334	C₂³	1	2	yes	—
351	#334	C₂³	1	1	yes	characteristic
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	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	#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	C₂²×C₄	1	2	yes	—
387	C₂×#41	C₂²×C₄	1	2	yes	—
388	C₂×#41	C₂×D₄	1	1	yes	characteristic
389	C₂²×D₄	C₂²×C₄	1	2	yes	—
390	C₂³×C₄	—	2	2	no	—
391	#135	—	4	2	no	—
392	#135	—	4	2	no	—
393	C₂×Q₁₆	C₂²×C₄	1	1	yes	characteristic
394	C₂×Q₁₆	C₂²×C₄	1	1	yes	characteristic
395	C₂×Q₁₆	C₂²×C₄	1	2	yes	—
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×SD₁₆	C₂²×C₄	1	2	yes	—
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	2	yes	—
404	C₂×M₁₆	—	2	2	no	—
405	C₂×M₁₆	—	2	1	no	—
406	C₂×M₁₆	—	2	1	no	—
407	C₂×M₁₆	—	2	2	no	—
408	C₂×M₁₆	—	2	2	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	C₂×D₄	1	2	yes	—
414	C₂²×C₈	—	2	2	no	—
415	C₂²×C₈	—	2	1	no	—
416	C₂²×C₈	—	2	2	no	—
417	C₂²×C₈	—	2	2	no	—
418	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
419	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
420	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
421	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
422	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
423	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
424	C₂²×C₈	C₂×D₄	1	2	yes	—
425	C₄⋊Q₈	C₂²×C₄	1	2	yes	—
426	C₄⋊Q₈	C₂²×C₄	1	2	yes	—
427	#126	—	2	2	no	—
428	#126	—	2	2	no	—
429	#126	—	2	2	no	—
430	#126	—	2	2	no	—
431	#126	—	2	2	no	—
432	#126	—	2	2	no	—
433	#125	—	2	2	no	—
434	#125	—	2	2	no	—
435	#125	—	2	2	no	—
436	#125	C₂²×C₄	1	2	yes	—
437	#125	C₂²×C₄	1	2	yes	—
438	#124	—	2	2	no	—
439	#124	—	2	2	no	—
440	#124	C₂²×C₄	1	2	yes	—
441	#124	C₂²×C₄	1	2	yes	—
442	#123	—	2	2	no	—
443	#123	—	2	2	no	—
444	#123	—	2	2	no	—
445	#123	—	2	2	no	—
446	#123	—	2	2	no	—
447	#123	—	2	2	no	—
448	#123	—	2	2	no	—
449	#123	—	2	2	no	—
450	C₂²⋊Q₈	—	2	2	no	—
451	C₂²⋊Q₈	—	2	2	no	—
452	C₂²⋊Q₈	—	2	2	no	—
453	C₂²⋊Q₈	—	2	2	no	—
454	C₂²⋊Q₈	—	2	2	no	—
455	C₂²⋊Q₈	C₂²×C₄	1	2	yes	—
456	C₂²⋊Q₈	C₂²×C₄	1	2	yes	—
