Subgroups — #6345955

Order 512.

1514 conjugacy classes of subgroups.

The subgroup lattice has 954 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	#18087	C₂	1	1	yes	maximal, characteristic, complemented
4	#18086	C₂	1	1	yes	maximal, characteristic, complemented
5	#18069	C₂	1	1	yes	maximal, characteristic, complemented
6	#18059	C₂	1	1	yes	maximal, characteristic, complemented
7	#18054	C₂	1	1	yes	maximal, characteristic, complemented
8	#18039	C₂	1	1	yes	maximal, characteristic, complemented
9	#18031	C₂	1	2	yes	maximal, complemented
10	#18028	C₂	1	2	yes	maximal, complemented
11	#18005	C₂	1	2	yes	maximal, complemented
12	#17973	C₂	1	1	yes	maximal, characteristic, complemented
13	#17972	C₂	1	1	yes	maximal, characteristic, complemented
14	#17959	C₂	1	1	yes	maximal, characteristic, complemented
15	#17955	C₂	1	2	yes	maximal, complemented
16	#17952	C₂	1	2	yes	maximal, complemented
17	#17937	C₂	1	2	yes	maximal, complemented
18	#17898	C₂	1	1	yes	maximal, characteristic, complemented
19	#17895	C₂	1	1	yes	maximal, characteristic, complemented
20	#17886	C₂	1	1	yes	maximal, characteristic, complemented
21	#17829	C₂	1	1	yes	maximal, characteristic, complemented
22	#17513	C₂	1	2	yes	maximal, complemented
23	#17328	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	2	yes	—
71	#1594	C₂²	1	2	yes	—
72	#1593	C₂²	1	2	yes	complemented
73	#1592	C₂²	1	2	yes	complemented
74	#1592	C₂²	1	2	yes	complemented
75	#1592	C₂²	1	2	yes	complemented
76	#1591	C₂²	1	1	yes	characteristic, complemented
77	#1591	C₂²	1	1	yes	characteristic, complemented
78	#1591	C₂²	1	1	yes	characteristic, complemented
79	#1591	C₂²	1	1	yes	characteristic, complemented
80	#1590	C₂²	1	2	yes	complemented
81	#1590	C₂²	1	2	yes	complemented
82	#1590	C₂²	1	2	yes	complemented
83	#1589	C₂²	1	1	yes	characteristic
84	#1589	C₂²	1	1	yes	characteristic
85	#1589	C₂²	1	1	yes	characteristic
86	#1589	C₂²	1	1	yes	characteristic
87	#1589	C₂²	1	1	yes	characteristic
88	#1589	C₂²	1	1	yes	characteristic
89	#1588	C₂²	1	2	yes	complemented
90	#1588	C₂²	1	2	yes	complemented
91	#1588	C₂²	1	2	yes	complemented
92	#1587	C₂²	1	2	yes	complemented
93	#1587	C₂²	1	2	yes	complemented
94	#1586	C₂²	1	2	yes	—
95	#1586	C₂²	1	2	yes	—
96	#1585	C₂²	1	2	yes	complemented
97	#1583	C₂²	1	2	yes	complemented
98	#1583	C₂²	1	2	yes	complemented
99	#1583	C₂²	1	2	yes	complemented
100	#1582	C₂²	1	2	yes	complemented
