Subgroups — #62301

Order 256.

964 conjugacy classes of subgroups.

The subgroup lattice has 913 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3519	C₂	1	1	yes	maximal, characteristic, complemented
2	#3505	C₂	1	1	yes	maximal, characteristic, complemented
3	#3355	C₂	1	1	yes	maximal, characteristic, complemented
4	#3347	C₂	1	1	yes	maximal, characteristic, complemented
5	#3344	C₂	1	1	yes	maximal, characteristic, complemented
6	#3337	C₂	1	1	yes	maximal, characteristic, complemented
7	#3326	C₂	1	1	yes	maximal, characteristic, complemented
8	#3322	C₂	1	1	yes	maximal, characteristic, complemented
9	#3321	C₂	1	1	yes	maximal, characteristic, complemented
10	#3314	C₂	1	1	yes	maximal, characteristic, complemented
11	#3310	C₂	1	1	yes	maximal, characteristic, complemented
12	#3309	C₂	1	1	yes	maximal, characteristic, complemented
13	#3297	C₂	1	1	yes	maximal, characteristic, complemented
14	#3296	C₂	1	1	yes	maximal, characteristic, complemented
15	#3280	C₂	1	1	yes	maximal, characteristic, complemented
16	#3275	C₂	1	1	yes	maximal, characteristic, complemented
17	#3271	C₂	1	1	yes	maximal, characteristic, complemented
18	#3264	C₂	1	1	yes	maximal, characteristic, complemented
19	#3256	C₂	1	1	yes	maximal, characteristic, complemented
20	#3251	C₂	1	1	yes	maximal, characteristic, complemented
21	#3197	C₂	1	1	yes	maximal, characteristic, complemented
22	#3194	C₂	1	1	yes	maximal, characteristic, complemented
23	#3194	C₂	1	1	yes	maximal, characteristic, complemented
24	#3193	C₂	1	1	yes	maximal, characteristic, complemented
25	#3183	C₂	1	1	yes	maximal, characteristic, complemented
26	#3171	C₂	1	1	yes	maximal, characteristic, complemented
27	#3056	C₂	1	1	yes	maximal, characteristic, complemented
28	#3055	C₂	1	1	yes	maximal, characteristic, complemented
29	#3054	C₂	1	1	yes	maximal, characteristic, complemented
30	C₂×#469	C₂	1	1	yes	maximal, characteristic, complemented
31	D₄×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×#137	C₂²	1	1	yes	characteristic, complemented
33	C₂×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic, complemented
34	C₂×#135	C₂²	1	1	yes	characteristic, complemented
35	C₂²×D₈	C₂²	1	1	yes	characteristic, complemented
36	C₂²×M₁₆	C₂²	1	1	yes	characteristic, complemented
37	C₂²×M₁₆	C₂²	1	1	yes	characteristic, complemented
38	#555	C₂²	1	1	yes	characteristic, complemented
39	#554	C₂²	1	1	yes	characteristic
40	#553	—	2	1	no	—
41	#553	—	2	1	no	—
42	#553	—	2	1	no	—
43	#553	C₂²	1	1	yes	characteristic
44	#553	C₂²	1	1	yes	characteristic, complemented
45	#553	C₂²	1	1	yes	characteristic, complemented
46	#553	C₂²	1	1	yes	characteristic, complemented
47	#552	C₂²	1	1	yes	characteristic
48	#552	C₂²	1	1	yes	characteristic, complemented
49	#551	—	2	1	no	—
50	#551	—	2	1	no	—
51	#550	C₂²	1	1	yes	characteristic, complemented
52	#548	C₂²	1	1	yes	characteristic, complemented
53	#548	C₂²	1	1	yes	characteristic, complemented
54	#546	—	2	1	no	—
55	#546	—	2	1	no	—
56	#546	C₂²	1	1	yes	characteristic
57	#546	C₂²	1	1	yes	characteristic
58	#546	C₂²	1	1	yes	characteristic, complemented
59	#546	C₂²	1	1	yes	characteristic, complemented
60	D₄²	—	2	1	no	—
61	D₄²	C₂²	1	1	yes	characteristic
62	#540	—	2	1	no	—
63	#539	—	2	1	no	—
64	#538	—	2	1	no	—
65	#538	—	2	1	no	—
66	#538	—	2	1	no	—
67	#534	—	2	1	no	—
68	#532	C₂²	1	1	yes	characteristic, complemented
69	#529	C₂²	1	1	yes	characteristic, complemented
70	#529	C₂²	1	1	yes	characteristic, complemented
71	#529	C₂²	1	1	yes	characteristic, complemented
72	#525	C₂²	1	1	yes	characteristic
73	#525	C₂²	1	1	yes	characteristic, complemented
74	#525	C₂²	1	1	yes	characteristic, complemented
75	#525	C₂²	1	1	yes	characteristic, complemented
76	C₂×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
77	C₂×#121	C₂²	1	1	yes	characteristic
78	C₂×#121	C₂²	1	1	yes	characteristic, complemented
79	C₂×#121	C₂²	1	1	yes	characteristic, complemented
80	#518	—	2	1	no	—
81	#518	—	2	1	no	—
82	C₂×C₄×D₄	C₂²	1	1	yes	characteristic
83	#501	C₂²	1	1	yes	characteristic, complemented
84	#499	C₂²	1	1	yes	characteristic, complemented
85	#496	C₂²	1	1	yes	characteristic, complemented
86	#495	C₂²	1	1	yes	characteristic, complemented
87	#490	C₂²	1	1	yes	characteristic, complemented
88	#489	C₂²	1	1	yes	characteristic, complemented
89	#488	C₂²	1	1	yes	characteristic, complemented