457	C₂²⋊Q₈	C₂²×C₄	1	2	yes	—
458	C₂²⋊Q₈	C₂²×C₄	1	2	yes	—
459	#121	—	2	2	no	—
460	#121	—	2	2	no	—
461	#121	—	2	2	no	—
462	#121	—	2	2	no	—
463	#121	C₂²×C₄	1	2	yes	—
464	#121	C₂²×C₄	1	2	yes	—
465	#120	—	2	2	no	—
466	#120	—	2	2	no	—
467	C₄×Q₈	—	2	2	no	—
468	C₄×Q₈	C₂²×C₄	1	2	yes	—
469	C₄×Q₈	C₂²×C₄	1	2	yes	—
470	C₄×Q₈	C₂²×C₄	1	1	yes	characteristic
471	C₄×Q₈	#41	1	1	yes	characteristic
472	C₄×Q₈	C₂⁴	1	2	yes	—
473	C₄×Q₈	C₂⁴	1	2	yes	—
474	C₄×D₄	—	2	2	no	—
475	C₄×D₄	—	2	2	no	—
476	C₄×D₄	—	2	2	no	—
477	C₄×D₄	—	2	2	no	—
478	C₄×D₄	—	2	2	no	—
479	C₄×D₄	—	2	2	no	—
480	C₄×D₄	—	2	2	no	—
481	C₄×D₄	—	2	2	no	—
482	C₄×D₄	C₂²×C₄	1	2	yes	—
483	C₄×D₄	C₂²×C₄	1	2	yes	—
484	C₄×D₄	C₂²×C₄	1	2	yes	—
485	C₄×D₄	C₂²×C₄	1	2	yes	—
486	C₄×D₄	C₂²×C₄	1	1	yes	characteristic
487	C₄×D₄	C₂²×C₄	1	1	yes	characteristic
488	C₄×D₄	C₂²×C₄	1	1	yes	characteristic
489	C₄×D₄	#41	1	1	yes	characteristic
490	C₄×D₄	#41	1	1	yes	characteristic
491	C₄×D₄	#41	1	1	yes	characteristic
492	C₄×D₄	C₂⁴	1	2	yes	—
493	C₄×D₄	C₂⁴	1	2	yes	—
494	#117	—	2	2	no	—
495	#117	—	2	2	no	—
496	#117	—	2	2	no	—
497	#117	—	2	2	no	—
498	#117	—	2	2	no	—
499	#117	—	2	2	no	—
500	#117	—	2	2	no	—
501	#117	—	2	2	no	—
502	#117	—	2	2	no	—
503	#117	C₂²×C₄	1	2	yes	—
504	#117	C₂²×C₄	1	2	yes	—
505	#117	C₂×D₄	1	1	yes	characteristic
506	#117	C₂×D₄	1	1	yes	characteristic
507	#117	C₂×D₄	1	1	yes	characteristic
508	C₂×C₄⋊C₄	—	2	2	no	—
509	C₂×C₄⋊C₄	—	2	2	no	—
510	C₂×C₄⋊C₄	C₂²×C₄	1	2	yes	—
511	C₂×C₂²⋊C₄	—	2	2	no	—
512	C₂×C₂²⋊C₄	—	2	2	no	—
513	C₂×C₂²⋊C₄	—	2	2	no	—
514	C₂×C₄²	—	2	2	no	—
515	C₂×C₄²	—	2	2	no	—
516	C₂×C₄²	C₂⁴	1	1	yes	characteristic
517	C₂×C₄²	C₂⁴	1	1	yes	characteristic
518	C₂×C₄²	C₂⁴	1	1	yes	characteristic
519	#107	C₂²×C₄	1	1	yes	characteristic
520	#107	C₂²×C₄	1	1	yes	characteristic
521	#107	C₂²×C₄	1	2	yes	—
522	#107	C₂²×C₄	1	1	yes	characteristic
523	#107	C₂²×C₄	1	1	yes	characteristic
524	#107	C₂²×C₄	1	2	yes	—
525	#106	C₂²×C₄	1	2	yes	—
526	#106	C₂²×C₄	1	2	yes	—
527	#106	C₂²×C₄	1	2	yes	—
528	#106	C₂²×C₄	1	2	yes	—
529	C₄⋊C₈	—	2	2	no	—