101	#1579	C₂²	1	2	yes	complemented
102	SD₁₆⋊C₈	C₂²	1	2	yes	complemented
103	C₈×Q₁₆	C₂²	1	1	yes	characteristic, complemented
104	C₈×Q₁₆	C₂²	1	1	yes	characteristic, complemented
105	C₈×Q₁₆	C₂²	1	1	yes	characteristic, complemented
106	C₈×Q₁₆	C₂²	1	1	yes	characteristic, complemented
107	C₈×SD₁₆	C₂²	1	2	yes	complemented
108	C₈×D₈	C₂²	1	1	yes	characteristic
109	C₈×D₈	C₂²	1	1	yes	characteristic
110	#1572	C₂²	1	2	yes	—
111	#1572	C₂²	1	2	yes	complemented
112	#1570	C₂²	1	2	yes	complemented
113	#1568	C₂²	1	1	yes	characteristic
114	#1568	C₂²	1	1	yes	characteristic, complemented
115	#1567	C₂²	1	1	yes	characteristic, complemented
116	#1564	C₂²	1	1	yes	characteristic
117	#1564	C₂²	1	1	yes	characteristic, complemented
118	C₂×#335	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	#1452	C₂²	1	1	yes	characteristic, complemented
136	#1451	C₂²	1	1	yes	characteristic, complemented
137	#1450	C₂²	1	1	yes	characteristic
138	#1450	C₂²	1	1	yes	characteristic, complemented
139	C₈×M₁₆	C₂²	1	1	yes	characteristic
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	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	1	yes	characteristic
293	#433	D₄	1	1	yes	characteristic
294	#433	D₄	1	1	yes	characteristic
295	#433	D₄	1	1	yes	characteristic
296	#432	—	2	2	no	—
297	#432	—	2	2	no	—
298	#432	C₂³	1	2	yes	—
299	#432	C₂³	1	2	yes	—
300	#431	—	2	2	no	—
301	#431	—	2	2	no	—
302	#431	C₂³	1	2	yes	—
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	#427	C₂×C₄	1	1	yes	characteristic
316	C₂×#107	C₂×C₄	1	1	yes	characteristic
317	#424	—	2	2	no	—
318	#424	—	2	2	no	—
319	#424	D₄	1	1	yes	characteristic
320	#424	D₄	1	1	yes	characteristic
321	#423	—	2	2	no	—
322	#423	—	2	2	no	—
323	#423	C₂³	1	2	yes	—
324	C₂×C₄⋊C₈	C₂³	1	2	yes	—
325	#416	C₂×C₄	1	2	yes	—
326	#416	C₂×C₄	1	2	yes	—
327	C₂×#102	C₂×C₄	1	2	yes	—
328	#408	—	2	2	no	—
329	#408	D₄	1	1	yes	characteristic
330	#408	D₄	1	1	yes	characteristic
331	#407	—	2	2	no	—
332	#407	—	2	2	no	—
333	#407	—	2	2	no	—
334	C₂×C₂²⋊C₈	—	2	2	no	—
335	#405	—	2	2	no	—
336	#405	—	2	2	no	—
337	#405	—	2	2	no	—
338	C₄×M₁₆	—	2	2	no	—
339	C₄×M₁₆	—	2	2	no	—
340	C₄×M₁₆	C₂³	1	1	yes	characteristic
341	C₄×M₁₆	C₂³	1	1	yes	characteristic
342	C₄×M₁₆	C₂³	1	1	yes	characteristic
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	2	yes	—
351	#335	C₂³	1	1	yes	characteristic
352	#335	C₂³	1	1	yes	characteristic
353	#335	C₂³	1	2	yes	—