90	#488	C₂²	1	1	yes	characteristic, complemented
91	#485	C₂²	1	1	yes	characteristic, complemented
92	#485	C₂²	1	1	yes	characteristic, complemented
93	#484	C₂²	1	1	yes	characteristic, complemented
94	#484	C₂²	1	1	yes	characteristic, complemented
95	#483	C₂²	1	1	yes	characteristic, complemented
96	#483	C₂²	1	1	yes	characteristic, complemented
97	#482	C₂²	1	1	yes	characteristic, complemented
98	#482	C₂²	1	1	yes	characteristic, complemented
99	#482	C₂²	1	1	yes	characteristic, complemented
100	#482	C₂²	1	1	yes	characteristic, complemented
101	#482	C₂²	1	1	yes	characteristic, complemented
102	#482	C₂²	1	1	yes	characteristic, complemented
103	#480	C₂²	1	1	yes	characteristic, complemented
104	#480	C₂²	1	1	yes	characteristic, complemented
105	#480	C₂²	1	1	yes	characteristic, complemented
106	#480	C₂²	1	1	yes	characteristic, complemented
107	#479	C₂²	1	1	yes	characteristic, complemented
108	#479	C₂²	1	1	yes	characteristic, complemented
109	#478	C₂²	1	1	yes	characteristic, complemented
110	#478	C₂²	1	1	yes	characteristic, complemented
111	#478	C₂²	1	1	yes	characteristic, complemented
112	#478	C₂²	1	1	yes	characteristic, complemented
113	#475	C₂²	1	1	yes	characteristic, complemented
114	#474	C₂²	1	1	yes	characteristic, complemented
115	#470	C₂²	1	1	yes	characteristic, complemented
116	#470	C₂²	1	1	yes	characteristic, complemented
117	#470	C₂²	1	1	yes	characteristic, complemented
118	#469	C₂²	1	1	yes	characteristic
119	#469	C₂²	1	1	yes	characteristic
120	#469	C₂²	1	1	yes	characteristic, complemented
121	#469	C₂²	1	1	yes	characteristic, complemented
122	#469	C₂²	1	1	yes	characteristic, complemented
123	#469	C₂²	1	1	yes	characteristic, complemented
124	#469	C₂²	1	1	yes	characteristic, complemented
125	#469	C₂²	1	1	yes	characteristic, complemented
126	#469	C₂²	1	1	yes	characteristic, complemented
127	#469	C₂²	1	1	yes	characteristic, complemented
128	#469	C₂²	1	1	yes	characteristic, complemented
129	#468	C₂²	1	1	yes	characteristic, complemented
130	#468	C₂²	1	1	yes	characteristic, complemented
131	#468	C₂²	1	1	yes	characteristic, complemented
132	#468	C₂²	1	1	yes	characteristic, complemented
133	#468	C₂²	1	1	yes	characteristic, complemented
134	#468	C₂²	1	1	yes	characteristic, complemented
135	#468	C₂²	1	1	yes	characteristic, complemented
136	#468	C₂²	1	1	yes	characteristic, complemented
137	#468	C₂²	1	1	yes	characteristic, complemented
138	#468	C₂²	1	1	yes	characteristic, complemented
139	#467	C₂²	1	1	yes	characteristic, complemented
140	#467	C₂²	1	1	yes	characteristic, complemented
141	#466	C₂²	1	1	yes	characteristic, complemented
142	#466	C₂²	1	1	yes	characteristic, complemented
143	#465	C₂²	1	1	yes	characteristic, complemented
144	#465	C₂²	1	1	yes	characteristic, complemented
145	#465	C₂²	1	1	yes	characteristic, complemented
146	#465	C₂²	1	1	yes	characteristic, complemented
147	#464	C₂²	1	1	yes	characteristic, complemented
148	#464	C₂²	1	1	yes	characteristic, complemented
149	#463	C₂²	1	1	yes	characteristic, complemented
150	#463	C₂²	1	1	yes	characteristic, complemented
151	#463	C₂²	1	1	yes	characteristic, complemented
152	#463	C₂²	1	1	yes	characteristic, complemented
153	#460	C₂²	1	1	yes	characteristic, complemented
154	#459	C₂²	1	1	yes	characteristic, complemented
155	#452	C₂²	1	1	yes	characteristic, complemented
156	#452	C₂²	1	1	yes	characteristic, complemented
157	#450	C₂²	1	1	yes	characteristic, complemented
158	#450	C₂²	1	1	yes	characteristic, complemented
159	#450	C₂²	1	1	yes	characteristic, complemented
160	#450	C₂²	1	1	yes	characteristic, complemented
161	#449	C₂²	1	1	yes	characteristic, complemented
162	#449	C₂²	1	1	yes	characteristic, complemented
163	#449	C₂²	1	1	yes	characteristic, complemented
164	#449	C₂²	1	1	yes	characteristic, complemented
165	#449	C₂²	1	1	yes	characteristic, complemented
166	#449	C₂²	1	1	yes	characteristic, complemented
167	#448	C₂²	1	1	yes	characteristic, complemented
168	#448	C₂²	1	1	yes	characteristic, complemented
169	#447	C₂²	1	1	yes	characteristic, complemented
170	#447	C₂²	1	1	yes	characteristic, complemented
171	#442	C₂²	1	1	yes	characteristic, complemented
172	#441	C₂²	1	1	yes	characteristic, complemented
173	#440	C₂²	1	1	yes	characteristic, complemented
174	#440	C₂²	1	1	yes	characteristic, complemented
175	C₄×SD₁₆	C₂²	1	1	yes	characteristic, complemented
