Subgroups — #6345901

Order 512.

1536 conjugacy classes of subgroups.

The subgroup lattice has 940 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#61433	C₂	1	1	yes	maximal, characteristic
2	#60335	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	#18068	C₂	1	1	yes	maximal, characteristic, complemented
6	#18058	C₂	1	1	yes	maximal, characteristic, complemented
7	#18039	C₂	1	1	yes	maximal, characteristic, complemented
8	M₁₆×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
9	#18023	C₂	1	2	yes	maximal, complemented
10	#18013	C₂	1	2	yes	maximal, complemented
11	#18012	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	#17921	C₂	1	2	yes	maximal, complemented
16	#17919	C₂	1	2	yes	maximal, complemented
17	#17915	C₂	1	2	yes	maximal, complemented
18	#17857	C₂	1	1	yes	maximal, characteristic, complemented
19	#17856	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×C₈×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
21	#17836	C₂	1	1	yes	maximal, characteristic, complemented
22	#17524	C₂	1	2	yes	maximal, complemented
23	#17328	C₂	1	1	yes	maximal, characteristic, complemented
24	#3482	C₂²	1	2	yes	—
25	#3393	C₄	1	1	yes	characteristic
26	#3383	C₄	1	1	yes	characteristic
27	#3364	C₄	1	2	yes	—
28	#3336	C₄	1	1	yes	characteristic
29	#3336	C₄	1	1	yes	characteristic
30	#3334	C₄	1	1	yes	characteristic
31	#3300	C₄	1	2	yes	—
32	#3300	C₄	1	2	yes	—
33	#3298	C₄	1	2	yes	—
34	D₄×Q₁₆	C₄	1	1	yes	characteristic
35	#3285	C₄	1	1	yes	characteristic
36	#3285	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	#3108	C₂²	1	2	yes	—
41	#3108	C₂²	1	2	yes	—
42	#3107	C₂²	1	2	yes	—
43	#2994	—	2	2	no	—
44	#2994	C₂²	1	2	yes	—
45	#2993	—	2	2	no	—
46	#2993	C₂²	1	2	yes	—
47	#2990	—	2	2	no	—
48	#2990	C₂²	1	2	yes	—
49	#2988	C₂²	1	2	yes	—
50	#2985	—	2	2	no	—
51	#2985	C₂²	1	2	yes	—
52	#2984	C₂²	1	2	yes	—
53	#2982	C₂²	1	2	yes	—
54	#2971	C₂²	1	2	yes	—
55	#2969	—	2	2	no	—
56	#2969	C₂²	1	2	yes	—
57	#2966	—	2	2	no	—
58	#2966	C₂²	1	2	yes	—
59	#2965	—	2	2	no	—
60	#2965	C₂²	1	1	yes	characteristic
61	C₈×#41	C₂²	1	1	yes	characteristic
62	Q₈×M₁₆	C₂²	1	2	yes	—
63	#2962	—	2	2	no	—
64	#2962	C₂²	1	2	yes	—
65	C₂×C₈×Q₈	C₂²	1	2	yes	—
66	C₄×#135	C₂²	1	1	yes	characteristic
67	C₂×C₄×Q₁₆	C₂²	1	1	yes	characteristic
68	C₂×C₄×Q₁₆	C₂²	1	1	yes	characteristic
69	#2922	C₂²	1	1	yes	characteristic
70	#1593	C₂²	1	2	yes	—
71	#1592	C₂²	1	2	yes	—
72	#1591	C₂²	1	1	yes	characteristic
73	#1591	C₂²	1	1	yes	characteristic
74	#1591	C₂²	1	1	yes	characteristic
75	#1591	C₂²	1	1	yes	characteristic
76	#1590	C₂²	1	2	yes	—
77	#1589	C₂²	1	1	yes	characteristic
78	#1589	C₂²	1	1	yes	characteristic