354	#334	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	Q₈⋊C₈	C₂³	1	2	yes	—
363	Q₈⋊C₈	C₂³	1	2	yes	—
364	Q₈⋊C₈	C₂³	1	2	yes	—
365	Q₈⋊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	C₂²×C₄	1	2	yes	—
391	C₂×#41	C₂²×C₄	1	2	yes	—
392	C₂×#41	C₂×D₄	1	1	yes	characteristic
393	C₂²×D₄	C₂²×C₄	1	2	yes	—
394	C₂³×C₄	—	2	2	no	—
395	#135	—	4	2	no	—
396	#135	—	4	2	no	—
397	C₂×Q₁₆	C₂²×C₄	1	1	yes	characteristic
398	C₂×Q₁₆	C₂²×C₄	1	1	yes	characteristic
399	C₂×Q₁₆	C₂²×C₄	1	2	yes	—
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×SD₁₆	C₂²×C₄	1	2	yes	—
404	C₂×D₈	—	4	2	no	—
405	C₂×D₈	C₂²×C₄	1	1	yes	characteristic
406	C₂×D₈	C₂²×C₄	1	1	yes	characteristic
407	C₂×D₈	C₂²×C₄	1	2	yes	—
408	C₂×M₁₆	—	2	1	no	—
409	C₂×M₁₆	—	2	1	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	C₂×D₄	1	1	yes	characteristic
418	C₂×M₁₆	C₂×D₄	1	1	yes	characteristic
419	C₂²×C₈	—	2	1	no	—
420	C₂²×C₈	—	2	2	no	—
421	C₂²×C₈	—	2	2	no	—
422	C₂²×C₈	—	2	2	no	—
423	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
424	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
425	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
426	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
427	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
428	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
429	C₂²×C₈	C₂×D₄	1	1	yes	characteristic
430	C₂²×C₈	C₂×D₄	1	1	yes	characteristic
431	C₄⋊Q₈	C₂²×C₄	1	2	yes	—
432	C₄⋊Q₈	C₂²×C₄	1	2	yes	—
433	#126	—	2	2	no	—
434	#126	—	2	2	no	—
435	#126	—	2	2	no	—
436	#126	—	2	2	no	—
437	#126	—	2	2	no	—
438	#126	—	2	2	no	—
439	#125	—	2	2	no	—
440	#125	—	2	2	no	—
441	#125	—	2	2	no	—
442	#125	C₂²×C₄	1	2	yes	—
443	#125	C₂²×C₄	1	2	yes	—
444	#124	—	2	2	no	—
445	#124	—	2	2	no	—
446	#124	C₂²×C₄	1	2	yes	—
447	#124	C₂²×C₄	1	2	yes	—
448	#123	—	2	2	no	—
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	C₂²⋊Q₈	—	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	C₂²×C₄	1	2	yes	—
462	C₂²⋊Q₈	C₂²×C₄	1	2	yes	—
463	C₂²⋊Q₈	C₂²×C₄	1	2	yes	—
464	C₂²⋊Q₈	C₂²×C₄	1	2	yes	—
465	#121	—	2	2	no	—
466	#121	—	2	2	no	—
467	#121	—	2	2	no	—
468	#121	—	2	2	no	—
469	#121	C₂²×C₄	1	2	yes	—
470	#121	C₂²×C₄	1	2	yes	—
471	#120	—	2	2	no	—
472	#120	—	2	2	no	—
473	C₄×Q₈	—	2	2	no	—
474	C₄×Q₈	C₂²×C₄	1	2	yes	—
475	C₄×Q₈	C₂²×C₄	1	2	yes	—
476	C₄×Q₈	C₂²×C₄	1	1	yes	characteristic
477	C₄×Q₈	#41	1	1	yes	characteristic
478	C₄×Q₈	C₂⁴	1	2	yes	—
479	C₄×Q₈	C₂⁴	1	2	yes	—
480	C₄×D₄	—	2	2	no	—
481	C₄×D₄	—	2	2	no	—