176	C₄×SD₁₆	C₂²	1	1	yes	characteristic, complemented
177	C₄×D₈	C₂²	1	1	yes	characteristic, complemented
178	C₄×D₈	C₂²	1	1	yes	characteristic, complemented
179	#436	C₂²	1	1	yes	characteristic, complemented
180	#436	C₂²	1	1	yes	characteristic, complemented
181	#435	C₂²	1	1	yes	characteristic
182	#435	C₂²	1	1	yes	characteristic
183	#435	C₂²	1	1	yes	characteristic, complemented
184	#435	C₂²	1	1	yes	characteristic, complemented
185	C₈×D₄	C₂²	1	1	yes	characteristic, complemented
186	C₈×D₄	C₂²	1	1	yes	characteristic, complemented
187	#428	C₂²	1	1	yes	characteristic, complemented
188	#428	C₂²	1	1	yes	characteristic, complemented
189	#427	C₂²	1	1	yes	characteristic, complemented
190	C₂×#106	C₂²	1	1	yes	characteristic, complemented
191	#423	C₂²	1	1	yes	characteristic, complemented
192	#419	C₂²	1	1	yes	characteristic, complemented
193	#418	C₂²	1	1	yes	characteristic, complemented
194	#417	C₂²	1	1	yes	characteristic, complemented
195	#417	C₂²	1	1	yes	characteristic, complemented
196	#416	C₂²	1	1	yes	characteristic, complemented
197	#416	C₂²	1	1	yes	characteristic, complemented
198	C₂×#102	C₂²	1	1	yes	characteristic, complemented
199	C₂×#102	C₂²	1	1	yes	characteristic, complemented
200	#407	C₂²	1	1	yes	characteristic, complemented
201	#407	C₂²	1	1	yes	characteristic, complemented
202	C₄×M₁₆	C₂²	1	1	yes	characteristic, complemented
203	C₂×#41	—	2	1	no	—
204	C₂×#41	C₂³	1	1	yes	characteristic
205	C₂×#41	C₂³	1	1	yes	characteristic
206	C₂×#41	C₂³	1	1	yes	characteristic
207	C₂×#41	C₂³	1	1	yes	characteristic
208	C₂²×Q₈	C₂³	1	1	yes	characteristic
209	C₂²×D₄	—	2	1	no	—
210	C₂²×D₄	—	2	1	no	—
211	C₂²×D₄	—	2	1	no	—
212	C₂²×D₄	—	2	1	no	—
213	C₂²×D₄	D₄	1	1	yes	characteristic
214	C₂²×D₄	C₂³	1	1	yes	characteristic
215	C₂²×D₄	C₂³	1	1	yes	characteristic
216	C₂²×D₄	C₂³	1	1	yes	characteristic
217	C₂³×C₄	C₂³	1	1	yes	characteristic
218	C₂³×C₄	C₂³	1	1	yes	characteristic
219	#137	—	4	2	no	—
220	AGL(1,ℤ/8)	—	4	2	no	—
221	#135	—	4	2	no	—
222	C₂×Q₁₆	C₂³	1	1	yes	characteristic
223	C₂×Q₁₆	C₂³	1	1	yes	characteristic
224	C₂×SD₁₆	C₂³	1	1	yes	characteristic
225	C₂×SD₁₆	C₂³	1	1	yes	characteristic
226	C₂×SD₁₆	C₂³	1	1	yes	characteristic
227	C₂×SD₁₆	C₂³	1	1	yes	characteristic
228	C₂×SD₁₆	C₂³	1	1	yes	characteristic
229	C₂×SD₁₆	C₂³	1	1	yes	characteristic
230	C₂×SD₁₆	C₂³	1	1	yes	characteristic
231	C₂×SD₁₆	C₂³	1	1	yes	characteristic
232	C₂×D₈	—	4	2	no	—
233	C₂×D₈	C₂³	1	1	yes	characteristic
234	C₂×D₈	C₂³	1	1	yes	characteristic
235	C₂×D₈	C₂³	1	1	yes	characteristic
236	C₂×D₈	C₂³	1	1	yes	characteristic
237	C₂×D₈	C₂³	1	1	yes	characteristic
238	C₂×D₈	C₂³	1	1	yes	characteristic
239	C₂×M₁₆	—	4	2	no	—
240	C₂×M₁₆	—	4	2	no	—
241	C₂×M₁₆	C₂³	1	1	yes	characteristic
242	C₂×M₁₆	C₂³	1	1	yes	characteristic
243	C₂×M₁₆	C₂³	1	1	yes	characteristic
244	C₂×M₁₆	C₂³	1	1	yes	characteristic
245	C₂×M₁₆	C₂³	1	1	yes	characteristic
246	C₂×M₁₆	C₂³	1	1	yes	characteristic
247	C₂×M₁₆	C₂³	1	1	yes	characteristic
248	C₂×M₁₆	C₂³	1	1	yes	characteristic
249	C₂²×C₈	C₂³	1	1	yes	characteristic
250	C₂²×C₈	C₂³	1	1	yes	characteristic
251	C₂²×C₈	C₂³	1	1	yes	characteristic
252	C₂²×C₈	C₂³	1	1	yes	characteristic
253	C₄⋊Q₈	C₂³	1	1	yes	characteristic
254	#127	—	2	1	no	—
255	#127	C₂³	1	1	yes	characteristic
256	#126	—	2	1	no	—
257	#126	—	2	1	no	—
258	#126	—	2	1	no	—
259	#126	—	2	1	no	—
260	#126	—	2	1	no	—
261	#126	—	2	1	no	—
262	#126	—	2	1	no	—
263	#126	—	2	1	no	—
264	#126	—	2	1	no	—
265	#125	—	2	1	no	—
266	#125	—	2	1	no	—
267	#125	—	2	1	no	—
268	#125	C₂³	1	1	yes	characteristic
269	#125	C₂³	1	1	yes	characteristic
270	#125	C₂³	1	1	yes	characteristic
271	#124	—	2	1	no	—
272	#124	—	2	1	no	—
273	#124	—	2	1	no	—
274	#124	—	2	1	no	—
275	#124	—	2	1	no	—
276	#124	C₂³	1	1	yes	characteristic
277	#124	C₂³	1	1	yes	characteristic
278	#124	C₂³	1	1	yes	characteristic
279	#123	—	2	1	no	—
280	#123	—	2	1	no	—
281	#123	—	2	1	no	—
282	#123	—	2	1	no	—
283	#123	—	2	1	no	—
284	#123	—	2	1	no	—
285	#123	—	2	1	no	—
286	#123	—	2	1	no	—
287	#123	—	2	1	no	—
288	#123	—	2	1	no	—
289	#123	—	2	1	no	—
290	#123	—	2	1	no	—
291	#123	—	2	1	no	—
292	#123	—	2	1	no	—
293	#123	—	2	1	no	—
294	#123	—	2	1	no	—
295	#123	—	2	1	no	—
296	C₂²⋊Q₈	—	2	1	no	—
297	C₂²⋊Q₈	—	2	1	no	—
298	C₂²⋊Q₈	—	2	1	no	—
299	C₂²⋊Q₈	—	2	1	no	—
300	C₂²⋊Q₈	—	2	1	no	—
301	C₂²⋊Q₈	—	2	1	no	—
302	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