79	#1588	C₂²	1	2	yes	—
80	#1587	C₂²	1	2	yes	—
81	#1587	C₂²	1	2	yes	—
82	#1585	C₂²	1	2	yes	—
83	#1584	C₂²	1	2	yes	—
84	#1584	C₂²	1	2	yes	—
85	#1584	C₂²	1	2	yes	—
86	#1584	C₂²	1	2	yes	—
87	#1583	C₂²	1	2	yes	—
88	#1583	C₂²	1	2	yes	—
89	#1583	C₂²	1	2	yes	—
90	#1582	C₂²	1	2	yes	—
91	#1579	C₂²	1	2	yes	—
92	#1579	C₂²	1	2	yes	—
93	#1579	C₂²	1	2	yes	—
94	SD₁₆⋊C₈	C₂²	1	2	yes	—
95	SD₁₆⋊C₈	C₂²	1	2	yes	—
96	SD₁₆⋊C₈	C₂²	1	2	yes	—
97	C₈×Q₁₆	C₂²	1	2	yes	—
98	C₈×Q₁₆	C₂²	1	1	yes	characteristic
99	C₈×Q₁₆	C₂²	1	1	yes	characteristic
100	C₈×Q₁₆	C₂²	1	2	yes	—
101	C₈×Q₁₆	C₂²	1	1	yes	characteristic
102	C₈×Q₁₆	C₂²	1	1	yes	characteristic
103	C₈×Q₁₆	C₂²	1	1	yes	characteristic
104	C₈×Q₁₆	C₂²	1	1	yes	characteristic
105	C₈×Q₁₆	C₂²	1	1	yes	characteristic
106	C₈×Q₁₆	C₂²	1	1	yes	characteristic
107	C₈×SD₁₆	C₂²	1	2	yes	—
108	C₈×D₈	C₂²	1	1	yes	characteristic
109	C₈×D₈	C₂²	1	1	yes	characteristic
110	#1574	C₂²	1	2	yes	—
111	#1573	C₂²	1	2	yes	—
112	#1573	C₂²	1	2	yes	—
113	#1568	C₂²	1	1	yes	characteristic
114	#1568	C₂²	1	1	yes	characteristic
115	#1567	C₂²	1	1	yes	characteristic
116	#1564	C₂²	1	1	yes	characteristic
117	C₂×#335	C₂²	1	1	yes	characteristic
118	C₂×#335	C₂²	1	1	yes	characteristic
119	#1497	C₂²	1	2	yes	—
120	#1495	C₂²	1	2	yes	—
121	#1494	C₂²	1	2	yes	—
122	#1491	C₂²	1	2	yes	—
123	#1488	C₂²	1	2	yes	—
124	#1487	C₂²	1	2	yes	—
125	#1483	C₂²	1	2	yes	—
126	#1482	C₂²	1	2	yes	—
127	#1481	C₂²	1	2	yes	—
128	#1479	C₂²	1	2	yes	—
129	#1477	C₂²	1	2	yes	—
130	C₂×Q₈⋊C₈	C₂²	1	2	yes	—
131	#1454	C₂²	1	1	yes	characteristic
132	#1454	C₂²	1	1	yes	characteristic
133	#1453	C₂²	1	1	yes	characteristic
134	#1453	C₂²	1	1	yes	characteristic
135	#1452	C₂²	1	1	yes	characteristic
136	#1451	C₂²	1	1	yes	characteristic
137	#1450	C₂²	1	1	yes	characteristic
138	#1450	C₂²	1	1	yes	characteristic
139	C₈×M₁₆	C₂²	1	1	yes	characteristic
140	C₈×M₁₆	C₂²	1	1	yes	characteristic
141	C₈×M₁₆	C₂²	1	1	yes	characteristic
142	C₂×C₈²	C₂²	1	1	yes	characteristic
143	C₂×#135	C₂×C₄	1	1	yes	characteristic
144	C₂²×Q₁₆	C₂×C₄	1	1	yes	characteristic
145	C₂²×Q₁₆	C₂×C₄	1	1	yes	characteristic
146	#557	C₂×C₄	1	2	yes	—
147	#556	—	2	2	no	—
148	#556	C₂×C₄	1	2	yes	—
149	#552	—	2	2	no	—
150	#552	—	2	2	no	—
151	#552	C₂×C₄	1	2	yes	—
152	#552	C₂×C₄	1	2	yes	—
153	D₄×Q₈	C₂×C₄	1	2	yes	—
154	#548	C₂×C₄	1	2	yes	—
155	#548	C₂×C₄	1	2	yes	—
156	#547	—	2	2	no	—
157	#547	C₂×C₄	1	2	yes	—
158	#533	—	2	2	no	—
159	#533	C₂³	1	2	yes	—
160	#529	—	2	2	no	—
161	#529	—	2	2	no	—
162	#529	C₂³	1	2	yes	—
163	#529	C₂³	1	2	yes	—
164	C₄×#41	—	2	2	no	—
165	C₄×#41	C₂³	1	2	yes	—
166	C₄×#41	C₂³	1	1	yes	characteristic
167	C₂×C₄×Q₈	C₂³	1	2	yes	—
168	C₂×C₄×Q₈	C₂³	1	2	yes	—
