Subgroups — #62467

Order 256.

943 conjugacy classes of subgroups.

The subgroup lattice has 908 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3562	C₂	1	1	yes	maximal, characteristic, complemented
2	#3561	C₂	1	1	yes	maximal, characteristic, complemented
3	#3402	C₂	1	1	yes	maximal, characteristic, complemented
4	#3401	C₂	1	1	yes	maximal, characteristic, complemented
5	#3394	C₂	1	1	yes	maximal, characteristic, complemented
6	#3393	C₂	1	1	yes	maximal, characteristic, complemented
7	#3285	C₂	1	1	yes	maximal, characteristic, complemented
8	#3282	C₂	1	1	yes	maximal, characteristic, complemented
9	#3278	C₂	1	1	yes	maximal, characteristic, complemented
10	#3277	C₂	1	1	yes	maximal, characteristic, complemented
11	#3276	C₂	1	1	yes	maximal, characteristic, complemented
12	#3275	C₂	1	1	yes	maximal, characteristic, complemented
13	#3275	C₂	1	1	yes	maximal, characteristic, complemented
14	#3273	C₂	1	1	yes	maximal, characteristic, complemented
15	#3270	C₂	1	1	yes	maximal, characteristic, complemented
16	#3268	C₂	1	1	yes	maximal, characteristic, complemented
17	#3267	C₂	1	1	yes	maximal, characteristic, complemented
18	#3266	C₂	1	1	yes	maximal, characteristic, complemented
19	#3225	C₂	1	1	yes	maximal, characteristic, complemented
20	#3224	C₂	1	1	yes	maximal, characteristic, complemented
21	#3223	C₂	1	1	yes	maximal, characteristic, complemented
22	#3221	C₂	1	1	yes	maximal, characteristic, complemented
23	#3211	C₂	1	1	yes	maximal, characteristic, complemented
24	#3210	C₂	1	1	yes	maximal, characteristic, complemented
25	#3179	C₂	1	1	yes	maximal, characteristic, complemented
26	#3178	C₂	1	1	yes	maximal, characteristic, complemented
27	#3172	C₂	1	1	yes	maximal, characteristic, complemented
28	#3156	C₂	1	1	yes	maximal, characteristic, complemented
29	#3154	C₂	1	1	yes	maximal, characteristic, complemented
30	#3153	C₂	1	1	yes	maximal, characteristic, complemented
31	#2969	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×#137	C₂²	1	1	yes	characteristic
33	C₂×#137	C₂²	1	1	yes	characteristic, complemented
34	C₂×#137	C₂²	1	1	yes	characteristic, complemented
35	C₂×#137	C₂²	1	1	yes	characteristic, complemented
36	C₂×#137	C₂²	1	1	yes	characteristic, complemented
37	C₂×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
38	C₂×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
39	C₂×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic, complemented
40	C₂×#135	C₂²	1	1	yes	characteristic
41	C₂×#135	C₂²	1	1	yes	characteristic
42	C₂²×Q₁₆	C₂²	1	1	yes	characteristic, complemented
43	C₂²×SD₁₆	C₂²	1	1	yes	characteristic, complemented
44	#563	—	2	1	no	—
45	#562	—	2	1	no	—
46	#562	—	2	1	no	—
47	#560	—	2	1	no	—
48	#559	C₂²	1	1	yes	characteristic, complemented
49	#556	C₂²	1	1	yes	characteristic, complemented
50	#556	C₂²	1	1	yes	characteristic, complemented
51	#556	C₂²	1	1	yes	characteristic, complemented
52	#553	—	2	1	no	—
53	#551	—	2	1	no	—
54	#551	—	2	1	no	—
55	#551	—	2	1	no	—
56	#550	C₂²	1	1	yes	characteristic
57	D₄×Q₈	C₂²	1	1	yes	characteristic
58	D₄×Q₈	C₂²	1	1	yes	characteristic, complemented
59	#548	C₂²	1	1	yes	characteristic
60	#548	C₂²	1	1	yes	characteristic
61	#548	C₂²	1	1	yes	characteristic
62	#548	C₂²	1	1	yes	characteristic, complemented
63	#547	C₂²	1	1	yes	characteristic
64	#546	C₂²	1	1	yes	characteristic
65	#546	C₂²	1	1	yes	characteristic
66	#546	C₂²	1	1	yes	characteristic, complemented
67	#546	C₂²	1	1	yes	characteristic, complemented
68	#543	—	2	1	no	—
69	#542	—	2	1	no	—
70	#542	—	2	1	no	—
71	#542	C₂²	1	1	yes	characteristic
72	#542	C₂²	1	1	yes	characteristic, complemented
73	#541	C₂²	1	1	yes	characteristic, complemented
74	#540	—	2	1	no	—
75	#540	C₂²	1	1	yes	characteristic, complemented
76	#539	—	2	1	no	—