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	C₂²×C₄	1	2	yes	—
489	C₄×D₄	C₂²×C₄	1	2	yes	—
490	C₄×D₄	C₂²×C₄	1	2	yes	—
491	C₄×D₄	C₂²×C₄	1	2	yes	—
492	C₄×D₄	C₂²×C₄	1	1	yes	characteristic
493	C₄×D₄	C₂²×C₄	1	1	yes	characteristic
494	C₄×D₄	C₂²×C₄	1	1	yes	characteristic
495	C₄×D₄	#41	1	1	yes	characteristic
496	C₄×D₄	#41	1	1	yes	characteristic
497	C₄×D₄	#41	1	1	yes	characteristic
498	C₄×D₄	C₂⁴	1	2	yes	—
499	C₄×D₄	C₂⁴	1	2	yes	—
500	#117	—	2	2	no	—
501	#117	—	2	2	no	—
502	#117	—	2	2	no	—
503	#117	—	2	2	no	—
504	#117	—	2	2	no	—
505	#117	—	2	2	no	—
506	#117	—	2	2	no	—
507	#117	—	2	2	no	—
508	#117	—	2	2	no	—
509	#117	C₂²×C₄	1	2	yes	—
510	#117	C₂²×C₄	1	2	yes	—
511	#117	C₂×D₄	1	1	yes	characteristic
512	#117	C₂×D₄	1	1	yes	characteristic
513	#117	C₂×D₄	1	1	yes	characteristic
514	C₂×C₄⋊C₄	—	2	2	no	—
515	C₂×C₄⋊C₄	—	2	2	no	—
516	C₂×C₄⋊C₄	C₂²×C₄	1	2	yes	—
517	C₂×C₂²⋊C₄	—	2	2	no	—
518	C₂×C₂²⋊C₄	—	2	2	no	—
519	C₂×C₂²⋊C₄	—	2	2	no	—
520	C₂×C₄²	—	2	2	no	—
521	C₂×C₄²	—	2	2	no	—
522	C₂×C₄²	C₂⁴	1	1	yes	characteristic
523	C₂×C₄²	C₂⁴	1	1	yes	characteristic
524	C₂×C₄²	C₂⁴	1	1	yes	characteristic
525	#107	C₂²×C₄	1	1	yes	characteristic
526	#107	C₂²×C₄	1	1	yes	characteristic
527	#107	C₂²×C₄	1	2	yes	—
528	#107	C₂²×C₄	1	1	yes	characteristic
529	#107	C₂²×C₄	1	1	yes	characteristic
530	#107	C₂²×C₄	1	2	yes	—
531	#106	C₂²×C₄	1	2	yes	—
532	#106	C₂²×C₄	1	2	yes	—
533	#106	C₂²×C₄	1	2	yes	—
534	#106	C₂²×C₄	1	2	yes	—
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	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	2	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	1	yes	characteristic
555	C₄⋊C₈	C₂×D₄	1	1	yes	characteristic
556	C₄⋊C₈	C₂×D₄	1	1	yes	characteristic
557	C₄⋊C₈	C₂×D₄	1	1	yes	characteristic
558	C₄⋊C₈	C₂×D₄	1	1	yes	characteristic
559	C₄⋊C₈	C₂×D₄	1	1	yes	characteristic
560	C₄⋊C₈	C₂×D₄	1	1	yes	characteristic
561	C₄⋊C₈	C₂×D₄	1	1	yes	characteristic
562	C₄⋊C₈	C₂⁴	1	2	yes	—
563	C₄⋊C₈	C₂⁴	1	2	yes	—
564	C₄⋊C₈	C₂⁴	1	2	yes	—
565	C₄⋊C₈	C₂⁴	1	2	yes	—
566	#103	C₂²×C₄	1	2	yes	—
567	#103	C₂²×C₄	1	2	yes	—
568	#103	C₂²×C₄	1	2	yes	—
569	#103	C₂²×C₄	1	2	yes	—
570	#103	C₂²×C₄	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	#102	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	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	1	no	—
587	C₂²⋊C₈	—	2	1	no	—
588	C₂²⋊C₈	—	2	1	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	—	2	2	no	—