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	#480	C₂×C₄	1	2	yes	—
183	#480	C₂×C₄	1	2	yes	—
184	#479	C₂×C₄	1	2	yes	—
185	#479	C₂×C₄	1	2	yes	—
186	#479	C₂×C₄	1	2	yes	—
187	#479	C₂×C₄	1	2	yes	—
188	#475	C₂×C₄	1	2	yes	—
189	#474	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	#464	C₂×C₄	1	2	yes	—
202	#464	C₂×C₄	1	2	yes	—
203	#462	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	#451	C₂×C₄	1	2	yes	—
208	#451	C₂×C₄	1	2	yes	—
209	#448	C₂×C₄	1	2	yes	—
210	#448	C₂×C₄	1	2	yes	—
211	#446	—	2	2	no	—
212	#446	—	2	2	no	—
213	#446	—	2	2	no	—
214	#446	—	2	2	no	—
215	#446	—	2	2	no	—
216	#446	—	2	2	no	—
217	#446	—	2	2	no	—
218	#446	—	2	2	no	—
219	#446	—	2	2	no	—
220	#446	D₄	1	1	yes	characteristic
221	#446	D₄	1	1	yes	characteristic
222	#446	C₂³	1	2	yes	—
223	#446	C₂³	1	2	yes	—
224	#446	C₂³	1	2	yes	—
225	#446	C₂³	1	2	yes	—
226	C₈×Q₈	—	2	2	no	—
227	C₈×Q₈	—	2	2	no	—
228	C₈×Q₈	—	2	2	no	—
229	C₈×Q₈	—	2	2	no	—
230	C₈×Q₈	C₂×C₄	1	1	yes	characteristic
231	C₈×Q₈	C₂×C₄	1	1	yes	characteristic
232	C₈×Q₈	C₂³	1	2	yes	—
233	C₈×Q₈	C₂³	1	2	yes	—
234	C₈×Q₈	C₂³	1	2	yes	—
235	C₈×Q₈	C₂³	1	2	yes	—
236	C₈×Q₈	C₂³	1	2	yes	—
237	C₈×Q₈	C₂³	1	2	yes	—
238	C₈×Q₈	C₂³	1	2	yes	—
239	C₈×Q₈	C₂³	1	2	yes	—
240	C₄×Q₁₆	C₂×C₄	1	1	yes	characteristic
241	C₄×Q₁₆	C₂×C₄	1	1	yes	characteristic
242	C₄×Q₁₆	C₂×C₄	1	2	yes	—
243	C₄×Q₁₆	C₂×C₄	1	2	yes	—
244	C₄×Q₁₆	C₂×C₄	1	1	yes	characteristic
245	C₄×Q₁₆	C₂×C₄	1	1	yes	characteristic
246	C₄×Q₁₆	C₂×C₄	1	1	yes	characteristic
247	C₄×Q₁₆	C₂³	1	2	yes	—
248	C₄×Q₁₆	C₂³	1	2	yes	—
249	C₄×Q₁₆	C₂³	1	2	yes	—
250	C₄×Q₁₆	C₂³	1	1	yes	characteristic
251	C₄×Q₁₆	C₂³	1	1	yes	characteristic
252	C₄×Q₁₆	C₂³	1	1	yes	characteristic
253	C₄×SD₁₆	C₂×C₄	1	2	yes	—
254	C₄×SD₁₆	C₂³	1	2	yes	—
255	C₄×SD₁₆	C₂³	1	2	yes	—
256	C₄×SD₁₆	C₂³	1	2	yes	—
257	C₄×D₈	C₂×C₄	1	1	yes	characteristic
258	C₄×D₈	C₂³	1	1	yes	characteristic
259	#436	—	2	2	no	—
260	#436	—	2	2	no	—
261	#436	—	2	2	no	—
262	#436	—	2	2	no	—
263	#436	D₄	1	1	yes	characteristic
264	#436	D₄	1	1	yes	characteristic
265	#436	C₂³	1	2	yes	—
266	#436	C₂³	1	2	yes	—
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	D₄	1	1	yes	characteristic
274	#435	D₄	1	1	yes	characteristic
275	#435	D₄	1	1	yes	characteristic
276	#435	D₄	1	1	yes	characteristic
277	C₈×D₄	—	2	2	no	—
278	C₈×D₄	—	2	2	no	—
279	C₈×D₄	—	2	2	no	—
280	C₈×D₄	—	2	2	no	—
281	C₈×D₄	—	2	2	no	—
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	C₂×C₄	1	1	yes	characteristic
286	C₈×D₄	C₂×C₄	1	1	yes	characteristic
287	C₈×D₄	C₂×C₄	1	1	yes	characteristic
288	C₈×D₄	C₂³	1	2	yes	—
289	C₈×D₄	C₂³	1	2	yes	—
290	#433	—	2	1	no	—
291	#433	—	2	1	no	—