530	C₄⋊C₈	—	2	2	no	—
531	C₄⋊C₈	—	2	2	no	—
532	C₄⋊C₈	—	2	2	no	—
533	C₄⋊C₈	—	2	2	no	—
534	C₄⋊C₈	—	2	2	no	—
535	C₄⋊C₈	—	2	2	no	—
536	C₄⋊C₈	—	2	2	no	—
537	C₄⋊C₈	—	2	2	no	—
538	C₄⋊C₈	—	2	2	no	—
539	C₄⋊C₈	—	2	1	no	—
540	C₄⋊C₈	—	2	1	no	—
541	C₄⋊C₈	—	2	1	no	—
542	C₄⋊C₈	C₂²×C₄	1	1	yes	characteristic
543	C₄⋊C₈	C₂²×C₄	1	1	yes	characteristic
544	C₄⋊C₈	C₂²×C₄	1	1	yes	characteristic
545	C₄⋊C₈	C₂²×C₄	1	1	yes	characteristic
546	C₄⋊C₈	C₂²×C₄	1	1	yes	characteristic
547	C₄⋊C₈	C₂²×C₄	1	1	yes	characteristic
548	C₄⋊C₈	C₂×D₄	1	2	yes	—
549	C₄⋊C₈	C₂×D₄	1	2	yes	—
550	C₄⋊C₈	C₂×D₄	1	2	yes	—
551	C₄⋊C₈	C₂×D₄	1	2	yes	—
552	C₄⋊C₈	C₂⁴	1	2	yes	—
553	C₄⋊C₈	C₂⁴	1	2	yes	—
554	C₄⋊C₈	C₂⁴	1	2	yes	—
555	C₄⋊C₈	C₂⁴	1	2	yes	—
556	#103	C₂²×C₄	1	2	yes	—
557	#103	C₂²×C₄	1	2	yes	—
558	#103	C₂²×C₄	1	2	yes	—
559	#103	C₂²×C₄	1	2	yes	—
560	#103	C₂²×C₄	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	#102	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	C₂²⋊C₈	—	2	2	no	—
573	C₂²⋊C₈	—	2	2	no	—
574	C₂²⋊C₈	—	2	2	no	—
575	C₂²⋊C₈	—	2	2	no	—
576	C₂²⋊C₈	—	2	1	no	—
577	C₂²⋊C₈	—	2	1	no	—
578	C₂²⋊C₈	—	2	1	no	—
579	C₂²⋊C₈	—	2	2	no	—
580	C₂²⋊C₈	—	2	2	no	—
581	C₂²⋊C₈	—	2	2	no	—
582	C₂²⋊C₈	—	2	2	no	—
583	C₂²⋊C₈	—	2	2	no	—
584	C₂²⋊C₈	—	2	2	no	—
585	C₂²⋊C₈	—	2	2	no	—
586	C₂²⋊C₈	—	2	2	no	—
587	C₂²⋊C₈	C₂²×C₄	1	1	yes	characteristic
588	C₂²⋊C₈	C₂²×C₄	1	1	yes	characteristic
589	C₂²⋊C₈	C₂²×C₄	1	1	yes	characteristic
590	C₂²⋊C₈	C₂²×C₄	1	1	yes	characteristic
591	C₂²⋊C₈	C₂²×C₄	1	1	yes	characteristic
592	C₂²⋊C₈	C₂²×C₄	1	1	yes	characteristic
593	C₂²⋊C₈	C₂×D₄	1	2	yes	—
594	C₂²⋊C₈	C₂×D₄	1	2	yes	—
595	C₂²⋊C₈	C₂×D₄	1	2	yes	—
596	C₂²⋊C₈	C₂×D₄	1	2	yes	—
597	#97	—	2	2	no	—
598	#97	—	2	2	no	—
599	#97	—	2	2	no	—
600	#97	—	2	2	no	—
601	#97	—	2	2	no	—
602	#97	—	2	2	no	—
603	#97	—	2	1	no	—
604	#97	—	2	1	no	—
605	#97	C₂×D₄	1	2	yes	—
606	C₄×C₈	—	2	2	no	—
607	C₄×C₈	—	2	2	no	—
608	C₄×C₈	—	2	2	no	—
609	C₄×C₈	—	2	2	no	—
610	C₄×C₈	—	2	2	no	—
611	C₄×C₈	—	2	2	no	—
612	C₄×C₈	—	2	1	no	—
613	C₄×C₈	C₂²×C₄	1	1	yes	characteristic