303	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
304	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
305	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
306	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
307	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
308	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
309	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
310	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
311	#121	—	2	1	no	—
312	#121	—	2	1	no	—
313	#121	—	2	1	no	—
314	#121	—	2	1	no	—
315	#121	—	2	1	no	—
316	#121	—	2	1	no	—
317	#121	—	2	1	no	—
318	#121	—	2	1	no	—
319	#121	—	2	1	no	—
320	#121	—	2	1	no	—
321	#121	—	2	1	no	—
322	#121	—	2	1	no	—
323	#121	—	2	1	no	—
324	#121	—	2	1	no	—
325	#121	—	2	1	no	—
326	#121	—	2	1	no	—
327	#121	—	2	1	no	—
328	#121	—	2	1	no	—
329	#121	—	2	1	no	—
330	#121	—	2	1	no	—
331	#121	—	2	1	no	—
332	#121	C₂³	1	1	yes	characteristic
333	#121	C₂³	1	1	yes	characteristic
334	#121	C₂³	1	1	yes	characteristic
335	#121	C₂³	1	1	yes	characteristic
336	#121	C₂³	1	1	yes	characteristic
337	#121	C₂³	1	1	yes	characteristic
338	#121	C₂³	1	1	yes	characteristic
339	#121	C₂³	1	1	yes	characteristic
340	#121	C₂³	1	1	yes	characteristic
341	#121	C₂³	1	1	yes	characteristic
342	#121	C₂³	1	1	yes	characteristic
343	#121	C₂³	1	1	yes	characteristic
344	#121	C₂³	1	1	yes	characteristic
345	#121	C₂³	1	1	yes	characteristic
346	#121	C₂³	1	1	yes	characteristic
347	#120	—	2	1	no	—
348	#120	—	2	1	no	—
349	#120	—	2	1	no	—
350	#120	—	2	1	no	—
351	#120	—	2	1	no	—
352	#120	—	2	1	no	—
353	#120	—	2	1	no	—
354	#120	—	2	1	no	—
355	#120	—	2	1	no	—
356	#120	—	2	1	no	—
357	C₄×Q₈	C₂³	1	1	yes	characteristic
358	C₄×Q₈	C₂³	1	1	yes	characteristic
359	C₄×Q₈	C₂³	1	1	yes	characteristic
360	C₄×D₄	—	2	1	no	—
361	C₄×D₄	—	2	1	no	—
362	C₄×D₄	—	2	1	no	—
363	C₄×D₄	—	2	1	no	—
364	C₄×D₄	—	2	1	no	—
365	C₄×D₄	—	2	1	no	—
366	C₄×D₄	—	2	1	no	—
367	C₄×D₄	—	2	1	no	—
368	C₄×D₄	—	2	1	no	—
369	C₄×D₄	—	2	1	no	—
370	C₄×D₄	—	2	1	no	—
371	C₄×D₄	—	2	1	no	—
372	C₄×D₄	—	2	1	no	—
373	C₄×D₄	—	2	1	no	—
374	C₄×D₄	—	2	1	no	—
375	C₄×D₄	—	2	1	no	—
376	C₄×D₄	—	2	1	no	—
377	C₄×D₄	—	2	1	no	—
378	C₄×D₄	—	2	1	no	—
379	C₄×D₄	—	2	1	no	—
380	C₄×D₄	D₄	1	1	yes	characteristic
381	C₄×D₄	D₄	1	1	yes	characteristic
382	C₄×D₄	D₄	1	1	yes	characteristic
383	C₄×D₄	D₄	1	1	yes	characteristic
384	C₄×D₄	C₂³	1	1	yes	characteristic
385	C₄×D₄	C₂³	1	1	yes	characteristic
386	C₄×D₄	C₂³	1	1	yes	characteristic
387	C₄×D₄	C₂³	1	1	yes	characteristic
388	C₄×D₄	C₂³	1	1	yes	characteristic
389	C₄×D₄	C₂³	1	1	yes	characteristic
390	C₄×D₄	C₂³	1	1	yes	characteristic
391	C₄×D₄	C₂³	1	1	yes	characteristic
392	C₄×D₄	C₂³	1	1	yes	characteristic
393	#117	—	2	1	no	—
394	#117	—	2	1	no	—
395	#117	—	2	1	no	—
396	#117	—	2	1	no	—
397	#117	—	2	1	no	—
398	#117	—	2	1	no	—
399	#117	C₂³	1	1	yes	characteristic
400	#117	C₂³	1	1	yes	characteristic
401	#117	C₂³	1	1	yes	characteristic
402	#117	C₂³	1	1	yes	characteristic
403	C₂×C₄⋊C₄	—	2	1	no	—
404	C₂×C₄⋊C₄	D₄	1	1	yes	characteristic
405	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
406	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
407	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
408	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
409	C₂×C₂²⋊C₄	—	2	1	no	—
410	C₂×C₂²⋊C₄	—	2	1	no	—
411	C₂×C₂²⋊C₄	—	2	1	no	—
412	C₂×C₂²⋊C₄	—	2	1	no	—
413	C₂×C₂²⋊C₄	—	2	1	no	—
414	C₂×C₂²⋊C₄	—	2	1	no	—
415	C₂×C₂²⋊C₄	—	2	1	no	—
416	C₂×C₂²⋊C₄	—	2	1	no	—
417	C₂×C₂²⋊C₄	D₄	1	1	yes	characteristic
418	C₂×C₂²⋊C₄	D₄	1	1	yes	characteristic
419	C₂×C₄²	C₂³	1	1	yes	characteristic
420	#107	C₂³	1	1	yes	characteristic
421	#107	C₂³	1	1	yes	characteristic
422	#107	C₂³	1	1	yes	characteristic
423	#107	C₂³	1	1	yes	characteristic
424	#107	C₂³	1	1	yes	characteristic
425	#107	C₂³	1	1	yes	characteristic
426	#107	C₂³	1	1	yes	characteristic
427	#107	C₂³	1	1	yes	characteristic
428	#106	C₂³	1	1	yes	characteristic
429	#106	C₂³	1	1	yes	characteristic
430	#106	C₂³	1	1	yes	characteristic
431	#106	C₂³	1	1	yes	characteristic
432	#106	C₂³	1	1	yes	characteristic
433	#106	C₂³	1	1	yes	characteristic
434	#106	C₂³	1	1	yes	characteristic
435	#106	C₂³	1	1	yes	characteristic
436	C₄⋊C₈	C₂³	1	1	yes	characteristic
437	C₄⋊C₈	C₂³	1	1	yes	characteristic
438	C₄⋊C₈	C₂³	1	1	yes	characteristic
439	C₄⋊C₈	C₂³	1	1	yes	characteristic
440	#103	C₂³	1	1	yes	characteristic