292	#433	—	2	2	no	—
293	#433	—	2	2	no	—
294	#433	—	2	2	no	—
295	#433	—	2	2	no	—
296	#433	—	2	2	no	—
297	#433	—	2	2	no	—
298	#432	—	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	—	2	2	no	—
304	#431	—	2	2	no	—
305	#431	—	2	2	no	—
306	#431	C₂³	1	2	yes	—
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	#431	C₂³	1	1	yes	characteristic
315	#431	C₂³	1	1	yes	characteristic
316	#431	C₂³	1	1	yes	characteristic
317	#427	C₂×C₄	1	1	yes	characteristic
318	C₂×#107	C₂×C₄	1	1	yes	characteristic
319	C₂×#107	C₂×C₄	1	1	yes	characteristic
320	#424	—	2	2	no	—
321	#424	—	2	1	no	—
322	#424	—	2	2	no	—
323	#424	—	2	2	no	—
324	#423	—	2	2	no	—
325	#423	C₂³	1	2	yes	—
326	C₂×C₄⋊C₈	—	2	2	no	—
327	C₂×C₄⋊C₈	—	2	2	no	—
328	C₂×C₄⋊C₈	C₂³	1	2	yes	—
329	C₂×C₄⋊C₈	C₂³	1	2	yes	—
330	#416	C₂×C₄	1	2	yes	—
331	C₂×#103	C₂×C₄	1	2	yes	—
332	C₂×#103	C₂×C₄	1	2	yes	—
333	#408	—	2	1	no	—
334	#405	—	2	2	no	—
335	#405	—	2	2	no	—
336	#405	—	2	2	no	—
337	C₄×M₁₆	—	2	2	no	—
338	C₄×M₁₆	—	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×C₄×C₈	—	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	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	Q₈⋊C₈	C₂³	1	2	yes	—
367	Q₈⋊C₈	C₂³	1	2	yes	—
368	Q₈⋊C₈	C₂³	1	2	yes	—
369	Q₈⋊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×Q₈	C₂²×C₄	1	2	yes	—
394	C₂²×Q₈	C₂²×C₄	1	2	yes	—
395	#135	—	2	4	no	—
396	C₂×Q₁₆	—	2	4	no	—
397	C₂×Q₁₆	—	2	4	no	—
398	C₂×Q₁₆	C₂²×C₄	1	2	yes	—
399	C₂×Q₁₆	C₂²×C₄	1	2	yes	—
400	C₂×Q₁₆	C₂²×C₄	1	1	yes	characteristic
401	C₂×Q₁₆	C₂²×C₄	1	1	yes	characteristic
402	C₂×Q₁₆	C₂²×C₄	1	2	yes	—
403	C₂×Q₁₆	C₂²×C₄	1	1	yes	characteristic
404	C₂×SD₁₆	C₂²×C₄	1	2	yes	—
405	C₂×SD₁₆	C₂²×C₄	1	2	yes	—
406	C₂×SD₁₆	C₂²×C₄	1	2	yes	—
407	C₂×D₈	C₂²×C₄	1	1	yes	characteristic
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	C₂×D₄	1	1	yes	characteristic
413	C₂×M₁₆	C₂×D₄	1	1	yes	characteristic
414	C₂×M₁₆	C₂×D₄	1	1	yes	characteristic
415	C₂×M₁₆	C₂×D₄	1	1	yes	characteristic
416	C₂²×C₈	—	2	1	no	—
417	C₂²×C₈	—	2	2	no	—
418	C₂²×C₈	—	2	2	no	—
419	C₂²×C₈	—	2	2	no	—
420	C₂²×C₈	—	2	2	no	—
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	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	C₂×D₄	1	1	yes	characteristic
428	C₂²×C₈	C₂×D₄	1	1	yes	characteristic
429	C₄⋊Q₈	—	2	2	no	—
430	C₄⋊Q₈	—	2	2	no	—
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	—	2	2	no	—
443	#125	—	2	2	no	—
444	#125	C₂²×C₄	1	2	yes	—
445	#125	C₂²×C₄	1	2	yes	—
446	#124	—	2	2	no	—
447	#124	—	2	2	no	—
448	#124	C₂²×C₄	1	2	yes	—
449	#124	C₂²×C₄	1	2	yes	—
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	—	2	2	no	—
462	C₂²⋊Q₈	—	2	2	no	—
463	C₂²⋊Q₈	C₂²×C₄	1	2	yes	—