614	C₄×C₈	C₂²×C₄	1	1	yes	characteristic
615	C₄×C₈	C₂²×C₄	1	1	yes	characteristic
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	C₂×D₄	1	2	yes	—
620	C₄×C₈	C₂⁴	1	1	yes	characteristic
621	C₄×C₈	C₂⁴	1	1	yes	characteristic
622	C₄×C₈	C₂⁴	1	1	yes	characteristic
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	C₂⁴	—	2	2	no	—
633	#41	—	4	2	no	—
634	#41	—	4	2	no	—
635	#41	—	4	2	no	—
636	#41	—	4	2	no	—
637	#41	—	4	2	no	—
638	C₂×Q₈	—	2	2	no	—
639	C₂×Q₈	C₄×D₄	1	1	yes	characteristic
640	C₂×Q₈	C₂³×C₄	1	2	yes	—
641	C₂×Q₈	C₂³×C₄	1	2	yes	—
642	C₂×D₄	—	2	2	no	—
643	C₂×D₄	—	2	2	no	—
644	C₂×D₄	—	2	2	no	—
645	C₂×D₄	—	2	2	no	—
646	C₂×D₄	—	2	2	no	—
647	C₂×D₄	—	4	2	no	—
648	C₂×D₄	—	4	2	no	—
649	C₂×D₄	C₄×D₄	1	1	yes	characteristic
650	C₂×D₄	C₄×D₄	1	1	yes	characteristic
651	C₂×D₄	C₄×D₄	1	1	yes	characteristic
652	C₂×D₄	C₂³×C₄	1	2	yes	—
653	C₂×D₄	C₂³×C₄	1	2	yes	—
654	C₂²×C₄	—	2	2	no	—
655	C₂²×C₄	—	2	2	no	—
656	C₂²×C₄	—	2	2	no	—
657	C₂²×C₄	—	2	2	no	—
658	C₂²×C₄	—	2	2	no	—
659	C₂²×C₄	—	2	2	no	—
660	C₂²×C₄	—	2	2	no	—
661	C₂²×C₄	—	2	2	no	—
662	C₂²×C₄	—	2	2	no	—
663	C₂²×C₄	—	8	2	no	—
664	C₂²×C₄	—	8	2	no	—
665	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
666	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
667	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
668	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
669	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
670	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
671	C₂²×C₄	C₂×#41	1	1	yes	characteristic
672	C₂²×C₄	C₂×#41	1	1	yes	characteristic
673	C₂²×C₄	C₂×#41	1	1	yes	characteristic
674	Q₁₆	—	2	2	no	—
675	Q₁₆	—	2	2	no	—
676	Q₁₆	—	4	2	no	—
677	SD₁₆	—	4	2	no	—
678	SD₁₆	—	4	2	no	—
679	SD₁₆	—	4	2	no	—
680	SD₁₆	—	4	2	no	—
681	D₈	—	2	2	no	—
682	D₈	—	2	2	no	—
683	D₈	—	4	2	no	—
684	M₁₆	—	4	2	no	—
685	M₁₆	—	8	2	no	—
686	M₁₆	—	8	2	no	—
687	M₁₆	—	8	2	no	—
688	M₁₆	—	8	2	no	—
689	M₁₆	—	8	2	no	—
690	M₁₆	—	8	2	no	—
691	M₁₆	—	8	2	no	—
692	M₁₆	—	8	1	no	—
693	M₁₆	—	8	1	no	—
694	C₂×C₈	—	2	2	no	—
695	C₂×C₈	—	2	2	no	—