77	#538	—	2	1	no	—
78	#538	—	2	1	no	—
79	#538	—	2	1	no	—
80	#536	C₂²	1	1	yes	characteristic
81	#536	C₂²	1	1	yes	characteristic, complemented
82	#536	C₂²	1	1	yes	characteristic, complemented
83	#535	C₂²	1	1	yes	characteristic, complemented
84	#533	C₂²	1	1	yes	characteristic, complemented
85	#532	C₂²	1	1	yes	characteristic
86	#529	C₂²	1	1	yes	characteristic
87	#529	C₂²	1	1	yes	characteristic
88	C₂×#124	C₂²	1	1	yes	characteristic, complemented
89	#501	C₂²	1	1	yes	characteristic, complemented
90	#497	C₂²	1	1	yes	characteristic, complemented
91	#497	C₂²	1	1	yes	characteristic, complemented
92	#497	C₂²	1	1	yes	characteristic, complemented
93	#497	C₂²	1	1	yes	characteristic, complemented
94	#497	C₂²	1	1	yes	characteristic, complemented
95	#497	C₂²	1	1	yes	characteristic, complemented
96	#496	C₂²	1	1	yes	characteristic
97	#496	C₂²	1	1	yes	characteristic
98	#496	C₂²	1	1	yes	characteristic
99	#495	C₂²	1	1	yes	characteristic
100	#495	C₂²	1	1	yes	characteristic
101	#495	C₂²	1	1	yes	characteristic
102	#495	C₂²	1	1	yes	characteristic
103	#495	C₂²	1	1	yes	characteristic
104	#495	C₂²	1	1	yes	characteristic
105	#495	C₂²	1	1	yes	characteristic, complemented
106	#495	C₂²	1	1	yes	characteristic, complemented
107	#494	C₂²	1	1	yes	characteristic, complemented
108	#494	C₂²	1	1	yes	characteristic, complemented
109	#492	C₂²	1	1	yes	characteristic, complemented
110	#492	C₂²	1	1	yes	characteristic, complemented
111	#491	C₂²	1	1	yes	characteristic, complemented
112	#489	C₂²	1	1	yes	characteristic, complemented
113	#488	C₂²	1	1	yes	characteristic, complemented
114	#488	C₂²	1	1	yes	characteristic, complemented
115	#487	C₂²	1	1	yes	characteristic, complemented
116	#486	C₂²	1	1	yes	characteristic, complemented
117	#470	C₂²	1	1	yes	characteristic, complemented
118	#470	C₂²	1	1	yes	characteristic, complemented
119	#470	C₂²	1	1	yes	characteristic, complemented
120	#469	C₂²	1	1	yes	characteristic
121	#468	C₂²	1	1	yes	characteristic
122	#468	C₂²	1	1	yes	characteristic
123	#468	C₂²	1	1	yes	characteristic
124	#468	C₂²	1	1	yes	characteristic, complemented
125	#467	C₂²	1	1	yes	characteristic, complemented
126	#466	C₂²	1	1	yes	characteristic, complemented
127	#465	C₂²	1	1	yes	characteristic
128	#465	C₂²	1	1	yes	characteristic, complemented
129	#464	C₂²	1	1	yes	characteristic, complemented
130	#464	C₂²	1	1	yes	characteristic, complemented
131	#464	C₂²	1	1	yes	characteristic, complemented
132	#464	C₂²	1	1	yes	characteristic, complemented
133	#464	C₂²	1	1	yes	characteristic, complemented
134	#464	C₂²	1	1	yes	characteristic, complemented
135	#464	C₂²	1	1	yes	characteristic, complemented
136	#464	C₂²	1	1	yes	characteristic, complemented
137	#464	C₂²	1	1	yes	characteristic, complemented
138	#464	C₂²	1	1	yes	characteristic, complemented
139	#463	C₂²	1	1	yes	characteristic
140	#463	C₂²	1	1	yes	characteristic
141	#463	C₂²	1	1	yes	characteristic
142	#463	C₂²	1	1	yes	characteristic
143	#463	C₂²	1	1	yes	characteristic
144	#463	C₂²	1	1	yes	characteristic, complemented
145	#462	C₂²	1	1	yes	characteristic, complemented
146	#462	C₂²	1	1	yes	characteristic, complemented
147	#462	C₂²	1	1	yes	characteristic, complemented
148	#461	C₂²	1	1	yes	characteristic, complemented
149	#461	C₂²	1	1	yes	characteristic, complemented
150	#461	C₂²	1	1	yes	characteristic, complemented
151	#460	C₂²	1	1	yes	characteristic, complemented
152	#459	C₂²	1	1	yes	characteristic
153	#452	C₂²	1	1	yes	characteristic
154	#452	C₂²	1	1	yes	characteristic
155	#452	C₂²	1	1	yes	characteristic
156	#452	C₂²	1	1	yes	characteristic
157	#452	C₂²	1	1	yes	characteristic, complemented
158	#452	C₂²	1	1	yes	characteristic, complemented
159	#452	C₂²	1	1	yes	characteristic, complemented