464	C₂²⋊Q₈	C₂²×C₄	1	2	yes	—
465	C₂²⋊Q₈	C₂²×C₄	1	2	yes	—
466	C₂²⋊Q₈	C₂²×C₄	1	2	yes	—
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	C₄×Q₈	—	2	2	no	—
472	C₄×Q₈	—	2	2	no	—
473	C₄×Q₈	—	2	2	no	—
474	C₄×Q₈	—	2	2	no	—
475	C₄×Q₈	—	2	2	no	—
476	C₄×Q₈	—	2	2	no	—
477	C₄×Q₈	C₂²×C₄	1	2	yes	—
478	C₄×Q₈	C₂²×C₄	1	2	yes	—
479	C₄×Q₈	C₂²×C₄	1	2	yes	—
480	C₄×Q₈	C₂²×C₄	1	2	yes	—
481	C₄×Q₈	C₂²×C₄	1	2	yes	—
482	C₄×Q₈	C₂²×C₄	1	1	yes	characteristic
483	C₄×Q₈	C₂×D₄	1	1	yes	characteristic
484	C₄×Q₈	C₂⁴	1	2	yes	—
485	C₄×Q₈	C₂⁴	1	2	yes	—
486	C₄×Q₈	C₂⁴	1	2	yes	—
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	C₂²×C₄	1	2	yes	—
495	C₄×D₄	C₂²×C₄	1	1	yes	characteristic
496	C₄×D₄	C₂²×C₄	1	1	yes	characteristic
497	C₄×D₄	C₂²×C₄	1	1	yes	characteristic
498	C₄×D₄	C₂×D₄	1	1	yes	characteristic
499	C₄×D₄	C₂×D₄	1	1	yes	characteristic
500	C₄×D₄	C₂×D₄	1	1	yes	characteristic
501	C₄×D₄	C₂⁴	1	2	yes	—
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	#41	1	1	yes	characteristic
511	#117	#41	1	1	yes	characteristic
512	#117	#41	1	1	yes	characteristic
513	C₂×C₄⋊C₄	—	2	2	no	—
514	C₂×C₄⋊C₄	—	2	2	no	—
515	C₂×C₄⋊C₄	C₂²×C₄	1	2	yes	—
516	C₂×C₄⋊C₄	C₂²×C₄	1	2	yes	—
517	C₂×C₄²	—	2	2	no	—
518	C₂×C₄²	—	2	2	no	—
519	C₂×C₄²	—	2	2	no	—
520	C₂×C₄²	C₂⁴	1	1	yes	characteristic
521	C₂×C₄²	C₂⁴	1	1	yes	characteristic
522	C₂×C₄²	C₂⁴	1	1	yes	characteristic
523	#107	C₂²×C₄	1	1	yes	characteristic
524	#107	C₂²×C₄	1	1	yes	characteristic
525	#107	C₂²×C₄	1	1	yes	characteristic
526	#107	C₂²×C₄	1	2	yes	—
527	#107	C₂²×C₄	1	2	yes	—
528	#107	C₂²×C₄	1	1	yes	characteristic
529	#107	C₂²×C₄	1	2	yes	—
530	#106	C₂²×C₄	1	2	yes	—
531	#106	C₂²×C₄	1	2	yes	—
532	#106	C₂²×C₄	1	2	yes	—
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	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	2	no	—
546	C₄⋊C₈	—	2	2	no	—
547	C₄⋊C₈	—	2	2	no	—
548	C₄⋊C₈	—	2	1	no	—
549	C₄⋊C₈	—	2	1	no	—
550	C₄⋊C₈	—	2	1	no	—
551	C₄⋊C₈	—	2	1	no	—
552	C₄⋊C₈	C₂²×C₄	1	1	yes	characteristic
553	C₄⋊C₈	C₂²×C₄	1	1	yes	characteristic
554	C₄⋊C₈	C₂²×C₄	1	1	yes	characteristic
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	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	C₂×D₄	1	1	yes	characteristic
563	C₄⋊C₈	C₂×D₄	1	1	yes	characteristic
564	C₄⋊C₈	C₂⁴	1	2	yes	—
565	C₄⋊C₈	C₂⁴	1	2	yes	—
566	C₄⋊C₈	C₂⁴	1	2	yes	—
567	C₄⋊C₈	C₂⁴	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	#103	C₂²×C₄	1	2	yes	—
575	#103	C₂²×C₄	1	2	yes	—
576	#103	C₂²×C₄	1	2	yes	—
577	#103	C₂²×C₄	1	2	yes	—
578	#103	C₂²×C₄	1	2	yes	—
579	#103	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	C₂²⋊C₈	—	2	2	no	—
585	C₂²⋊C₈	—	2	2	no	—
586	C₂²⋊C₈	—	2	2	no	—