441	#103	C₂³	1	1	yes	characteristic
442	#103	C₂³	1	1	yes	characteristic
443	#103	C₂³	1	1	yes	characteristic
444	#103	C₂³	1	1	yes	characteristic
445	#103	C₂³	1	1	yes	characteristic
446	#103	C₂³	1	1	yes	characteristic
447	#103	C₂³	1	1	yes	characteristic
448	#103	C₂³	1	1	yes	characteristic
449	#103	C₂³	1	1	yes	characteristic
450	#103	C₂³	1	1	yes	characteristic
451	#103	C₂³	1	1	yes	characteristic
452	#102	C₂³	1	1	yes	characteristic
453	#102	C₂³	1	1	yes	characteristic
454	#102	C₂³	1	1	yes	characteristic
455	#102	C₂³	1	1	yes	characteristic
456	#102	C₂³	1	1	yes	characteristic
457	#102	C₂³	1	1	yes	characteristic
458	#102	C₂³	1	1	yes	characteristic
459	#102	C₂³	1	1	yes	characteristic
460	#102	C₂³	1	1	yes	characteristic
461	#102	C₂³	1	1	yes	characteristic
462	#102	C₂³	1	1	yes	characteristic
463	#102	C₂³	1	1	yes	characteristic
464	#102	C₂³	1	1	yes	characteristic
465	#102	C₂³	1	1	yes	characteristic
466	#102	C₂³	1	1	yes	characteristic
467	#102	C₂³	1	1	yes	characteristic
468	#102	C₂³	1	1	yes	characteristic
469	#102	C₂³	1	1	yes	characteristic
470	#102	C₂³	1	1	yes	characteristic
471	#102	C₂³	1	1	yes	characteristic
472	C₂²⋊C₈	C₂³	1	1	yes	characteristic
473	C₂²⋊C₈	C₂³	1	1	yes	characteristic
474	C₂²⋊C₈	C₂³	1	1	yes	characteristic
475	C₂²⋊C₈	C₂³	1	1	yes	characteristic
476	C₂²⋊C₈	C₂³	1	1	yes	characteristic
477	C₂²⋊C₈	C₂³	1	1	yes	characteristic
478	C₂²⋊C₈	C₂³	1	1	yes	characteristic
479	C₂²⋊C₈	C₂³	1	1	yes	characteristic
480	#97	C₂³	1	1	yes	characteristic
481	#97	C₂³	1	1	yes	characteristic
482	C₄×C₈	C₂³	1	1	yes	characteristic
483	C₄×C₈	C₂³	1	1	yes	characteristic
484	C₂⁴	—	2	1	no	—
485	C₂⁴	—	2	1	no	—
486	C₂⁴	—	2	1	no	—
487	C₂⁴	C₂×D₄	1	1	yes	characteristic
488	C₂⁴	C₂×D₄	1	1	yes	characteristic
489	#41	—	4	1	no	—
490	#41	—	4	1	no	—
491	#41	—	4	1	no	—
492	#41	—	4	1	no	—
493	#41	—	4	1	no	—
494	#41	—	4	1	no	—
495	#41	—	4	1	no	—
496	#41	—	4	1	no	—
497	#41	—	8	2	no	—
498	C₂×Q₈	—	2	1	no	—
499	C₂×Q₈	—	2	1	no	—
500	C₂×Q₈	—	4	1	no	—
501	C₂×Q₈	—	4	1	no	—
502	C₂×Q₈	C₂⁴	1	1	yes	characteristic
503	C₂×Q₈	C₂⁴	1	1	yes	characteristic
504	C₂×Q₈	C₂⁴	1	1	yes	characteristic
505	C₂×D₄	—	2	1	no	—
506	C₂×D₄	—	2	1	no	—
507	C₂×D₄	—	2	1	no	—
508	C₂×D₄	—	2	1	no	—
509	C₂×D₄	—	2	1	no	—
510	C₂×D₄	—	2	1	no	—
511	C₂×D₄	—	2	1	no	—
512	C₂×D₄	—	2	1	no	—
513	C₂×D₄	—	2	1	no	—
514	C₂×D₄	—	2	1	no	—
515	C₂×D₄	—	2	1	no	—
516	C₂×D₄	—	2	1	no	—
517	C₂×D₄	—	2	1	no	—
518	C₂×D₄	—	2	1	no	—
519	C₂×D₄	—	2	1	no	—
520	C₂×D₄	—	2	1	no	—
521	C₂×D₄	—	2	1	no	—
522	C₂×D₄	—	2	1	no	—
523	C₂×D₄	—	2	1	no	—
524	C₂×D₄	—	2	1	no	—
525	C₂×D₄	—	2	1	no	—
526	C₂×D₄	—	2	1	no	—
527	C₂×D₄	—	2	1	no	—
528	C₂×D₄	—	2	1	no	—
529	C₂×D₄	—	4	1	no	—
530	C₂×D₄	—	4	1	no	—
531	C₂×D₄	—	4	1	no	—
532	C₂×D₄	—	4	1	no	—
533	C₂×D₄	—	4	1	no	—
534	C₂×D₄	—	4	1	no	—
535	C₂×D₄	—	4	2	no	—
536	C₂×D₄	—	4	4	no	—
537	C₂×D₄	—	4	4	no	—
538	C₂×D₄	—	8	2	no	—
539	C₂×D₄	—	8	2	no	—
540	C₂×D₄	C₂×D₄	1	1	yes	characteristic
541	C₂×D₄	C₂×D₄	1	1	yes	characteristic
542	C₂×D₄	C₂×D₄	1	1	yes	characteristic
543	C₂×D₄	C₂×D₄	1	1	yes	characteristic
544	C₂×D₄	C₂⁴	1	1	yes	characteristic
545	C₂×D₄	C₂⁴	1	1	yes	characteristic
546	C₂×D₄	C₂⁴	1	1	yes	characteristic
547	C₂×D₄	C₂⁴	1	1	yes	characteristic
548	C₂×D₄	C₂⁴	1	1	yes	characteristic
549	C₂²×C₄	—	2	1	no	—
550	C₂²×C₄	—	2	1	no	—
551	C₂²×C₄	—	2	1	no	—
552	C₂²×C₄	—	2	1	no	—
553	C₂²×C₄	—	2	1	no	—
554	C₂²×C₄	—	2	1	no	—
555	C₂²×C₄	—	2	1	no	—
556	C₂²×C₄	—	2	1	no	—
557	C₂²×C₄	—	2	1	no	—
558	C₂²×C₄	—	2	1	no	—
559	C₂²×C₄	—	2	1	no	—
560	C₂²×C₄	—	2	1	no	—
561	C₂²×C₄	—	2	1	no	—
562	C₂²×C₄	—	2	1	no	—
563	C₂²×C₄	—	4	1	no	—
564	C₂²×C₄	—	4	1	no	—
565	C₂²×C₄	—	4	1	no	—
566	C₂²×C₄	—	4	1	no	—
567	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
568	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
569	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
570	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
571	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
572	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
573	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
574	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
575	C₂²×C₄	C₂⁴	1	1	yes	characteristic
576	C₂²×C₄	C₂⁴	1	1	yes	characteristic
577	C₂²×C₄	C₂⁴	1	1	yes	characteristic
578	C₂²×C₄	C₂⁴	1	1	yes	characteristic
579	C₂²×C₄	C₂⁴	1	1	yes	characteristic
580	Q₁₆	—	2	2	no	—
581	Q₁₆	—	4	1	no	—
582	SD₁₆	—	2	2	no	—