160	#452	C₂²	1	1	yes	characteristic, complemented
161	#451	C₂²	1	1	yes	characteristic, complemented
162	#451	C₂²	1	1	yes	characteristic, complemented
163	#451	C₂²	1	1	yes	characteristic, complemented
164	#451	C₂²	1	1	yes	characteristic, complemented
165	#450	C₂²	1	1	yes	characteristic, complemented
166	#450	C₂²	1	1	yes	characteristic, complemented
167	#449	C₂²	1	1	yes	characteristic
168	#449	C₂²	1	1	yes	characteristic
169	#449	C₂²	1	1	yes	characteristic
170	#449	C₂²	1	1	yes	characteristic, complemented
171	#448	C₂²	1	1	yes	characteristic
172	#448	C₂²	1	1	yes	characteristic, complemented
173	#448	C₂²	1	1	yes	characteristic, complemented
174	#448	C₂²	1	1	yes	characteristic, complemented
175	#447	C₂²	1	1	yes	characteristic
176	#447	C₂²	1	1	yes	characteristic
177	#446	C₂²	1	1	yes	characteristic, complemented
178	C₈×Q₈	C₂²	1	1	yes	characteristic, complemented
179	#442	C₂²	1	1	yes	characteristic, complemented
180	#441	C₂²	1	1	yes	characteristic, complemented
181	#440	C₂²	1	1	yes	characteristic, complemented
182	#440	C₂²	1	1	yes	characteristic, complemented
183	C₄×Q₁₆	C₂²	1	1	yes	characteristic, complemented
184	C₄×Q₁₆	C₂²	1	1	yes	characteristic, complemented
185	C₄×Q₁₆	C₂²	1	1	yes	characteristic, complemented
186	C₄×SD₁₆	C₂²	1	1	yes	characteristic, complemented
187	C₄×SD₁₆	C₂²	1	1	yes	characteristic, complemented
188	C₄×SD₁₆	C₂²	1	1	yes	characteristic, complemented
189	C₄×SD₁₆	C₂²	1	1	yes	characteristic, complemented
190	C₄×D₈	C₂²	1	1	yes	characteristic
191	#436	C₂²	1	1	yes	characteristic
192	#436	C₂²	1	1	yes	characteristic, complemented
193	#436	C₂²	1	1	yes	characteristic, complemented
194	#435	C₂²	1	1	yes	characteristic
195	#435	C₂²	1	1	yes	characteristic, complemented
196	C₈×D₄	C₂²	1	1	yes	characteristic, complemented
197	#433	C₂²	1	1	yes	characteristic, complemented
198	#433	C₂²	1	1	yes	characteristic, complemented
199	#431	C₂²	1	1	yes	characteristic, complemented
200	#405	C₂²	1	1	yes	characteristic, complemented
201	#405	C₂²	1	1	yes	characteristic, complemented
202	C₄×M₁₆	C₂²	1	1	yes	characteristic, complemented
203	C₂×#41	C₂³	1	1	yes	characteristic
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	C₂×#41	C₂³	1	1	yes	characteristic
209	C₂²×Q₈	C₂³	1	1	yes	characteristic
210	C₂²×Q₈	C₂³	1	1	yes	characteristic
211	C₂²×Q₈	C₂³	1	1	yes	characteristic
212	C₂²×Q₈	C₂³	1	1	yes	characteristic
213	C₂²×D₄	C₂³	1	1	yes	characteristic
214	C₂²×D₄	C₂³	1	1	yes	characteristic
215	#137	—	4	2	no	—
216	#137	—	4	2	no	—
217	#137	—	4	2	no	—
218	#137	—	4	2	no	—
219	#137	—	4	2	no	—
220	AGL(1,ℤ/8)	—	4	2	no	—
221	AGL(1,ℤ/8)	—	4	2	no	—
222	AGL(1,ℤ/8)	—	4	2	no	—
223	#135	—	4	2	no	—
224	#135	—	4	2	no	—
225	C₂×Q₁₆	—	4	2	no	—
226	C₂×Q₁₆	C₂³	1	1	yes	characteristic
227	C₂×Q₁₆	C₂³	1	1	yes	characteristic
228	C₂×Q₁₆	C₂³	1	1	yes	characteristic
229	C₂×Q₁₆	C₂³	1	1	yes	characteristic
230	C₂×Q₁₆	C₂³	1	1	yes	characteristic
231	C₂×Q₁₆	C₂³	1	1	yes	characteristic
232	C₂×Q₁₆	C₂³	1	1	yes	characteristic
233	C₂×Q₁₆	C₂³	1	1	yes	characteristic
234	C₂×Q₁₆	C₂³	1	1	yes	characteristic
235	C₂×Q₁₆	C₂³	1	1	yes	characteristic
236	C₂×Q₁₆	C₂³	1	1	yes	characteristic
237	C₂×Q₁₆	C₂³	1	1	yes	characteristic
238	C₂×SD₁₆	—	4	2	no	—
239	C₂×SD₁₆	C₂³	1	1	yes	characteristic
240	C₂×SD₁₆	C₂³	1	1	yes	characteristic
241	C₂×SD₁₆	C₂³	1	1	yes	characteristic
242	C₂×SD₁₆	C₂³	1	1	yes	characteristic
243	C₂×SD₁₆	C₂³	1	1	yes	characteristic
244	C₂×SD₁₆	C₂³	1	1	yes	characteristic
245	C₂×SD₁₆	C₂³	1	1	yes	characteristic
246	C₂×SD₁₆	C₂³	1	1	yes	characteristic
247	C₂×SD₁₆	C₂³	1	1	yes	characteristic
248	C₂×SD₁₆	C₂³	1	1	yes	characteristic
249	C₂×SD₁₆	C₂³	1	1	yes	characteristic
250	C₂×SD₁₆	C₂³	1	1	yes	characteristic
251	C₂×SD₁₆	C₂³	1	1	yes	characteristic
252	C₂×SD₁₆	C₂³	1	1	yes	characteristic