587	C₂²⋊C₈	—	2	1	no	—
588	C₂²⋊C₈	—	2	1	no	—
589	C₂²⋊C₈	—	2	1	no	—
590	C₂²⋊C₈	—	2	1	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	C₂²×C₄	1	1	yes	characteristic
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	C₂×D₄	1	1	yes	characteristic
602	C₂²⋊C₈	C₂×D₄	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	#97	—	2	2	no	—
608	#97	—	2	2	no	—
609	#97	—	2	2	no	—
610	#97	—	2	2	no	—
611	#97	—	2	2	no	—
612	#97	—	2	2	no	—
613	#97	—	2	1	no	—
614	#97	C₂×D₄	1	1	yes	characteristic
615	#97	C₂×D₄	1	1	yes	characteristic
616	#97	C₂×D₄	1	1	yes	characteristic
617	#97	C₂×D₄	1	1	yes	characteristic
618	C₄×C₈	—	2	2	no	—
619	C₄×C₈	—	2	2	no	—
620	C₄×C₈	—	2	2	no	—
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	#41	—	2	4	no	—
649	#41	—	4	2	no	—
650	#41	—	4	2	no	—
651	#41	—	8	4	no	—
652	C₂×Q₈	—	2	2	no	—
653	C₂×Q₈	—	2	2	no	—
654	C₂×Q₈	—	2	2	no	—
655	C₂×Q₈	—	2	4	no	—
656	C₂×Q₈	—	2	4	no	—
657	C₂×Q₈	—	4	2	no	—
658	C₂×Q₈	—	4	2	no	—
659	C₂×Q₈	C₄×D₄	1	1	yes	characteristic
660	C₂×Q₈	C₂³×C₄	1	2	yes	—
661	C₂×Q₈	C₂³×C₄	1	2	yes	—
662	C₂×Q₈	C₂³×C₄	1	2	yes	—
663	C₂×D₄	—	2	2	no	—
664	C₂×D₄	—	2	2	no	—
665	C₂×D₄	—	2	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	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	—	2	2	no	—
677	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
678	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
679	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
680	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
681	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
682	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
683	C₂²×C₄	C₂×#41	1	1	yes	characteristic
684	C₂²×C₄	C₂×#41	1	1	yes	characteristic
685	C₂²×C₄	C₂×#41	1	1	yes	characteristic
686	Q₁₆	—	2	4	no	—
687	Q₁₆	—	2	4	no	—
688	Q₁₆	—	2	2	no	—
689	Q₁₆	—	2	2	no	—
690	Q₁₆	—	4	2	no	—
691	Q₁₆	#131	1	4	yes	—
692	SD₁₆	—	2	4	no	—
693	SD₁₆	—	4	2	no	—
694	SD₁₆	—	4	2	no	—
695	D₈	—	2	2	no	—
696	M₁₆	—	2	2	no	—
697	M₁₆	—	2	2	no	—
698	M₁₆	—	4	1	no	—
699	M₁₆	—	4	1	no	—
700	M₁₆	—	4	2	no	—
701	M₁₆	—	4	4	no	—
702	M₁₆	—	8	2	no	—
703	M₁₆	—	8	2	no	—
704	C₂×C₈	—	2	2	no	—
705	C₂×C₈	—	2	2	no	—
706	C₂×C₈	—	2	2	no	—
707	C₂×C₈	—	2	2	no	—
708	C₂×C₈	—	2	2	no	—
709	C₂×C₈	—	2	2	no	—
710	C₂×C₈	—	2	2	no	—
711	C₂×C₈	—	2	2	no	—
712	C₂×C₈	—	2	1	no	—
713	C₂×C₈	—	2	1	no	—
714	C₂×C₈	—	2	1	no	—
715	C₂×C₈	—	2	1	no	—
716	C₂×C₈	—	4	1	no	—
717	C₂×C₈	—	4	1	no	—
718	C₂×C₈	—	4	1	no	—
719	C₂×C₈	—	4	1	no	—
720	C₂×C₈	—	4	2	no	—
721	C₂×C₈	—	8	2	no	—
722	C₂×C₈	—	8	2	no	—
723	C₂×C₈	—	8	2	no	—
724	C₂×C₈	—	8	2	no	—
725	C₂×C₈	C₂³×C₄	1	1	yes	characteristic
726	C₂×C₈	C₂³×C₄	1	1	yes	characteristic