583	SD₁₆	—	4	1	no	—
584	SD₁₆	—	4	1	no	—
585	SD₁₆	—	4	1	no	—
586	SD₁₆	—	4	1	no	—
587	SD₁₆	—	4	1	no	—
588	SD₁₆	—	4	1	no	—
589	SD₁₆	—	4	1	no	—
590	D₈	—	2	2	no	—
591	D₈	—	2	2	no	—
592	D₈	—	4	1	no	—
593	D₈	—	4	1	no	—
594	D₈	—	4	1	no	—
595	D₈	—	4	1	no	—
596	M₁₆	—	2	2	no	—
597	M₁₆	—	2	2	no	—
598	M₁₆	—	2	2	no	—
599	M₁₆	—	4	1	no	—
600	M₁₆	—	4	1	no	—
601	M₁₆	—	4	1	no	—
602	M₁₆	—	4	1	no	—
603	M₁₆	—	4	1	no	—
604	C₂×C₈	—	2	2	no	—
605	C₂×C₈	—	2	2	no	—
606	C₂×C₈	—	4	1	no	—
607	C₂×C₈	—	4	1	no	—
608	C₂×C₈	C₂⁴	1	1	yes	characteristic
609	C₂×C₈	C₂⁴	1	1	yes	characteristic
610	C₂×C₈	C₂⁴	1	1	yes	characteristic
611	C₂×C₈	C₂⁴	1	1	yes	characteristic
612	C₂×C₈	C₂⁴	1	1	yes	characteristic
613	C₂×C₈	C₂⁴	1	1	yes	characteristic
614	C₂×C₈	C₂⁴	1	1	yes	characteristic
615	C₂×C₈	C₂⁴	1	1	yes	characteristic
616	C₄⋊C₄	—	2	1	no	—
617	C₄⋊C₄	—	2	1	no	—
618	C₄⋊C₄	—	2	1	no	—
619	C₄⋊C₄	—	2	1	no	—
620	C₄⋊C₄	—	2	1	no	—
621	C₄⋊C₄	—	2	1	no	—
622	C₄⋊C₄	—	2	1	no	—
623	C₄⋊C₄	—	2	1	no	—
624	C₄⋊C₄	—	2	1	no	—
625	C₄⋊C₄	—	2	1	no	—
626	C₄⋊C₄	—	2	1	no	—
627	C₄⋊C₄	—	2	1	no	—
628	C₄⋊C₄	—	2	1	no	—
629	C₄⋊C₄	—	2	1	no	—
630	C₄⋊C₄	—	2	1	no	—
631	C₄⋊C₄	—	2	1	no	—
632	C₄⋊C₄	—	2	1	no	—
633	C₄⋊C₄	—	2	1	no	—
634	C₄⋊C₄	—	2	1	no	—
635	C₄⋊C₄	—	2	1	no	—
636	C₄⋊C₄	—	2	1	no	—
637	C₄⋊C₄	—	2	1	no	—
638	C₄⋊C₄	—	2	1	no	—
639	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
640	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
641	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
642	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
643	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
644	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
645	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
646	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
647	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
648	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
649	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
650	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
651	C₂²⋊C₄	—	2	1	no	—
652	C₂²⋊C₄	—	2	1	no	—
653	C₂²⋊C₄	—	2	1	no	—
654	C₂²⋊C₄	—	2	1	no	—
655	C₂²⋊C₄	—	2	1	no	—
656	C₂²⋊C₄	—	2	1	no	—
657	C₂²⋊C₄	—	2	1	no	—
658	C₂²⋊C₄	—	2	1	no	—
659	C₂²⋊C₄	—	2	1	no	—
660	C₂²⋊C₄	—	2	1	no	—
661	C₂²⋊C₄	—	2	1	no	—
662	C₂²⋊C₄	—	2	1	no	—
663	C₂²⋊C₄	—	2	1	no	—
664	C₂²⋊C₄	—	2	1	no	—
665	C₂²⋊C₄	—	2	1	no	—
666	C₂²⋊C₄	—	2	1	no	—
667	C₂²⋊C₄	—	2	1	no	—
668	C₂²⋊C₄	—	2	1	no	—
669	C₂²⋊C₄	—	2	1	no	—
670	C₂²⋊C₄	—	2	1	no	—
671	C₂²⋊C₄	—	2	1	no	—
672	C₂²⋊C₄	—	2	1	no	—
673	C₂²⋊C₄	—	2	1	no	—
674	C₂²⋊C₄	—	2	1	no	—
675	C₂²⋊C₄	—	2	1	no	—
676	C₂²⋊C₄	—	2	1	no	—
677	C₂²⋊C₄	—	2	1	no	—
678	C₂²⋊C₄	—	2	1	no	—
679	C₂²⋊C₄	—	2	1	no	—
680	C₂²⋊C₄	—	2	1	no	—
681	C₂²⋊C₄	—	2	1	no	—
682	C₂²⋊C₄	—	2	1	no	—
683	C₂²⋊C₄	—	2	1	no	—
684	C₂²⋊C₄	—	2	1	no	—
685	C₂²⋊C₄	—	2	1	no	—
686	C₂²⋊C₄	—	2	1	no	—
687	C₂²⋊C₄	—	2	1	no	—
688	C₂²⋊C₄	—	2	1	no	—
689	C₂²⋊C₄	—	2	1	no	—
690	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
691	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
692	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
693	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
694	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
695	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
696	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
697	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
698	C₄²	—	2	1	no	—
699	C₄²	—	2	1	no	—
700	C₄²	—	2	1	no	—
701	C₄²	—	2	1	no	—
702	C₄²	—	2	1	no	—
703	C₄²	—	2	1	no	—
704	C₄²	—	2	1	no	—
705	C₄²	C₂×D₄	1	1	yes	characteristic
706	C₄²	C₂×D₄	1	1	yes	characteristic
707	C₄²	C₂⁴	1	1	yes	characteristic
708	C₄²	C₂⁴	1	1	yes	characteristic
709	C₂³	—	2	2	no	—
710	C₂³	—	2	1	no	—
711	C₂³	—	2	1	no	—
712	C₂³	—	2	1	no	—
713	C₂³	—	2	1	no	—
714	C₂³	—	2	1	no	—
715	C₂³	—	4	1	no	—
716	C₂³	—	4	1	no	—
717	C₂³	—	4	1	no	—
718	C₂³	—	4	1	no	—
719	C₂³	—	4	1	no	—
720	C₂³	—	4	2	no	—
721	C₂³	—	4	2	no	—
722	C₂³	—	4	2	no	—
723	C₂³	—	8	1	no	—
724	C₂³	—	8	1	no	—
725	C₂³	—	8	1	no	—
726	C₂³	—	8	1	no	—
727	C₂³	—	8	1	no	—
728	C₂³	—	8	1	no	—
729	C₂³	C₂²×D₄	1	1	yes	characteristic
730	C₂³	C₂²×D₄	1	1	yes	characteristic
731	C₂³	C₂²×D₄	1	1	yes	characteristic
732	C₂³	C₂²×D₄	1	1	yes	characteristic
733	C₂³	C₂²×D₄	1	1	yes	characteristic
734	Q₈	—	2	1	no	—
735	Q₈	—	2	1	no	—
736	Q₈	—	2	1	no	—
737	Q₈	—	2	1	no	—
738	Q₈	—	2	1	no	—
739	Q₈	—	2	1	no	—