696	C₂×C₈	—	2	2	no	—
697	C₂×C₈	—	2	2	no	—
698	C₂×C₈	—	2	2	no	—
699	C₂×C₈	—	2	2	no	—
700	C₂×C₈	—	2	2	no	—
701	C₂×C₈	—	2	1	no	—
702	C₂×C₈	—	2	1	no	—
703	C₂×C₈	—	2	1	no	—
704	C₂×C₈	—	2	1	no	—
705	C₂×C₈	—	4	1	no	—
706	C₂×C₈	—	4	1	no	—
707	C₂×C₈	—	4	1	no	—
708	C₂×C₈	—	4	2	no	—
709	C₂×C₈	—	8	2	no	—
710	C₂×C₈	—	8	2	no	—
711	C₂×C₈	—	8	2	no	—
712	C₂×C₈	—	8	1	no	—
713	C₂×C₈	C₂³×C₄	1	1	yes	characteristic
714	C₂×C₈	C₂³×C₄	1	1	yes	characteristic
715	C₂×C₈	C₂³×C₄	1	1	yes	characteristic
716	C₂×C₈	C₂³×C₄	1	1	yes	characteristic
717	C₂×C₈	C₂³×C₄	1	1	yes	characteristic
718	C₂×C₈	C₂³×C₄	1	1	yes	characteristic
719	C₂×C₈	C₂³×C₄	1	1	yes	characteristic
720	C₂×C₈	C₂³×C₄	1	1	yes	characteristic
721	C₂×C₈	C₂²×D₄	1	2	yes	—
722	C₂×C₈	C₂²×D₄	1	2	yes	—
723	C₂×C₈	C₂²×D₄	1	2	yes	—
724	C₂×C₈	C₂²×D₄	1	2	yes	—
725	C₄⋊C₄	—	2	2	no	—
726	C₄⋊C₄	—	2	2	no	—
727	C₄⋊C₄	—	2	2	no	—
728	C₄⋊C₄	—	2	2	no	—
729	C₄⋊C₄	—	2	2	no	—
730	C₄⋊C₄	—	2	2	no	—
731	C₄⋊C₄	—	2	2	no	—
732	C₄⋊C₄	—	2	2	no	—
733	C₄⋊C₄	—	2	2	no	—
734	C₄⋊C₄	—	2	2	no	—
735	C₄⋊C₄	—	2	2	no	—
736	C₄⋊C₄	—	2	2	no	—
737	C₄⋊C₄	—	2	2	no	—
738	C₄⋊C₄	—	2	2	no	—
739	C₄⋊C₄	—	2	2	no	—
740	C₄⋊C₄	—	2	2	no	—
741	C₄⋊C₄	C₄×D₄	1	1	yes	characteristic
742	C₄⋊C₄	C₄×D₄	1	1	yes	characteristic
743	C₄⋊C₄	C₄×D₄	1	1	yes	characteristic
744	C₄⋊C₄	C₄×D₄	1	1	yes	characteristic
745	C₄⋊C₄	C₄×D₄	1	1	yes	characteristic
746	C₄⋊C₄	C₄×D₄	1	1	yes	characteristic
747	C₄⋊C₄	C₂³×C₄	1	2	yes	—
748	C₄⋊C₄	C₂³×C₄	1	2	yes	—
749	C₄⋊C₄	C₂³×C₄	1	2	yes	—
750	C₄⋊C₄	C₂³×C₄	1	2	yes	—
751	C₂²⋊C₄	—	2	2	no	—
752	C₂²⋊C₄	—	2	2	no	—
753	C₂²⋊C₄	—	2	2	no	—
754	C₂²⋊C₄	—	2	2	no	—
755	C₂²⋊C₄	—	2	2	no	—
756	C₂²⋊C₄	—	2	2	no	—
757	C₂²⋊C₄	—	2	2	no	—
758	C₂²⋊C₄	—	2	2	no	—
759	C₂²⋊C₄	—	2	2	no	—
760	C₂²⋊C₄	—	2	2	no	—
761	C₂²⋊C₄	—	2	2	no	—
762	C₂²⋊C₄	—	2	2	no	—
763	C₂²⋊C₄	—	2	2	no	—
764	C₂²⋊C₄	—	2	2	no	—
765	C₂²⋊C₄	—	2	2	no	—
766	C₂²⋊C₄	—	2	2	no	—
767	C₂²⋊C₄	—	2	2	no	—
768	C₂²⋊C₄	—	2	2	no	—
769	C₂²⋊C₄	C₄×D₄	1	1	yes	characteristic
770	C₂²⋊C₄	C₄×D₄	1	1	yes	characteristic
771	C₂²⋊C₄	C₄×D₄	1	1	yes	characteristic