253	C₂×SD₁₆	C₂³	1	1	yes	characteristic
254	C₂×SD₁₆	C₂³	1	1	yes	characteristic
255	C₂×SD₁₆	C₂³	1	1	yes	characteristic
256	C₂×SD₁₆	C₂³	1	1	yes	characteristic
257	C₂×D₈	C₂³	1	1	yes	characteristic
258	C₂×D₈	C₂³	1	1	yes	characteristic
259	C₂×D₈	C₂³	1	1	yes	characteristic
260	C₂×D₈	C₂³	1	1	yes	characteristic
261	C₂×D₈	C₂³	1	1	yes	characteristic
262	C₂×D₈	C₂³	1	1	yes	characteristic
263	C₂×M₁₆	C₂³	1	1	yes	characteristic
264	C₂×M₁₆	C₂³	1	1	yes	characteristic
265	C₂×M₁₆	C₂³	1	1	yes	characteristic
266	C₂×M₁₆	C₂³	1	1	yes	characteristic
267	C₂²×C₈	C₂³	1	1	yes	characteristic
268	C₂²×C₈	C₂³	1	1	yes	characteristic
269	C₄⋊Q₈	—	2	1	no	—
270	C₄⋊Q₈	—	2	1	no	—
271	C₄⋊Q₈	C₂³	1	1	yes	characteristic
272	C₄⋊Q₈	C₂³	1	1	yes	characteristic
273	C₄⋊Q₈	C₂³	1	1	yes	characteristic
274	C₄⋊Q₈	C₂³	1	1	yes	characteristic
275	C₄⋊Q₈	C₂³	1	1	yes	characteristic
276	C₄⋊Q₈	C₂³	1	1	yes	characteristic
277	#127	—	2	1	no	—
278	#127	C₂³	1	1	yes	characteristic
279	#127	C₂³	1	1	yes	characteristic
280	#126	—	2	1	no	—
281	#126	—	2	1	no	—
282	#126	—	2	1	no	—
283	#126	—	2	1	no	—
284	#126	—	2	1	no	—
285	#126	—	2	1	no	—
286	#126	—	2	1	no	—
287	#126	—	2	1	no	—
288	#126	—	2	1	no	—
289	#126	—	2	1	no	—
290	#126	—	2	1	no	—
291	#126	D₄	1	1	yes	characteristic
292	#126	D₄	1	1	yes	characteristic
293	#125	—	2	1	no	—
294	#125	—	2	1	no	—
295	#125	—	2	1	no	—
296	#125	D₄	1	1	yes	characteristic
297	#125	C₂³	1	1	yes	characteristic
298	#124	—	2	1	no	—
299	#124	—	2	1	no	—
300	#124	—	2	1	no	—
301	#124	—	2	1	no	—
302	#124	—	2	1	no	—
303	#124	—	2	1	no	—
304	#124	—	2	1	no	—
305	#124	—	2	1	no	—
306	#124	—	2	1	no	—
307	#124	D₄	1	1	yes	characteristic
308	#124	C₂³	1	1	yes	characteristic
309	#124	C₂³	1	1	yes	characteristic
310	#124	C₂³	1	1	yes	characteristic
311	#124	C₂³	1	1	yes	characteristic
312	#124	C₂³	1	1	yes	characteristic
313	#124	C₂³	1	1	yes	characteristic
314	#124	C₂³	1	1	yes	characteristic
315	#124	C₂³	1	1	yes	characteristic
316	#124	C₂³	1	1	yes	characteristic
317	#124	C₂³	1	1	yes	characteristic
318	#124	C₂³	1	1	yes	characteristic
319	#123	—	2	1	no	—
320	#123	—	2	1	no	—
321	#123	—	2	1	no	—
322	#123	—	2	1	no	—
323	#123	—	2	1	no	—
324	#123	—	2	1	no	—
325	#123	—	2	1	no	—
326	#123	—	2	1	no	—
327	#123	—	2	1	no	—
328	#123	—	2	1	no	—
329	#123	—	2	1	no	—
330	#123	—	2	1	no	—
331	#123	—	2	1	no	—
332	#123	—	2	1	no	—
333	#123	—	2	1	no	—
334	#123	—	2	1	no	—
335	#123	—	2	1	no	—
336	#123	—	2	1	no	—
337	#123	—	2	1	no	—
338	#123	D₄	1	1	yes	characteristic
339	#123	D₄	1	1	yes	characteristic
340	C₂²⋊Q₈	—	2	1	no	—
341	C₂²⋊Q₈	—	2	1	no	—
342	C₂²⋊Q₈	—	2	1	no	—
343	C₂²⋊Q₈	—	2	1	no	—
344	C₂²⋊Q₈	—	2	1	no	—
345	C₂²⋊Q₈	—	2	1	no	—
346	C₂²⋊Q₈	—	2	1	no	—
347	C₂²⋊Q₈	—	2	1	no	—
348	C₂²⋊Q₈	—	2	1	no	—
349	C₂²⋊Q₈	—	2	1	no	—
350	C₂²⋊Q₈	—	2	1	no	—
351	C₂²⋊Q₈	—	2	1	no	—
352	C₂²⋊Q₈	—	2	1	no	—
353	C₂²⋊Q₈	—	2	1	no	—
354	C₂²⋊Q₈	—	2	1	no	—
355	C₂²⋊Q₈	—	2	1	no	—
356	C₂²⋊Q₈	—	2	1	no	—
357	C₂²⋊Q₈	—	2	1	no	—
358	C₂²⋊Q₈	—	2	1	no	—
359	C₂²⋊Q₈	—	2	1	no	—
360	C₂²⋊Q₈	D₄	1	1	yes	characteristic
361	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
362	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
363	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
364	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
365	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
366	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
367	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
368	#121	—	2	1	no	—
369	#121	—	2	1	no	—
370	#121	—	2	1	no	—
371	#121	—	2	1	no	—
372	#121	—	2	1	no	—
373	#121	—	2	1	no	—
374	#121	—	2	1	no	—
375	#121	—	2	1	no	—
376	#121	—	2	1	no	—
377	#121	—	2	1	no	—
378	#121	—	2	1	no	—
379	#121	—	2	1	no	—
380	#121	—	2	1	no	—
381	#121	—	2	1	no	—
382	#121	—	2	1	no	—
383	#121	—	2	1	no	—
384	#121	—	2	1	no	—