740	Q₈	—	8	1	no	—
741	Q₈	—	8	1	no	—
742	D₄	—	2	2	no	—
743	D₄	—	2	2	no	—
744	D₄	—	2	1	no	—
745	D₄	—	2	1	no	—
746	D₄	—	2	1	no	—
747	D₄	—	2	1	no	—
748	D₄	—	2	1	no	—
749	D₄	—	2	1	no	—
750	D₄	—	2	1	no	—
751	D₄	—	2	1	no	—
752	D₄	—	2	1	no	—
753	D₄	—	2	1	no	—
754	D₄	—	4	1	no	—
755	D₄	—	4	1	no	—
756	D₄	—	4	2	no	—
757	D₄	—	4	2	no	—
758	D₄	—	4	2	no	—
759	D₄	—	4	2	no	—
760	D₄	—	4	2	no	—
761	D₄	—	4	2	no	—
762	D₄	—	4	2	no	—
763	D₄	—	4	2	no	—
764	D₄	—	4	2	no	—
765	D₄	—	4	2	no	—
766	D₄	—	8	1	no	—
767	D₄	—	8	1	no	—
768	D₄	—	8	1	no	—
769	D₄	—	8	1	no	—
770	D₄	—	8	1	no	—
771	D₄	—	8	1	no	—
772	D₄	—	8	1	no	—
773	D₄	—	8	1	no	—
774	D₄	—	8	1	no	—
775	D₄	—	8	1	no	—
776	D₄	—	8	1	no	—
777	D₄	—	8	1	no	—
778	D₄	—	8	1	no	—
779	D₄	—	8	1	no	—
780	C₂×C₄	—	2	1	no	—
781	C₂×C₄	—	2	1	no	—
782	C₂×C₄	—	2	1	no	—
783	C₂×C₄	—	2	1	no	—
784	C₂×C₄	—	2	1	no	—
785	C₂×C₄	—	2	1	no	—
786	C₂×C₄	—	2	1	no	—
787	C₂×C₄	—	2	1	no	—
788	C₂×C₄	—	2	1	no	—
789	C₂×C₄	—	2	1	no	—
790	C₂×C₄	—	2	1	no	—
791	C₂×C₄	—	2	1	no	—
792	C₂×C₄	—	2	1	no	—
793	C₂×C₄	—	2	1	no	—
794	C₂×C₄	—	2	1	no	—
795	C₂×C₄	—	2	1	no	—
796	C₂×C₄	—	2	1	no	—
797	C₂×C₄	—	2	1	no	—
798	C₂×C₄	—	2	1	no	—
799	C₂×C₄	—	2	1	no	—
800	C₂×C₄	—	2	1	no	—
801	C₂×C₄	—	4	1	no	—
802	C₂×C₄	—	4	1	no	—
803	C₂×C₄	—	4	1	no	—
804	C₂×C₄	—	4	1	no	—
805	C₂×C₄	—	4	1	no	—
806	C₂×C₄	—	4	1	no	—
807	C₂×C₄	—	4	1	no	—
808	C₂×C₄	—	4	1	no	—
809	C₂×C₄	—	4	2	no	—
810	C₂×C₄	—	4	2	no	—
811	C₂×C₄	—	8	1	no	—
812	C₂×C₄	—	8	1	no	—
813	C₂×C₄	—	8	1	no	—
814	C₂×C₄	—	8	1	no	—
815	C₂×C₄	—	8	1	no	—
816	C₂×C₄	—	8	1	no	—
817	C₂×C₄	—	8	1	no	—
818	C₂×C₄	—	8	1	no	—
819	C₂×C₄	—	8	1	no	—
820	C₂×C₄	—	8	1	no	—
821	C₂×C₄	—	8	1	no	—
822	C₂×C₄	—	8	1	no	—
823	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
824	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
825	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
826	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
827	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
828	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
829	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
830	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
831	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
832	C₂×C₄	C₂⁵	1	1	yes	characteristic
833	C₈	—	2	1	no	—
834	C₈	—	2	1	no	—
835	C₈	—	2	1	no	—
836	C₈	—	2	1	no	—
837	C₈	—	2	1	no	—
838	C₈	—	2	1	no	—
839	C₈	—	2	1	no	—
840	C₈	H(5,𝔽₂)	1	2	yes	—
841	C₂²	—	2	1	no	—
842	C₂²	—	2	1	no	—
843	C₂²	—	2	1	no	—
844	C₂²	—	2	1	no	—
845	C₂²	—	2	1	no	—
846	C₂²	—	2	1	no	—
847	C₂²	—	2	1	no	—
848	C₂²	—	2	1	no	—
849	C₂²	—	2	1	no	—
850	C₂²	—	2	1	no	—
851	C₂²	—	2	1	no	—
852	C₂²	—	2	1	no	—
853	C₂²	—	2	1	no	—
854	C₂²	—	2	1	no	—
855	C₂²	—	4	1	no	—
856	C₂²	—	4	1	no	—
857	C₂²	—	4	1	no	—
858	C₂²	—	4	1	no	—
859	C₂²	—	4	1	no	—
860	C₂²	—	4	1	no	—
861	C₂²	—	4	1	no	—
862	C₂²	—	4	1	no	—
863	C₂²	—	4	1	no	—
864	C₂²	—	4	1	no	—
865	C₂²	—	4	1	no	—
866	C₂²	—	4	1	no	—
867	C₂²	—	4	1	no	—
868	C₂²	—	4	1	no	—
869	C₂²	—	4	1	no	—
870	C₂²	—	8	2	no	—
871	C₂²	—	8	2	no	—
872	C₂²	—	16	2	no	—
873	C₂²	—	16	2	no	—
874	C₂²	—	16	2	no	—
875	C₂²	#575	1	2	yes	—
876	C₂²	C₂³×D₄	1	1	yes	characteristic
877	C₄	—	2	1	no	—
878	C₄	—	2	1	no	—
879	C₄	—	2	1	no	—
880	C₄	—	2	1	no	—
881	C₄	—	2	1	no	—
882	C₄	—	2	1	no	—
883	C₄	—	2	1	no	—
884	C₄	—	2	1	no	—
885	C₄	—	2	1	no	—
886	C₄	—	4	1	no	—
887	C₄	—	4	1	no	—
888	C₄	—	4	1	no	—
889	C₄	—	4	1	no	—
890	C₄	—	4	1	no	—
891	C₄	—	4	1	no	—
892	C₄	—	4	1	no	—
893	C₄	—	4	1	no	—
894	C₄	—	4	1	no	—
895	C₄	—	4	1	no	—
896	C₄	—	4	1	no	—
897	C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
898	C₄	#585	1	1	yes	characteristic
899	C₂	—	2	2	no	—
900	C₂	—	4	1	no	—
901	C₂	—	4	1	no	—
902	C₂	—	4	1	no	—
903	C₂	—	4	1	no	—
904	C₂	—	8	1	no	—
905	C₂	—	8	1	no	—
906	C₂	—	8	1	no	—
907	C₂	—	8	1	no	—
908	C₂	—	8	1	no	—
909	C₂	#3496	1	1	yes	characteristic
910	C₂	C₂×#575	1	1	yes	characteristic
911	C₂	#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄×D₄ ◁ G
LECS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #3519	C₂	semidirect
2. #3505	C₂	semidirect
3. #3355	C₂	semidirect
4. #3347	C₂	semidirect
5. #3344	C₂	semidirect
6. #3337	C₂	semidirect
7. #3326	C₂	semidirect
8. #3322	C₂	semidirect
9. #3321	C₂	semidirect
10. #3314	C₂	semidirect
11. #3310	C₂	semidirect
12. #3309	C₂	semidirect
13. #3297	C₂	semidirect
14. #3296	C₂	semidirect
15. #3280	C₂	semidirect
16. #3275	C₂	semidirect