772	C₂²⋊C₄	C₄×D₄	1	1	yes	characteristic
773	C₂²⋊C₄	C₄×D₄	1	1	yes	characteristic
774	C₂²⋊C₄	C₄×D₄	1	1	yes	characteristic
775	C₄²	—	2	2	no	—
776	C₄²	—	2	2	no	—
777	C₄²	—	2	2	no	—
778	C₄²	—	2	2	no	—
779	C₄²	—	2	2	no	—
780	C₄²	—	2	2	no	—
781	C₄²	C₂³×C₄	1	1	yes	characteristic
782	C₄²	C₂³×C₄	1	1	yes	characteristic
783	C₄²	C₂³×C₄	1	1	yes	characteristic
784	C₄²	C₂²×D₄	1	1	yes	characteristic
785	C₄²	C₂²×D₄	1	1	yes	characteristic
786	C₄²	C₂²×D₄	1	1	yes	characteristic
787	C₄²	C₂×#41	1	1	yes	characteristic
788	C₄²	C₂×#41	1	1	yes	characteristic
789	C₄²	C₂×#41	1	1	yes	characteristic
790	C₄²	C₂⁵	1	1	yes	characteristic
791	C₂³	—	2	2	no	—
792	C₂³	—	2	2	no	—
793	C₂³	—	8	2	no	—
794	C₂³	—	8	2	no	—
795	C₂³	—	8	2	no	—
796	C₂³	C₂×C₄×D₄	1	1	yes	characteristic
797	C₂³	C₂×C₄×D₄	1	1	yes	characteristic
798	C₂³	C₂×C₄×D₄	1	1	yes	characteristic
799	Q₈	—	2	2	no	—
800	Q₈	—	2	2	no	—
801	Q₈	—	2	2	no	—
802	Q₈	—	2	2	no	—
803	Q₈	—	4	1	no	—
804	Q₈	—	8	2	no	—
805	D₄	—	2	2	no	—
806	D₄	—	2	2	no	—
807	D₄	—	2	2	no	—
808	D₄	—	2	2	no	—
809	D₄	—	4	1	no	—
810	D₄	—	4	1	no	—
811	D₄	—	4	1	no	—
812	D₄	—	8	2	no	—
813	D₄	—	8	2	no	—
814	D₄	—	8	2	no	—
815	D₄	—	8	2	no	—
816	D₄	—	8	2	no	—
817	C₂×C₄	—	2	2	no	—
818	C₂×C₄	—	2	2	no	—
819	C₂×C₄	—	2	2	no	—
820	C₂×C₄	—	2	1	no	—
821	C₂×C₄	—	2	1	no	—
822	C₂×C₄	—	2	1	no	—
823	C₂×C₄	—	2	1	no	—
824	C₂×C₄	—	2	1	no	—
825	C₂×C₄	—	2	1	no	—
826	C₂×C₄	—	2	2	no	—
827	C₂×C₄	—	2	2	no	—
828	C₂×C₄	—	2	2	no	—
829	C₂×C₄	—	2	2	no	—
830	C₂×C₄	—	2	2	no	—
831	C₂×C₄	—	2	2	no	—
832	C₂×C₄	—	4	1	no	—
833	C₂×C₄	—	4	1	no	—
834	C₂×C₄	—	4	1	no	—
835	C₂×C₄	—	4	2	no	—
836	C₂×C₄	—	4	2	no	—
837	C₂×C₄	—	4	2	no	—
838	C₂×C₄	—	4	2	no	—
839	C₂×C₄	—	8	2	no	—
840	C₂×C₄	—	8	2	no	—
841	C₂×C₄	—	8	2	no	—
842	C₂×C₄	—	8	2	no	—
843	C₂×C₄	—	8	2	no	—
844	C₂×C₄	—	8	2	no	—
845	C₂×C₄	—	8	2	no	—
846	C₂×C₄	C₂×C₄×D₄	1	1	yes	characteristic
847	C₂×C₄	C₂×C₄×D₄	1	1	yes	characteristic
848	C₂×C₄	C₂×C₄×D₄	1	1	yes	characteristic
849	C₂×C₄	C₂×C₄×D₄	1	1	yes	characteristic
850	C₂×C₄	C₂×C₄×D₄	1	1	yes	characteristic