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	C₂²×C₄	1	1	yes	characteristic
603	C₂²⋊C₈	C₂×D₄	1	1	yes	characteristic
604	C₂²⋊C₈	C₂×D₄	1	1	yes	characteristic
605	C₂²⋊C₈	C₂×D₄	1	1	yes	characteristic
606	C₂²⋊C₈	C₂×D₄	1	1	yes	characteristic
607	C₂²⋊C₈	C₂×D₄	1	1	yes	characteristic
608	C₂²⋊C₈	C₂×D₄	1	1	yes	characteristic
609	C₂²⋊C₈	C₂×D₄	1	1	yes	characteristic
610	C₂²⋊C₈	C₂×D₄	1	1	yes	characteristic
611	#97	—	2	2	no	—
612	#97	—	2	2	no	—
613	#97	—	2	2	no	—
614	#97	—	2	2	no	—
615	#97	—	2	2	no	—
616	#97	—	2	2	no	—
617	#97	—	2	1	no	—
618	#97	—	2	1	no	—
619	#97	C₂×D₄	1	1	yes	characteristic
620	#97	C₂×D₄	1	1	yes	characteristic
621	C₄×C₈	—	2	2	no	—
622	C₄×C₈	—	2	2	no	—
623	C₄×C₈	—	2	2	no	—
624	C₄×C₈	—	2	2	no	—
625	C₄×C₈	—	2	2	no	—
626	C₄×C₈	—	2	2	no	—
627	C₄×C₈	—	2	1	no	—
628	C₄×C₈	C₂²×C₄	1	1	yes	characteristic
629	C₄×C₈	C₂²×C₄	1	1	yes	characteristic
630	C₄×C₈	C₂²×C₄	1	1	yes	characteristic
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	C₂×D₄	1	1	yes	characteristic
635	C₄×C₈	C₂×D₄	1	1	yes	characteristic
636	C₄×C₈	C₂⁴	1	1	yes	characteristic
637	C₄×C₈	C₂⁴	1	1	yes	characteristic
638	C₄×C₈	C₂⁴	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	C₂⁴	—	2	2	no	—
649	#41	—	4	1	no	—
650	#41	—	4	1	no	—
651	#41	—	4	2	no	—
652	#41	—	4	2	no	—
653	#41	—	4	2	no	—
654	#41	—	4	2	no	—
655	C₂×Q₈	—	2	2	no	—
656	C₂×Q₈	C₄×D₄	1	1	yes	characteristic
657	C₂×Q₈	C₂³×C₄	1	2	yes	—
658	C₂×Q₈	C₂³×C₄	1	2	yes	—
659	C₂×D₄	—	2	2	no	—
660	C₂×D₄	—	2	2	no	—
661	C₂×D₄	—	2	2	no	—
662	C₂×D₄	—	2	2	no	—
663	C₂×D₄	—	2	2	no	—
664	C₂×D₄	—	4	2	no	—
665	C₂×D₄	—	4	2	no	—
666	C₂×D₄	C₄×D₄	1	1	yes	characteristic
667	C₂×D₄	C₄×D₄	1	1	yes	characteristic
668	C₂×D₄	C₄×D₄	1	1	yes	characteristic
669	C₂×D₄	C₂³×C₄	1	2	yes	—
670	C₂×D₄	C₂³×C₄	1	2	yes	—
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	—	2	2	no	—
677	C₂²×C₄	—	2	2	no	—
678	C₂²×C₄	—	2	2	no	—
679	C₂²×C₄	—	2	2	no	—
680	C₂²×C₄	—	8	2	no	—
681	C₂²×C₄	—	8	2	no	—
682	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
683	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
684	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
685	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
686	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
687	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
688	C₂²×C₄	C₂×#41	1	1	yes	characteristic
689	C₂²×C₄	C₂×#41	1	1	yes	characteristic
690	C₂²×C₄	C₂×#41	1	1	yes	characteristic