385	#121	D₄	1	1	yes	characteristic
386	#121	C₂³	1	1	yes	characteristic
387	#121	C₂³	1	1	yes	characteristic
388	#121	C₂³	1	1	yes	characteristic
389	#121	C₂³	1	1	yes	characteristic
390	#121	C₂³	1	1	yes	characteristic
391	#120	—	2	1	no	—
392	#120	—	2	1	no	—
393	#120	—	2	1	no	—
394	#120	—	2	1	no	—
395	#120	—	2	1	no	—
396	#120	—	2	1	no	—
397	C₄×Q₈	—	2	1	no	—
398	C₄×Q₈	C₂³	1	1	yes	characteristic
399	C₄×Q₈	C₂³	1	1	yes	characteristic
400	C₄×Q₈	C₂³	1	1	yes	characteristic
401	C₄×Q₈	C₂³	1	1	yes	characteristic
402	C₄×Q₈	C₂³	1	1	yes	characteristic
403	C₄×Q₈	C₂³	1	1	yes	characteristic
404	C₄×Q₈	C₂³	1	1	yes	characteristic
405	C₄×Q₈	C₂³	1	1	yes	characteristic
406	C₄×D₄	—	2	1	no	—
407	C₄×D₄	—	2	1	no	—
408	C₄×D₄	—	2	1	no	—
409	C₄×D₄	—	2	1	no	—
410	C₄×D₄	—	2	1	no	—
411	C₄×D₄	—	2	1	no	—
412	C₄×D₄	—	2	1	no	—
413	C₄×D₄	—	2	1	no	—
414	C₄×D₄	—	2	1	no	—
415	C₄×D₄	—	2	1	no	—
416	C₄×D₄	—	2	1	no	—
417	C₄×D₄	C₂³	1	1	yes	characteristic
418	C₄×D₄	C₂³	1	1	yes	characteristic
419	C₄×D₄	C₂³	1	1	yes	characteristic
420	C₄×D₄	C₂³	1	1	yes	characteristic
421	C₄×D₄	C₂³	1	1	yes	characteristic
422	C₄×D₄	C₂³	1	1	yes	characteristic
423	C₄×D₄	C₂³	1	1	yes	characteristic
424	C₄×D₄	C₂³	1	1	yes	characteristic
425	#117	—	2	1	no	—
426	#117	—	2	1	no	—
427	#117	—	2	1	no	—
428	#117	—	2	1	no	—
429	#117	—	2	1	no	—
430	#117	C₂³	1	1	yes	characteristic
431	#117	C₂³	1	1	yes	characteristic
432	C₂×C₄⋊C₄	—	2	1	no	—
433	C₂×C₂²⋊C₄	—	2	1	no	—
434	C₂×C₂²⋊C₄	—	2	1	no	—
435	C₂×C₂²⋊C₄	—	2	1	no	—
436	C₂×C₂²⋊C₄	—	2	1	no	—
437	C₂×C₂²⋊C₄	—	2	1	no	—
438	C₂×C₂²⋊C₄	—	2	1	no	—
439	C₂×C₄²	C₂³	1	1	yes	characteristic
440	#107	C₂³	1	1	yes	characteristic
441	#107	C₂³	1	1	yes	characteristic
442	#106	C₂³	1	1	yes	characteristic
443	#106	C₂³	1	1	yes	characteristic
444	C₄⋊C₈	C₂³	1	1	yes	characteristic
445	C₄⋊C₈	C₂³	1	1	yes	characteristic
446	C₄⋊C₈	C₂³	1	1	yes	characteristic
447	C₄⋊C₈	C₂³	1	1	yes	characteristic
448	C₄⋊C₈	C₂³	1	1	yes	characteristic
449	C₄⋊C₈	C₂³	1	1	yes	characteristic
450	#103	C₂³	1	1	yes	characteristic
451	#103	C₂³	1	1	yes	characteristic
452	#103	C₂³	1	1	yes	characteristic
453	#103	C₂³	1	1	yes	characteristic
454	#103	C₂³	1	1	yes	characteristic
455	#103	C₂³	1	1	yes	characteristic
456	#103	C₂³	1	1	yes	characteristic
457	#103	C₂³	1	1	yes	characteristic
458	#103	C₂³	1	1	yes	characteristic
459	#103	C₂³	1	1	yes	characteristic
460	#103	C₂³	1	1	yes	characteristic
461	#103	C₂³	1	1	yes	characteristic
462	#103	C₂³	1	1	yes	characteristic
463	#103	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	#102	C₂³	1	1	yes	characteristic
473	#102	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	#97	C₂³	1	1	yes	characteristic
483	#97	C₂³	1	1	yes	characteristic
484	C₄×C₈	C₂³	1	1	yes	characteristic
485	C₄×C₈	C₂³	1	1	yes	characteristic
486	C₄×C₈	C₂³	1	1	yes	characteristic
487	C₄×C₈	C₂³	1	1	yes	characteristic
488	C₄×C₈	C₂³	1	1	yes	characteristic
489	C₄×C₈	C₂³	1	1	yes	characteristic
490	C₂⁴	—	2	1	no	—
491	C₂⁴	—	2	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	—	4	1	no	—
498	#41	—	4	1	no	—
499	#41	—	4	1	no	—
500	#41	—	4	1	no	—
501	#41	—	4	1	no	—
502	#41	—	4	1	no	—
503	#41	—	4	1	no	—
504	C₂×Q₈	—	2	1	no	—
505	C₂×Q₈	—	2	1	no	—
506	C₂×Q₈	—	2	1	no	—
507	C₂×Q₈	—	2	1	no	—
508	C₂×Q₈	—	2	1	no	—
509	C₂×Q₈	—	4	1	no	—
510	C₂×Q₈	—	4	1	no	—
511	C₂×Q₈	—	4	1	no	—
512	C₂×Q₈	—	4	1	no	—
513	C₂×Q₈	—	4	1	no	—
514	C₂×Q₈	—	4	1	no	—
515	C₂×Q₈	—	4	1	no	—
516	C₂×Q₈	—	4	1	no	—
517	C₂×Q₈	C₂×D₄	1	1	yes	characteristic
518	C₂×Q₈	C₂⁴	1	1	yes	characteristic
519	C₂×Q₈	C₂⁴	1	1	yes	characteristic
520	C₂×Q₈	C₂⁴	1	1	yes	characteristic
521	C₂×Q₈	C₂⁴	1	1	yes	characteristic
522	C₂×Q₈	C₂⁴	1	1	yes	characteristic
523	C₂×Q₈	C₂⁴	1	1	yes	characteristic
524	C₂×Q₈	C₂⁴	1	1	yes	characteristic
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	—	2	1	no	—