851	C₂×C₄	C₂×C₄×D₄	1	1	yes	characteristic
852	C₂×C₄	C₂×C₄×D₄	1	1	yes	characteristic
853	C₂×C₄	C₂×C₄×D₄	1	1	yes	characteristic
854	C₂×C₄	C₂×C₄×D₄	1	1	yes	characteristic
855	C₂×C₄	C₂⁴×C₄	1	1	yes	characteristic
856	C₂×C₄	C₂³×D₄	1	1	yes	characteristic
857	C₂×C₄	C₂²×#41	1	1	yes	characteristic
858	C₈	—	2	2	no	—
859	C₈	—	2	2	no	—
860	C₈	—	2	2	no	—
861	C₈	—	2	2	no	—
862	C₈	—	2	1	no	—
863	C₈	—	2	1	no	—
864	C₈	—	2	1	no	—
865	C₈	—	2	1	no	—
866	C₈	—	2	1	no	—
867	C₈	—	2	1	no	—
868	C₈	—	2	1	no	—
869	C₈	—	4	1	no	—
870	C₈	—	4	1	no	—
871	C₈	—	4	1	no	—
872	C₈	—	4	1	no	—
873	C₈	—	4	2	no	—
874	C₈	—	4	2	no	—
875	C₈	—	4	2	no	—
876	C₈	—	4	2	no	—
877	C₈	#568	1	2	yes	—
878	C₂²	—	2	1	no	—
879	C₂²	—	2	1	no	—
880	C₂²	—	2	1	no	—
881	C₂²	—	2	1	no	—
882	C₂²	—	2	1	no	—
883	C₂²	—	2	1	no	—
884	C₂²	—	2	1	no	—
885	C₂²	—	2	1	no	—
886	C₂²	—	2	1	no	—
887	C₂²	—	4	2	no	—
888	C₂²	—	4	2	no	—
889	C₂²	—	4	2	no	—
890	C₂²	—	4	2	no	—
891	C₂²	—	4	2	no	—
892	C₂²	—	4	2	no	—
893	C₂²	—	16	4	no	—
894	C₂²	C₂²×C₄×D₄	1	1	yes	characteristic
895	C₄	—	2	1	no	—
896	C₄	—	2	1	no	—
897	C₄	—	2	1	no	—
898	C₄	—	2	1	no	—
899	C₄	—	2	1	no	—
900	C₄	—	2	1	no	—
901	C₄	—	2	1	no	—
902	C₄	—	2	1	no	—
903	C₄	—	2	1	no	—
904	C₄	—	2	1	no	—
905	C₄	—	4	2	no	—
906	C₄	—	4	2	no	—
907	C₄	—	4	2	no	—
908	C₄	—	4	2	no	—
909	C₄	—	4	2	no	—
910	C₄	—	4	2	no	—
911	C₄	C₂×#568	1	1	yes	characteristic
912	C₄	#3573	1	1	yes	characteristic
913	C₄	#3584	1	2	yes	—
914	C₂	—	4	1	no	—
915	C₂	—	4	1	no	—
916	C₂	—	4	1	no	—
917	C₂	—	8	2	no	—
918	C₂	—	8	2	no	—
919	C₂	#60147	1	1	yes	characteristic
920	C₂	#60167	1	1	yes	characteristic
921	C₂	#60184	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	#61427	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄ ◁ #2922 ◁ G
LECS	G ▷ C₄² ▷ C₂² ▷ C₁

Complements

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

N	H ≅ G/N	type
2. #60300	C₂	semidirect
3. #18093	C₂	semidirect
4. #18090	C₂	semidirect
5. #18075	C₂	semidirect
6. #18064	C₂	semidirect
7. #18063	C₂	semidirect
8. #18043	C₂	semidirect
9. #18033	C₂	semidirect