691	Q₁₆	—	2	2	no	—
692	Q₁₆	—	2	2	no	—
693	Q₁₆	—	4	2	no	—
694	SD₁₆	—	4	2	no	—
695	SD₁₆	—	4	2	no	—
696	SD₁₆	—	4	2	no	—
697	SD₁₆	—	4	2	no	—
698	D₈	—	2	2	no	—
699	D₈	—	2	2	no	—
700	D₈	—	4	2	no	—
701	M₁₆	—	4	1	no	—
702	M₁₆	—	4	1	no	—
703	M₁₆	—	4	2	no	—
704	M₁₆	—	4	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	M₁₆	—	8	2	no	—
712	C₂×C₈	—	2	1	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	2	no	—
719	C₂×C₈	—	2	2	no	—
720	C₂×C₈	—	2	1	no	—
721	C₂×C₈	—	2	1	no	—
722	C₂×C₈	—	2	1	no	—
723	C₂×C₈	—	4	1	no	—
724	C₂×C₈	—	4	1	no	—
725	C₂×C₈	—	4	1	no	—
726	C₂×C₈	—	4	1	no	—
727	C₂×C₈	—	4	1	no	—
728	C₂×C₈	—	4	2	no	—
729	C₂×C₈	—	8	2	no	—
730	C₂×C₈	—	8	2	no	—
731	C₂×C₈	—	8	2	no	—
732	C₂×C₈	C₂³×C₄	1	1	yes	characteristic
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	C₂²×D₄	1	1	yes	characteristic
741	C₂×C₈	C₂²×D₄	1	1	yes	characteristic
742	C₂×C₈	C₂²×D₄	1	1	yes	characteristic
743	C₂×C₈	C₂²×D₄	1	1	yes	characteristic
744	C₂×C₈	C₂²×D₄	1	1	yes	characteristic
745	C₂×C₈	C₂²×D₄	1	1	yes	characteristic
746	C₂×C₈	C₂²×D₄	1	1	yes	characteristic
747	C₂×C₈	C₂²×D₄	1	1	yes	characteristic
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	—	2	2	no	—
757	C₄⋊C₄	—	2	2	no	—
758	C₄⋊C₄	—	2	2	no	—
759	C₄⋊C₄	—	2	2	no	—
760	C₄⋊C₄	—	2	2	no	—
761	C₄⋊C₄	—	2	2	no	—
762	C₄⋊C₄	—	2	2	no	—
763	C₄⋊C₄	—	2	2	no	—
764	C₄⋊C₄	C₄×D₄	1	1	yes	characteristic
765	C₄⋊C₄	C₄×D₄	1	1	yes	characteristic
766	C₄⋊C₄	C₄×D₄	1	1	yes	characteristic
767	C₄⋊C₄	C₄×D₄	1	1	yes	characteristic
768	C₄⋊C₄	C₄×D₄	1	1	yes	characteristic
769	C₄⋊C₄	C₄×D₄	1	1	yes	characteristic
770	C₄⋊C₄	C₂³×C₄	1	2	yes	—
771	C₄⋊C₄	C₂³×C₄	1	2	yes	—
772	C₄⋊C₄	C₂³×C₄	1	2	yes	—
773	C₄⋊C₄	C₂³×C₄	1	2	yes	—
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	—	2	2	no	—
786	C₂²⋊C₄	—	2	2	no	—
787	C₂²⋊C₄	—	2	2	no	—
788	C₂²⋊C₄	—	2	2	no	—
789	C₂²⋊C₄	—	2	2	no	—
790	C₂²⋊C₄	—	2	2	no	—
791	C₂²⋊C₄	—	2	2	no	—
792	C₂²⋊C₄	C₄×D₄	1	1	yes	characteristic
793	C₂²⋊C₄	C₄×D₄	1	1	yes	characteristic
794	C₂²⋊C₄	C₄×D₄	1	1	yes	characteristic
795	C₂²⋊C₄	C₄×D₄	1	1	yes	characteristic
796	C₂²⋊C₄	C₄×D₄	1	1	yes	characteristic
797	C₂²⋊C₄	C₄×D₄	1	1	yes	characteristic
798	C₄²	—	2	2	no	—
799	C₄²	—	2	2	no	—
800	C₄²	—	2	2	no	—
801	C₄²	—	2	2	no	—
802	C₄²	—	2	2	no	—
803	C₄²	—	2	2	no	—
804	C₄²	C₂³×C₄	1	1	yes	characteristic
805	C₄²	C₂³×C₄	1	1	yes	characteristic
806	C₄²	C₂³×C₄	1	1	yes	characteristic
807	C₄²	C₂²×D₄	1	1	yes	characteristic