727	C₂×C₈	C₂³×C₄	1	1	yes	characteristic
728	C₂×C₈	C₂³×C₄	1	1	yes	characteristic
729	C₂×C₈	C₂³×C₄	1	1	yes	characteristic
730	C₂×C₈	C₂³×C₄	1	1	yes	characteristic
731	C₂×C₈	C₂³×C₄	1	1	yes	characteristic
732	C₂×C₈	C₂³×C₄	1	1	yes	characteristic
733	C₂×C₈	C₂²×D₄	1	1	yes	characteristic
734	C₂×C₈	C₂²×D₄	1	1	yes	characteristic
735	C₂×C₈	C₂²×D₄	1	1	yes	characteristic
736	C₂×C₈	C₂²×D₄	1	1	yes	characteristic
737	C₂×C₈	C₂²×D₄	1	1	yes	characteristic
738	C₂×C₈	C₂²×D₄	1	1	yes	characteristic
739	C₂×C₈	C₂²×D₄	1	1	yes	characteristic
740	C₂×C₈	C₂²×D₄	1	1	yes	characteristic
741	C₄⋊C₄	—	2	2	no	—
742	C₄⋊C₄	—	2	2	no	—
743	C₄⋊C₄	—	2	2	no	—
744	C₄⋊C₄	—	2	2	no	—
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	—	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	C₄×D₄	1	1	yes	characteristic
763	C₄⋊C₄	C₄×D₄	1	1	yes	characteristic
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	C₂³×C₄	1	2	yes	—
769	C₄⋊C₄	C₂³×C₄	1	2	yes	—
770	C₄⋊C₄	C₂³×C₄	1	2	yes	—
771	C₄⋊C₄	C₂³×C₄	1	2	yes	—
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	—	2	2	no	—
795	C₄²	—	2	2	no	—
796	C₄²	—	2	2	no	—
797	C₄²	—	2	2	no	—
798	C₄²	—	2	2	no	—
799	C₄²	—	2	2	no	—
800	C₄²	C₂³×C₄	1	1	yes	characteristic
801	C₄²	C₂³×C₄	1	1	yes	characteristic
802	C₄²	C₂³×C₄	1	1	yes	characteristic
803	C₄²	C₂²×D₄	1	1	yes	characteristic
804	C₄²	C₂²×D₄	1	1	yes	characteristic
805	C₄²	C₂²×D₄	1	1	yes	characteristic
806	C₄²	C₂×#41	1	1	yes	characteristic
807	C₄²	C₂×#41	1	1	yes	characteristic
808	C₄²	C₂×#41	1	1	yes	characteristic
809	C₄²	C₂⁵	1	1	yes	characteristic
810	C₂³	—	2	2	no	—
811	C₂³	C₂×C₄×D₄	1	1	yes	characteristic
812	C₂³	C₂×C₄×D₄	1	1	yes	characteristic
813	C₂³	C₂×C₄×D₄	1	1	yes	characteristic
814	Q₈	—	2	2	no	—
815	Q₈	—	2	2	no	—
816	Q₈	—	2	2	no	—
817	Q₈	—	2	2	no	—
818	Q₈	—	2	2	no	—
819	Q₈	—	4	1	no	—
820	Q₈	—	4	4	no	—
821	Q₈	—	4	4	no	—
822	Q₈	—	8	2	no	—
823	Q₈	C₂×#131	1	4	yes	—
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	—	4	4	no	—
831	D₄	—	8	2	no	—
832	C₂×C₄	—	2	2	no	—
833	C₂×C₄	—	2	2	no	—
834	C₂×C₄	—	2	1	no	—
835	C₂×C₄	—	2	1	no	—
836	C₂×C₄	—	2	1	no	—
837	C₂×C₄	—	2	1	no	—
838	C₂×C₄	—	2	1	no	—
839	C₂×C₄	—	2	1	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	2	no	—
847	C₂×C₄	—	2	2	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	—	4	1	no	—
853	C₂×C₄	—	4	1	no	—
854	C₂×C₄	—	4	4	no	—
855	C₂×C₄	—	4	4	no	—
856	C₂×C₄	—	4	4	no	—
857	C₂×C₄	—	4	4	no	—
858	C₂×C₄	—	4	2	no	—
859	C₂×C₄	—	4	2	no	—
860	C₂×C₄	—	8	2	no	—
861	C₂×C₄	—	8	2	no	—
862	C₂×C₄	C₂×C₄×D₄	1	1	yes	characteristic
863	C₂×C₄	C₂×C₄×D₄	1	1	yes	characteristic
864	C₂×C₄	C₂×C₄×D₄	1	1	yes	characteristic
865	C₂×C₄	C₂×C₄×D₄	1	1	yes	characteristic