10. #18028	C₂	semidirect
11. #17999	C₂	semidirect
12. #17974	C₂	semidirect
13. #17972	C₂	semidirect
14. #17963	C₂	semidirect
15. #17954	C₂	semidirect
16. #17952	C₂	semidirect
17. #17932	C₂	semidirect
18. #17899	C₂	semidirect
19. #17895	C₂	semidirect
20. #17890	C₂	semidirect
21. #17827	C₂	semidirect
22. #17513	C₂	semidirect
23. #17330	C₂	semidirect
44. #2994	C₂²	semidirect
46. #2993	C₂²	semidirect
47. #2991	C₂²	semidirect
48. #2989	C₂²	semidirect
55. #2971	C₂²	semidirect
57. #2969	C₂²	semidirect
59. #2966	C₂²	semidirect
61. #2965	C₂²	semidirect
76. #1593	C₂²	semidirect
77. #1593	C₂²	semidirect
78. #1593	C₂²	semidirect
79. #1593	C₂²	semidirect
80. #1592	C₂²	semidirect
81. #1592	C₂²	semidirect
82. #1592	C₂²	semidirect
83. #1591	C₂²	semidirect
84. #1590	C₂²	semidirect
85. #1590	C₂²	semidirect
86. #1590	C₂²	semidirect
89. #1588	C₂²	semidirect
90. #1588	C₂²	semidirect
91. #1588	C₂²	semidirect
92. #1585	C₂²	semidirect
93. #1584	C₂²	semidirect
94. #1584	C₂²	semidirect
95. #1583	C₂²	semidirect
96. #1583	C₂²	semidirect
97. #1583	C₂²	semidirect
98. #1582	C₂²	semidirect
103. #1579	C₂²	semidirect
104. #1579	C₂²	semidirect
105. #1579	C₂²	semidirect
106. #1579	C₂²	semidirect
107. SD₁₆⋊C₈	C₂²	semidirect
108. C₈×Q₁₆	C₂²	semidirect
109. C₈×SD₁₆	C₂²	semidirect
111. #1572	C₂²	semidirect
112. #1571	C₂²	semidirect
114. #1568	C₂²	semidirect
115. #1566	C₂²	semidirect
117. #1564	C₂²	semidirect
118. C₂×#334	C₂²	semidirect
120. #1495	C₂²	semidirect
121. #1494	C₂²	semidirect
123. #1489	C₂²	semidirect
124. #1488	C₂²	semidirect
126. #1483	C₂²	semidirect
127. #1482	C₂²	semidirect
129. #1477	C₂²	semidirect
130. #1476	C₂²	semidirect
132. #1454	C₂²	semidirect
134. #1453	C₂²	semidirect
136. #1451	C₂²	semidirect
137. #1451	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
#61427	2
#60300	2
#18093	2
#18090	2
#18075	2
#18064	2
#18063	2
#18043	2
#18033	2
#18028	2
#17999	2
#17974	2
#17972	2
#17963	2
#17954	2
#17952	2
#17932	2
#17899	2
#17895	2
#17890	2
#17827	2
#17513	2
#17330	2