530	C₂×D₄	—	2	1	no	—
531	C₂×D₄	—	2	1	no	—
532	C₂×D₄	—	2	1	no	—
533	C₂×D₄	—	2	1	no	—
534	C₂×D₄	—	2	1	no	—
535	C₂×D₄	—	2	1	no	—
536	C₂×D₄	—	2	1	no	—
537	C₂×D₄	—	2	1	no	—
538	C₂×D₄	—	2	1	no	—
539	C₂×D₄	—	2	1	no	—
540	C₂×D₄	—	2	1	no	—
541	C₂×D₄	—	2	1	no	—
542	C₂×D₄	—	4	1	no	—
543	C₂×D₄	—	4	1	no	—
544	C₂×D₄	—	4	1	no	—
545	C₂×D₄	—	4	1	no	—
546	C₂×D₄	C₂×D₄	1	1	yes	characteristic
547	C₂×D₄	C₂×D₄	1	1	yes	characteristic
548	C₂×D₄	C₂×D₄	1	1	yes	characteristic
549	C₂×D₄	C₂⁴	1	1	yes	characteristic
550	C₂×D₄	C₂⁴	1	1	yes	characteristic
551	C₂×D₄	C₂⁴	1	1	yes	characteristic
552	C₂×D₄	C₂⁴	1	1	yes	characteristic
553	C₂×D₄	C₂⁴	1	1	yes	characteristic
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	—	2	1	no	—
564	C₂²×C₄	—	2	1	no	—
565	C₂²×C₄	—	2	1	no	—
566	C₂²×C₄	—	2	1	no	—
567	C₂²×C₄	—	2	1	no	—
568	C₂²×C₄	—	2	1	no	—
569	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
570	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
571	C₂²×C₄	C₂⁴	1	1	yes	characteristic
572	C₂²×C₄	C₂⁴	1	1	yes	characteristic
573	C₂²×C₄	C₂⁴	1	1	yes	characteristic
574	Q₁₆	—	2	2	no	—
575	Q₁₆	—	2	2	no	—
576	Q₁₆	—	2	2	no	—
577	Q₁₆	—	2	2	no	—
578	Q₁₆	—	4	1	no	—
579	Q₁₆	—	4	1	no	—
580	Q₁₆	—	4	1	no	—
581	Q₁₆	—	4	1	no	—
582	Q₁₆	—	4	1	no	—
583	Q₁₆	—	4	1	no	—
584	Q₁₆	—	4	1	no	—
585	Q₁₆	—	4	1	no	—
586	SD₁₆	—	2	2	no	—
587	SD₁₆	—	2	2	no	—
588	SD₁₆	—	2	2	no	—
589	SD₁₆	—	2	2	no	—
590	SD₁₆	—	2	2	no	—
591	SD₁₆	—	2	2	no	—
592	SD₁₆	—	4	1	no	—
593	SD₁₆	—	4	1	no	—
594	SD₁₆	—	4	1	no	—
595	SD₁₆	—	4	1	no	—
596	SD₁₆	—	4	1	no	—
597	SD₁₆	—	4	1	no	—
598	SD₁₆	—	4	1	no	—
599	SD₁₆	—	4	1	no	—
600	SD₁₆	—	4	1	no	—
601	SD₁₆	—	4	1	no	—
602	SD₁₆	—	4	1	no	—
603	SD₁₆	—	4	1	no	—
604	D₈	—	2	2	no	—
605	D₈	—	2	2	no	—
606	D₈	—	4	1	no	—
607	D₈	—	4	1	no	—
608	D₈	—	4	1	no	—
609	D₈	—	4	1	no	—
610	M₁₆	—	2	2	no	—
611	M₁₆	—	2	2	no	—
612	M₁₆	—	2	2	no	—
613	M₁₆	—	2	2	no	—
614	C₂×C₈	—	2	2	no	—
615	C₂×C₈	—	2	2	no	—
616	C₂×C₈	C₂⁴	1	1	yes	characteristic
617	C₂×C₈	C₂⁴	1	1	yes	characteristic
618	C₂×C₈	C₂⁴	1	1	yes	characteristic
619	C₂×C₈	C₂⁴	1	1	yes	characteristic
620	C₂×C₈	C₂⁴	1	1	yes	characteristic
621	C₂×C₈	C₂⁴	1	1	yes	characteristic
622	C₂×C₈	C₂⁴	1	1	yes	characteristic
623	C₂×C₈	C₂⁴	1	1	yes	characteristic
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	—	2	1	no	—
640	C₄⋊C₄	—	2	1	no	—
641	C₄⋊C₄	—	2	1	no	—
642	C₄⋊C₄	—	2	1	no	—
643	C₄⋊C₄	—	2	1	no	—
644	C₄⋊C₄	—	2	1	no	—
645	C₄⋊C₄	—	2	1	no	—
646	C₄⋊C₄	—	2	1	no	—
647	C₄⋊C₄	—	2	1	no	—
648	C₄⋊C₄	—	2	1	no	—
649	C₄⋊C₄	—	2	1	no	—
650	C₄⋊C₄	—	2	1	no	—
651	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
652	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
653	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
654	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
655	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
656	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
657	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
658	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
659	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
660	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
661	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
662	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
663	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
664	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
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	—	2	1	no	—
691	C₂²⋊C₄	—	2	1	no	—
692	C₂²⋊C₄	—	2	1	no	—
693	C₂²⋊C₄	—	2	1	no	—
694	C₂²⋊C₄	—	2	1	no	—
695	C₂²⋊C₄	—	2	1	no	—
696	C₂²⋊C₄	—	2	1	no	—
697	C₂²⋊C₄	—	2	1	no	—
698	C₂²⋊C₄	—	2	1	no	—
699	C₂²⋊C₄	—	2	1	no	—
700	C₂²⋊C₄	—	2	1	no	—
701	C₂²⋊C₄	—	2	1	no	—
702	C₂²⋊C₄	—	2	1	no	—
703	C₂²⋊C₄	—	2	1	no	—