808	C₄²	C₂²×D₄	1	1	yes	characteristic
809	C₄²	C₂²×D₄	1	1	yes	characteristic
810	C₄²	C₂×#41	1	1	yes	characteristic
811	C₄²	C₂×#41	1	1	yes	characteristic
812	C₄²	C₂×#41	1	1	yes	characteristic
813	C₄²	C₂⁵	1	1	yes	characteristic
814	C₂³	—	2	2	no	—
815	C₂³	—	2	2	no	—
816	C₂³	—	8	2	no	—
817	C₂³	—	8	2	no	—
818	C₂³	—	8	2	no	—
819	C₂³	C₂×C₄×D₄	1	1	yes	characteristic
820	C₂³	C₂×C₄×D₄	1	1	yes	characteristic
821	C₂³	C₂×C₄×D₄	1	1	yes	characteristic
822	Q₈	—	2	2	no	—
823	Q₈	—	2	2	no	—
824	Q₈	—	2	2	no	—
825	Q₈	—	2	2	no	—
826	Q₈	—	4	1	no	—
827	Q₈	—	8	2	no	—
828	D₄	—	2	2	no	—
829	D₄	—	2	2	no	—
830	D₄	—	2	2	no	—
831	D₄	—	2	2	no	—
832	D₄	—	4	1	no	—
833	D₄	—	4	1	no	—
834	D₄	—	4	1	no	—
835	D₄	—	8	2	no	—
836	D₄	—	8	2	no	—
837	D₄	—	8	2	no	—
838	D₄	—	8	2	no	—
839	D₄	—	8	2	no	—
840	C₂×C₄	—	2	1	no	—
841	C₂×C₄	—	2	1	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	1	no	—
849	C₂×C₄	—	2	1	no	—
850	C₂×C₄	—	2	1	no	—
851	C₂×C₄	—	2	1	no	—
852	C₂×C₄	—	2	2	no	—
853	C₂×C₄	—	2	2	no	—
854	C₂×C₄	—	2	2	no	—
855	C₂×C₄	—	2	2	no	—
856	C₂×C₄	—	2	2	no	—
857	C₂×C₄	—	2	2	no	—
858	C₂×C₄	—	4	1	no	—
859	C₂×C₄	—	4	1	no	—
860	C₂×C₄	—	4	1	no	—
861	C₂×C₄	—	4	2	no	—
862	C₂×C₄	—	4	2	no	—
863	C₂×C₄	—	4	2	no	—
864	C₂×C₄	—	4	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	—	8	2	no	—
870	C₂×C₄	—	8	2	no	—
871	C₂×C₄	—	8	2	no	—
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	C₂×C₄×D₄	1	1	yes	characteristic
879	C₂×C₄	C₂×C₄×D₄	1	1	yes	characteristic
880	C₂×C₄	C₂×C₄×D₄	1	1	yes	characteristic
881	C₂×C₄	C₂⁴×C₄	1	1	yes	characteristic
882	C₂×C₄	C₂³×D₄	1	1	yes	characteristic
883	C₂×C₄	C₂²×#41	1	1	yes	characteristic
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	—	2	1	no	—
893	C₈	—	2	1	no	—
894	C₈	—	2	1	no	—
895	C₈	—	2	1	no	—
896	C₈	—	2	1	no	—
897	C₈	—	2	1	no	—
898	C₈	—	2	1	no	—
899	C₈	—	2	1	no	—
900	C₈	—	4	1	no	—
901	C₈	—	4	1	no	—
902	C₈	—	4	1	no	—
903	C₈	—	4	2	no	—
904	C₈	—	4	2	no	—
905	C₈	—	4	2	no	—
906	C₈	—	4	2	no	—
907	C₈	#568	1	2	yes	—
908	C₂²	—	2	1	no	—
909	C₂²	—	2	1	no	—
910	C₂²	—	2	1	no	—
911	C₂²	—	2	1	no	—
912	C₂²	—	2	1	no	—
913	C₂²	—	2	1	no	—
914	C₂²	—	2	1	no	—
915	C₂²	—	2	1	no	—
916	C₂²	—	2	1	no	—
917	C₂²	—	4	2	no	—
918	C₂²	—	4	2	no	—
919	C₂²	—	4	2	no	—
920	C₂²	—	4	2	no	—
921	C₂²	—	4	2	no	—
922	C₂²	—	4	2	no	—
923	C₂²	—	16	4	no	—
924	C₂²	C₂²×C₄×D₄	1	1	yes	characteristic
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	—	2	1	no	—
933	C₄	—	2	1	no	—