17. #3271	C₂	semidirect
18. #3264	C₂	semidirect
19. #3256	C₂	semidirect
20. #3251	C₂	semidirect
21. #3197	C₂	semidirect
22. #3194	C₂	semidirect
23. #3194	C₂	semidirect
24. #3193	C₂	semidirect
25. #3183	C₂	semidirect
26. #3171	C₂	semidirect
27. #3056	C₂	semidirect
28. #3055	C₂	semidirect
29. #3054	C₂	semidirect
30. C₂×#469	C₂	semidirect
31. D₄×M₁₆	C₂	semidirect
32. C₂×#137	C₂²	semidirect
33. C₂×AGL(1,ℤ/8)	C₂²	semidirect
34. C₂×#135	C₂²	semidirect
35. C₂²×D₈	C₂²	semidirect
36. C₂²×M₁₆	C₂²	semidirect
37. C₂²×M₁₆	C₂²	semidirect
38. #555	C₂²	semidirect
44. #553	C₂²	semidirect
45. #553	C₂²	semidirect
46. #553	C₂²	semidirect
48. #552	C₂²	semidirect
51. #550	C₂²	semidirect
52. #548	C₂²	semidirect
53. #548	C₂²	semidirect
58. #546	C₂²	semidirect
59. #546	C₂²	semidirect
68. #532	C₂²	semidirect
69. #529	C₂²	semidirect
70. #529	C₂²	semidirect
71. #529	C₂²	semidirect
73. #525	C₂²	semidirect
74. #525	C₂²	semidirect
75. #525	C₂²	semidirect
76. C₂×C₂²⋊Q₈	C₂²	semidirect
78. C₂×#121	C₂²	semidirect
79. C₂×#121	C₂²	semidirect
83. #501	C₂²	semidirect
84. #499	C₂²	semidirect
85. #496	C₂²	semidirect
86. #495	C₂²	semidirect
87. #490	C₂²	semidirect
88. #489	C₂²	semidirect
89. #488	C₂²	semidirect
90. #488	C₂²	semidirect
91. #485	C₂²	semidirect
92. #485	C₂²	semidirect
93. #484	C₂²	semidirect
94. #484	C₂²	semidirect
95. #483	C₂²	semidirect
96. #483	C₂²	semidirect
97. #482	C₂²	semidirect
98. #482	C₂²	semidirect
99. #482	C₂²	semidirect
100. #482	C₂²	semidirect
101. #482	C₂²	semidirect
102. #482	C₂²	semidirect
103. #480	C₂²	semidirect
104. #480	C₂²	semidirect
105. #480	C₂²	semidirect
106. #480	C₂²	semidirect
107. #479	C₂²	semidirect
108. #479	C₂²	semidirect
109. #478	C₂²	semidirect
110. #478	C₂²	semidirect
111. #478	C₂²	semidirect
112. #478	C₂²	semidirect
113. #475	C₂²	semidirect
114. #474	C₂²	semidirect
115. #470	C₂²	semidirect
116. #470	C₂²	semidirect
117. #470	C₂²	semidirect
120. #469	C₂²	semidirect
121. #469	C₂²	semidirect
122. #469	C₂²	semidirect
123. #469	C₂²	semidirect
124. #469	C₂²	semidirect
125. #469	C₂²	semidirect
126. #469	C₂²	semidirect
127. #469	C₂²	semidirect
128. #469	C₂²	semidirect
129. #468	C₂²	semidirect
130. #468	C₂²	semidirect
131. #468	C₂²	semidirect
132. #468	C₂²	semidirect
133. #468	C₂²	semidirect
134. #468	C₂²	semidirect
135. #468	C₂²	semidirect
136. #468	C₂²	semidirect
137. #468	C₂²	semidirect
138. #468	C₂²	semidirect
139. #467	C₂²	semidirect
140. #467	C₂²	semidirect
141. #466	C₂²	semidirect
142. #466	C₂²	semidirect
143. #465	C₂²	semidirect
144. #465	C₂²	semidirect
145. #465	C₂²	semidirect
146. #465	C₂²	semidirect
147. #464	C₂²	semidirect
148. #464	C₂²	semidirect
149. #463	C₂²	semidirect
150. #463	C₂²	semidirect
151. #463	C₂²	semidirect
152. #463	C₂²	semidirect
153. #460	C₂²	semidirect
154. #459	C₂²	semidirect
155. #452	C₂²	semidirect
156. #452	C₂²	semidirect
157. #450	C₂²	semidirect
158. #450	C₂²	semidirect
159. #450	C₂²	semidirect
160. #450	C₂²	semidirect
161. #449	C₂²	semidirect
162. #449	C₂²	semidirect
163. #449	C₂²	semidirect
164. #449	C₂²	semidirect
165. #449	C₂²	semidirect
166. #449	C₂²	semidirect
167. #448	C₂²	semidirect
168. #448	C₂²	semidirect
169. #447	C₂²	semidirect
170. #447	C₂²	semidirect
171. #442	C₂²	semidirect
172. #441	C₂²	semidirect
173. #440	C₂²	semidirect
174. #440	C₂²	semidirect
175. C₄×SD₁₆	C₂²	semidirect
176. C₄×SD₁₆	C₂²	semidirect
177. C₄×D₈	C₂²	semidirect
178. C₄×D₈	C₂²	semidirect
179. #436	C₂²	semidirect
180. #436	C₂²	semidirect
183. #435	C₂²	semidirect
184. #435	C₂²	semidirect
185. C₈×D₄	C₂²	semidirect
186. C₈×D₄	C₂²	semidirect
187. #428	C₂²	semidirect
188. #428	C₂²	semidirect
189. #427	C₂²	semidirect
190. C₂×#106	C₂²	semidirect
191. #423	C₂²	semidirect
192. #419	C₂²	semidirect
193. #418	C₂²	semidirect
194. #417	C₂²	semidirect
195. #417	C₂²	semidirect
196. #416	C₂²	semidirect
197. #416	C₂²	semidirect
198. C₂×#102	C₂²	semidirect
199. C₂×#102	C₂²	semidirect
200. #407	C₂²	semidirect
201. #407	C₂²	semidirect
202. C₄×M₁₆	C₂²	semidirect

Maximal subgroups

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

subgroup	index
#3519	2
#3505	2
#3355	2
#3347	2
#3344	2
#3337	2
#3326	2
#3322	2
#3321	2
#3314	2
#3310	2
#3309	2
#3297	2
#3296	2
#3280	2
#3275	2
#3271	2
#3264	2
#3256	2
#3251	2
#3197	2
#3194	2
#3193	2
#3183	2
#3171	2
#3056	2
#3055	2
#3054	2
C₂×#469	2
D₄×M₁₆	2