866	C₂×C₄	C₂×C₄×D₄	1	1	yes	characteristic
867	C₂×C₄	C₂×C₄×D₄	1	1	yes	characteristic
868	C₂×C₄	C₂×C₄×D₄	1	1	yes	characteristic
869	C₂×C₄	C₂×C₄×D₄	1	1	yes	characteristic
870	C₂×C₄	C₂×C₄×D₄	1	1	yes	characteristic
871	C₂×C₄	C₂⁴×C₄	1	1	yes	characteristic
872	C₂×C₄	C₂³×D₄	1	1	yes	characteristic
873	C₂×C₄	C₂²×#41	1	1	yes	characteristic
874	C₈	—	2	1	no	—
875	C₈	—	2	1	no	—
876	C₈	—	2	1	no	—
877	C₈	—	2	1	no	—
878	C₈	—	2	1	no	—
879	C₈	—	2	1	no	—
880	C₈	—	2	1	no	—
881	C₈	—	2	1	no	—
882	C₈	—	2	1	no	—
883	C₈	—	2	1	no	—
884	C₈	—	2	1	no	—
885	C₈	—	2	1	no	—
886	C₈	—	2	1	no	—
887	C₈	—	2	1	no	—
888	C₈	—	4	1	no	—
889	C₈	—	4	1	no	—
890	C₈	—	4	1	no	—
891	C₈	—	4	1	no	—
892	C₈	—	4	2	no	—
893	C₈	—	4	2	no	—
894	C₈	—	4	2	no	—
895	C₈	—	4	2	no	—
896	C₈	C₂×#131	1	2	yes	—
897	C₈	#578	1	2	yes	—
898	C₂²	—	2	1	no	—
899	C₂²	—	2	1	no	—
900	C₂²	—	2	1	no	—
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	—	4	2	no	—
907	C₂²	—	4	2	no	—
908	C₂²	—	4	2	no	—
909	C₂²	#2957	1	2	yes	—
910	C₂²	C₂²×C₄×D₄	1	1	yes	characteristic
911	C₄	—	2	1	no	—
912	C₄	—	2	1	no	—
913	C₄	—	2	1	no	—
914	C₄	—	2	1	no	—
915	C₄	—	2	1	no	—
916	C₄	—	2	1	no	—
917	C₄	—	2	1	no	—
918	C₄	—	2	1	no	—
919	C₄	—	2	1	no	—
920	C₄	—	2	1	no	—
921	C₄	—	2	4	no	—
922	C₄	—	4	2	no	—
923	C₄	—	4	2	no	—
924	C₄	—	4	2	no	—
925	C₄	—	4	2	no	—
926	C₄	—	4	2	no	—
927	C₄	—	4	2	no	—
928	C₄	C₂²×#131	1	1	yes	characteristic
929	C₄	#3573	1	1	yes	characteristic
930	C₄	C₂×#578	1	1	yes	characteristic
931	C₄	#3584	1	1	yes	characteristic
932	C₂	—	2	2	no	—
933	C₂	—	4	1	no	—
934	C₂	—	4	1	no	—
935	C₂	—	8	2	no	—
936	C₂	D₄×#131	1	1	yes	characteristic
937	C₂	C₄×#578	1	1	yes	characteristic
938	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	#61433	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. #60335	C₂	semidirect
3. #18087	C₂	semidirect
4. #18069	C₂	semidirect
5. #18068	C₂	semidirect
6. #18058	C₂	semidirect
7. #18039	C₂	semidirect
8. M₁₆×Q₁₆	C₂	semidirect
9. #18023	C₂	semidirect
10. #18013	C₂	semidirect
11. #18012	C₂	semidirect
12. #17973	C₂	semidirect
13. #17972	C₂	semidirect
14. #17959	C₂	semidirect
15. #17921	C₂	semidirect
16. #17919	C₂	semidirect
17. #17915	C₂	semidirect
18. #17857	C₂	semidirect
19. #17856	C₂	semidirect
20. C₂×C₈×Q₁₆	C₂	semidirect
21. #17836	C₂	semidirect
22. #17524	C₂	semidirect
23. #17328	C₂	semidirect

Maximal subgroups

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

subgroup	index
#61433	2
#60335	2
#18087	2
#18069	2
#18068	2
#18058	2
#18039	2
M₁₆×Q₁₆	2
#18023	2
#18013	2
#18012	2
#17973	2
#17972	2
#17959	2
#17921	2
#17919	2
#17915	2
#17857	2
#17856	2
C₂×C₈×Q₁₆	2
#17836	2
#17524	2
#17328	2