934	C₄	—	2	1	no	—
935	C₄	—	4	2	no	—
936	C₄	—	4	2	no	—
937	C₄	—	4	2	no	—
938	C₄	—	4	2	no	—
939	C₄	—	4	2	no	—
940	C₄	—	4	2	no	—
941	C₄	C₂×#568	1	1	yes	characteristic
942	C₄	#3573	1	1	yes	characteristic
943	C₄	#3584	1	1	yes	characteristic
944	C₄	#3584	1	1	yes	characteristic
945	C₂	—	4	1	no	—
946	C₂	—	4	1	no	—
947	C₂	—	4	1	no	—
948	C₂	—	8	2	no	—
949	C₂	—	8	2	no	—
950	C₂	#60147	1	1	yes	characteristic
951	C₂	#60167	1	1	yes	characteristic
952	C₂	#60183	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. #18087	C₂	semidirect
4. #18086	C₂	semidirect
5. #18069	C₂	semidirect
6. #18059	C₂	semidirect
7. #18054	C₂	semidirect
8. #18039	C₂	semidirect
9. #18031	C₂	semidirect
10. #18028	C₂	semidirect
11. #18005	C₂	semidirect
12. #17973	C₂	semidirect
13. #17972	C₂	semidirect
14. #17959	C₂	semidirect
15. #17955	C₂	semidirect
16. #17952	C₂	semidirect
17. #17937	C₂	semidirect
18. #17898	C₂	semidirect
19. #17895	C₂	semidirect
20. #17886	C₂	semidirect
21. #17829	C₂	semidirect
22. #17513	C₂	semidirect
23. #17328	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
72. #1593	C₂²	semidirect
73. #1592	C₂²	semidirect
74. #1592	C₂²	semidirect
75. #1592	C₂²	semidirect
76. #1591	C₂²	semidirect
77. #1591	C₂²	semidirect
78. #1591	C₂²	semidirect
79. #1591	C₂²	semidirect
80. #1590	C₂²	semidirect
81. #1590	C₂²	semidirect
82. #1590	C₂²	semidirect
89. #1588	C₂²	semidirect
90. #1588	C₂²	semidirect
91. #1588	C₂²	semidirect
92. #1587	C₂²	semidirect
93. #1587	C₂²	semidirect
96. #1585	C₂²	semidirect
97. #1583	C₂²	semidirect
98. #1583	C₂²	semidirect
99. #1583	C₂²	semidirect
100. #1582	C₂²	semidirect
101. #1579	C₂²	semidirect
102. SD₁₆⋊C₈	C₂²	semidirect
103. C₈×Q₁₆	C₂²	semidirect
104. C₈×Q₁₆	C₂²	semidirect
105. C₈×Q₁₆	C₂²	semidirect
106. C₈×Q₁₆	C₂²	semidirect
107. C₈×SD₁₆	C₂²	semidirect
111. #1572	C₂²	semidirect
112. #1570	C₂²	semidirect
114. #1568	C₂²	semidirect
115. #1567	C₂²	semidirect
117. #1564	C₂²	semidirect
118. C₂×#335	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
135. #1452	C₂²	semidirect
136. #1451	C₂²	semidirect
138. #1450	C₂²	semidirect
140. C₈×M₁₆	C₂²	semidirect
141. C₈×M₁₆	C₂²	semidirect
142. C₂×C₈²	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
#18087	2
#18086	2
#18069	2
#18059	2
#18054	2
#18039	2
#18031	2
#18028	2
#18005	2
#17973	2
#17972	2
#17959	2
#17955	2
#17952	2
#17937	2
#17898	2
#17895	2
#17886	2
#17829	2
#17513	2
#17328	2