704	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
705	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
706	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
707	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
708	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
709	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
710	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
711	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
712	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
713	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
714	C₄²	—	2	1	no	—
715	C₄²	—	2	1	no	—
716	C₄²	—	2	1	no	—
717	C₄²	—	2	1	no	—
718	C₄²	—	2	1	no	—
719	C₄²	—	2	1	no	—
720	C₄²	—	2	1	no	—
721	C₄²	C₂×D₄	1	1	yes	characteristic
722	C₄²	C₂×D₄	1	1	yes	characteristic
723	C₄²	C₂⁴	1	1	yes	characteristic
724	C₄²	C₂⁴	1	1	yes	characteristic
725	C₄²	C₂⁴	1	1	yes	characteristic
726	C₄²	C₂⁴	1	1	yes	characteristic
727	C₂³	—	2	1	no	—
728	C₂³	—	2	1	no	—
729	C₂³	—	2	1	no	—
730	C₂³	—	2	1	no	—
731	C₂³	—	2	1	no	—
732	C₂³	—	4	2	no	—
733	C₂³	—	8	1	no	—
734	C₂³	—	8	1	no	—
735	C₂³	—	8	1	no	—
736	C₂³	—	8	1	no	—
737	C₂³	—	8	1	no	—
738	C₂³	C₂²×D₄	1	1	yes	characteristic
739	C₂³	C₂²×D₄	1	1	yes	characteristic
740	C₂³	C₂²×D₄	1	1	yes	characteristic
741	Q₈	—	2	1	no	—
742	Q₈	—	2	1	no	—
743	Q₈	—	2	1	no	—
744	Q₈	—	2	1	no	—
745	Q₈	—	2	1	no	—
746	Q₈	—	2	1	no	—
747	Q₈	—	2	1	no	—
748	Q₈	—	2	1	no	—
749	Q₈	—	2	1	no	—
750	Q₈	—	2	1	no	—
751	Q₈	—	2	1	no	—
752	Q₈	—	2	1	no	—
753	Q₈	—	2	1	no	—
754	Q₈	—	2	1	no	—
755	Q₈	—	4	1	no	—
756	Q₈	—	8	1	no	—
757	Q₈	—	8	1	no	—
758	Q₈	—	8	1	no	—
759	Q₈	—	8	1	no	—
760	Q₈	—	8	1	no	—
761	D₄	—	2	1	no	—
762	D₄	—	2	1	no	—
763	D₄	—	2	1	no	—
764	D₄	—	2	1	no	—
765	D₄	—	2	1	no	—
766	D₄	—	2	1	no	—
767	D₄	—	2	1	no	—
768	D₄	—	2	1	no	—
769	D₄	—	2	1	no	—
770	D₄	—	2	1	no	—
771	D₄	—	4	1	no	—
772	D₄	—	4	1	no	—
773	D₄	—	4	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	D₄	—	8	1	no	—
781	D₄	—	8	1	no	—
782	D₄	—	8	1	no	—
783	D₄	—	8	1	no	—
784	D₄	—	8	1	no	—
785	D₄	—	8	1	no	—
786	D₄	—	8	1	no	—
787	D₄	—	8	1	no	—
788	D₄	—	8	1	no	—
789	D₄	—	8	1	no	—
790	D₄	—	8	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	—	2	1	no	—
802	C₂×C₄	—	2	1	no	—
803	C₂×C₄	—	2	1	no	—
804	C₂×C₄	—	2	1	no	—
805	C₂×C₄	—	2	1	no	—
806	C₂×C₄	—	2	1	no	—
807	C₂×C₄	—	2	1	no	—
808	C₂×C₄	—	4	1	no	—
809	C₂×C₄	—	4	1	no	—
810	C₂×C₄	—	8	1	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	—	8	1	no	—
824	C₂×C₄	—	8	1	no	—
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	C₂²×D₄	1	1	yes	characteristic
833	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
834	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
835	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
836	C₂×C₄	C₂⁵	1	1	yes	characteristic
837	C₈	—	2	1	no	—
838	C₈	—	2	1	no	—
839	C₈	—	2	1	no	—
840	C₈	—	2	1	no	—
841	C₈	—	2	1	no	—
842	C₈	—	2	1	no	—
843	C₈	H(5,𝔽₂)	1	2	yes	—
844	C₈	H(5,𝔽₂)	1	2	yes	—
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	—	4	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	—	16	2	no	—
870	C₂²	—	16	2	no	—
871	C₂²	C₂³×D₄	1	1	yes	characteristic
872	C₄	—	2	1	no	—
873	C₄	—	2	1	no	—
874	C₄	—	2	1	no	—
875	C₄	—	2	1	no	—
876	C₄	—	2	1	no	—
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	—	4	1	no	—
884	C₄	—	4	1	no	—
885	C₄	—	4	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	C₂×H(5,𝔽₂)	1	1	yes	characteristic
895	C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
896	C₂	—	4	1	no	—
897	C₂	—	4	1	no	—
898	C₂	—	4	1	no	—
899	C₂	—	8	1	no	—
900	C₂	—	8	1	no	—
901	C₂	—	8	1	no	—
902	C₂	—	8	1	no	—
903	C₂	—	8	1	no	—
904	C₂	#3498	1	1	yes	characteristic
905	C₂	#3584	1	1	yes	characteristic
906	C₂	#3586	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 ◁ #529 ◁ G
LECS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #3562	C₂	semidirect
2. #3561	C₂	semidirect
3. #3402	C₂	semidirect
4. #3401	C₂	semidirect
5. #3394	C₂	semidirect
6. #3393	C₂	semidirect
7. #3285	C₂	semidirect
8. #3282	C₂	semidirect
9. #3278	C₂	semidirect
10. #3277	C₂	semidirect
11. #3276	C₂	semidirect
12. #3275	C₂	semidirect
13. #3275	C₂	semidirect
14. #3273	C₂	semidirect
15. #3270	C₂	semidirect
16. #3268	C₂	semidirect
17. #3267	C₂	semidirect
18. #3266	C₂	semidirect
19. #3225	C₂	semidirect
20. #3224	C₂	semidirect
21. #3223	C₂	semidirect
22. #3221	C₂	semidirect
23. #3211	C₂	semidirect
24. #3210	C₂	semidirect
25. #3179	C₂	semidirect
26. #3178	C₂	semidirect
27. #3172	C₂	semidirect
28. #3156	C₂	semidirect
29. #3154	C₂	semidirect
30. #3153	C₂	semidirect
31. #2969	C₂	semidirect
33. C₂×#137	C₂²	semidirect
34. C₂×#137	C₂²	semidirect
35. C₂×#137	C₂²	semidirect
36. C₂×#137	C₂²	semidirect
39. C₂×AGL(1,ℤ/8)	C₂²	semidirect
42. C₂²×Q₁₆	C₂²	semidirect
43. C₂²×SD₁₆	C₂²	semidirect
48. #559	C₂²	semidirect
49. #556	C₂²	semidirect
50. #556	C₂²	semidirect
51. #556	C₂²	semidirect
58. D₄×Q₈	C₂²	semidirect
62. #548	C₂²	semidirect
66. #546	C₂²	semidirect
67. #546	C₂²	semidirect
72. #542	C₂²	semidirect
73. #541	C₂²	semidirect
75. #540	C₂²	semidirect
81. #536	C₂²	semidirect
82. #536	C₂²	semidirect
83. #535	C₂²	semidirect
84. #533	C₂²	semidirect
88. C₂×#124	C₂²	semidirect
89. #501	C₂²	semidirect
90. #497	C₂²	semidirect
91. #497	C₂²	semidirect
92. #497	C₂²	semidirect
93. #497	C₂²	semidirect
94. #497	C₂²	semidirect
95. #497	C₂²	semidirect
105. #495	C₂²	semidirect
106. #495	C₂²	semidirect
107. #494	C₂²	semidirect
108. #494	C₂²	semidirect
109. #492	C₂²	semidirect
110. #492	C₂²	semidirect
111. #491	C₂²	semidirect
112. #489	C₂²	semidirect
113. #488	C₂²	semidirect
114. #488	C₂²	semidirect
115. #487	C₂²	semidirect
116. #486	C₂²	semidirect
117. #470	C₂²	semidirect
118. #470	C₂²	semidirect
119. #470	C₂²	semidirect
124. #468	C₂²	semidirect
125. #467	C₂²	semidirect
126. #466	C₂²	semidirect
128. #465	C₂²	semidirect
129. #464	C₂²	semidirect
130. #464	C₂²	semidirect
131. #464	C₂²	semidirect
132. #464	C₂²	semidirect
133. #464	C₂²	semidirect
134. #464	C₂²	semidirect
135. #464	C₂²	semidirect
136. #464	C₂²	semidirect
137. #464	C₂²	semidirect
138. #464	C₂²	semidirect
144. #463	C₂²	semidirect
145. #462	C₂²	semidirect
146. #462	C₂²	semidirect
147. #462	C₂²	semidirect
148. #461	C₂²	semidirect
149. #461	C₂²	semidirect
150. #461	C₂²	semidirect
151. #460	C₂²	semidirect
157. #452	C₂²	semidirect
158. #452	C₂²	semidirect
159. #452	C₂²	semidirect
160. #452	C₂²	semidirect
161. #451	C₂²	semidirect
162. #451	C₂²	semidirect
163. #451	C₂²	semidirect
164. #451	C₂²	semidirect
165. #450	C₂²	semidirect
166. #450	C₂²	semidirect
170. #449	C₂²	semidirect
172. #448	C₂²	semidirect
173. #448	C₂²	semidirect
174. #448	C₂²	semidirect
177. #446	C₂²	semidirect
178. C₈×Q₈	C₂²	semidirect
179. #442	C₂²	semidirect
180. #441	C₂²	semidirect
181. #440	C₂²	semidirect
182. #440	C₂²	semidirect
183. C₄×Q₁₆	C₂²	semidirect
184. C₄×Q₁₆	C₂²	semidirect
185. C₄×Q₁₆	C₂²	semidirect
186. C₄×SD₁₆	C₂²	semidirect
187. C₄×SD₁₆	C₂²	semidirect
188. C₄×SD₁₆	C₂²	semidirect
189. C₄×SD₁₆	C₂²	semidirect
192. #436	C₂²	semidirect
193. #436	C₂²	semidirect
195. #435	C₂²	semidirect
196. C₈×D₄	C₂²	semidirect
197. #433	C₂²	semidirect
198. #433	C₂²	semidirect
199. #431	C₂²	semidirect
200. #405	C₂²	semidirect
201. #405	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
#3562	2
#3561	2
#3402	2
#3401	2
#3394	2
#3393	2
#3285	2
#3282	2
#3278	2
#3277	2
#3276	2
#3275	2
#3273	2
#3270	2
#3268	2
#3267	2
#3266	2
#3225	2
#3224	2
#3223	2
#3221	2
#3211	2
#3210	2
#3179	2
#3178	2
#3172	2
#3156	2
#3154	2
#3153	2
#2969	2