Subgroups — #61610

Order 256.

1113 conjugacy classes of subgroups.

The subgroup lattice has 971 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3541	C₂	1	1	yes	maximal, characteristic, complemented
2	#3484	C₂	1	1	yes	maximal, characteristic, complemented
3	#3324	C₂	1	1	yes	maximal, characteristic, complemented
4	#3323	C₂	1	1	yes	maximal, characteristic, complemented
5	#3318	C₂	1	1	yes	maximal, characteristic, complemented
6	#3314	C₂	1	1	yes	maximal, characteristic, complemented
7	#3311	C₂	1	1	yes	maximal, characteristic, complemented
8	#3310	C₂	1	1	yes	maximal, characteristic, complemented
9	#3297	C₂	1	1	yes	maximal, characteristic, complemented
10	#3295	C₂	1	1	yes	maximal, characteristic, complemented
11	#3282	C₂	1	1	yes	maximal, characteristic, complemented
12	D₄×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
13	#3275	C₂	1	1	yes	maximal, characteristic, complemented
14	#3272	C₂	1	1	yes	maximal, characteristic, complemented
15	#3267	C₂	1	1	yes	maximal, characteristic, complemented
16	#3266	C₂	1	1	yes	maximal, characteristic, complemented
17	#3265	C₂	1	1	yes	maximal, characteristic, complemented
18	#3265	C₂	1	1	yes	maximal, characteristic, complemented
19	#3224	C₂	1	1	yes	maximal, characteristic, complemented
20	#3222	C₂	1	1	yes	maximal, characteristic, complemented
21	#3200	C₂	1	1	yes	maximal, characteristic, complemented
22	#3198	C₂	1	1	yes	maximal, characteristic, complemented
23	#3196	C₂	1	1	yes	maximal, characteristic, complemented
24	#3191	C₂	1	1	yes	maximal, characteristic, complemented
25	#3123	C₂	1	1	yes	maximal, characteristic, complemented
26	#3118	C₂	1	1	yes	maximal, characteristic, complemented
27	#3012	C₂	1	1	yes	maximal, characteristic, complemented
28	#3009	C₂	1	1	yes	maximal, characteristic, complemented
29	#3003	C₂	1	1	yes	maximal, characteristic, complemented
30	C₂×#450	C₂	1	1	yes	maximal, characteristic, complemented
31	#2976	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
33	C₂³×D₄	C₂²	1	1	yes	characteristic
34	C₂×#137	C₂²	1	1	yes	characteristic, complemented
35	C₂×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic, complemented
36	C₂×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic, complemented
37	C₂×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic, complemented
38	C₂×#135	C₂²	1	1	yes	characteristic, complemented
39	C₂²×SD₁₆	C₂²	1	1	yes	characteristic, complemented
40	C₂²×SD₁₆	C₂²	1	1	yes	characteristic, complemented
41	C₂²×SD₁₆	C₂²	1	1	yes	characteristic, complemented
42	#563	—	2	1	no	—
43	#562	—	2	1	no	—
44	#556	C₂²	1	1	yes	characteristic, complemented
45	#554	—	2	1	no	—
46	#554	C₂²	1	1	yes	characteristic, complemented
47	#553	—	2	1	no	—
48	#553	C₂²	1	1	yes	characteristic, complemented
49	#552	C₂²	1	1	yes	characteristic, complemented
50	D₄×Q₈	C₂²	1	1	yes	characteristic, complemented
51	#548	C₂²	1	1	yes	characteristic, complemented
52	#548	C₂²	1	1	yes	characteristic, complemented
53	#547	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
59	#546	C₂²	1	1	yes	characteristic
60	D₄²	—	2	1	no	—
61	D₄²	—	2	1	no	—
62	D₄²	C₂²	1	1	yes	characteristic
63	D₄²	C₂²	1	1	yes	characteristic
64	D₄²	C₂²	1	1	yes	characteristic
65	D₄²	C₂²	1	1	yes	characteristic
66	#542	—	2	1	no	—
67	#542	C₂²	1	1	yes	characteristic, complemented
68	#541	C₂²	1	1	yes	characteristic, complemented
69	#539	—	2	1	no	—
70	#538	—	2	1	no	—
71	#538	—	2	1	no	—
72	#537	C₂²	1	1	yes	characteristic, complemented
73	#536	C₂²	1	1	yes	characteristic, complemented
74	#535	C₂²	1	1	yes	characteristic
75	#535	C₂²	1	1	yes	characteristic
76	#534	—	2	1	no	—
77	#534	—	2	1	no	—
78	#525	C₂²	1	1	yes	characteristic
79	#525	C₂²	1	1	yes	characteristic
80	#525	C₂²	1	1	yes	characteristic, complemented
81	C₂×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
82	C₂×#120	—	2	1	no	—
83	C₂×#120	—	2	1	no	—
84	#518	C₂²	1	1	yes	characteristic
85	#497	C₂²	1	1	yes	characteristic, complemented
86	#496	C₂²	1	1	yes	characteristic, complemented
87	#495	C₂²	1	1	yes	characteristic, complemented
88	#492	C₂²	1	1	yes	characteristic, complemented
89	#490	C₂²	1	1	yes	characteristic, complemented
90	#489	C₂²	1	1	yes	characteristic, complemented
91	#488	C₂²	1	1	yes	characteristic, complemented
92	#486	C₂²	1	1	yes	characteristic, complemented
93	#485	C₂²	1	1	yes	characteristic, complemented
94	#485	C₂²	1	1	yes	characteristic, complemented
95	#485	C₂²	1	1	yes	characteristic, complemented
96	#485	C₂²	1	1	yes	characteristic, complemented
97	#484	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	#481	C₂²	1	1	yes	characteristic, complemented
103	#481	C₂²	1	1	yes	characteristic, complemented
104	#480	C₂²	1	1	yes	characteristic, complemented
105	#478	C₂²	1	1	yes	characteristic, complemented
106	#478	C₂²	1	1	yes	characteristic, complemented
107	#476	C₂²	1	1	yes	characteristic, complemented
108	#474	C₂²	1	1	yes	characteristic, complemented
109	#470	C₂²	1	1	yes	characteristic, complemented
110	#470	C₂²	1	1	yes	characteristic, complemented
111	#469	C₂²	1	1	yes	characteristic, complemented
112	#468	C₂²	1	1	yes	characteristic, complemented
113	#468	C₂²	1	1	yes	characteristic, complemented
114	#468	C₂²	1	1	yes	characteristic, complemented
115	#468	C₂²	1	1	yes	characteristic, complemented
116	#468	C₂²	1	1	yes	characteristic, complemented
117	#467	C₂²	1	1	yes	characteristic, complemented
118	#466	C₂²	1	1	yes	characteristic, complemented
119	#466	C₂²	1	1	yes	characteristic, complemented
120	#465	C₂²	1	1	yes	characteristic, complemented
121	#465	C₂²	1	1	yes	characteristic, complemented
122	#465	C₂²	1	1	yes	characteristic, complemented
123	#465	C₂²	1	1	yes	characteristic, complemented
124	#465	C₂²	1	1	yes	characteristic, complemented
125	#464	C₂²	1	1	yes	characteristic, complemented
126	#464	C₂²	1	1	yes	characteristic, complemented
127	#464	C₂²	1	1	yes	characteristic, complemented
128	#463	C₂²	1	1	yes	characteristic, complemented
129	#463	C₂²	1	1	yes	characteristic, complemented
130	#463	C₂²	1	1	yes	characteristic, complemented
131	#461	C₂²	1	1	yes	characteristic, complemented
132	#461	C₂²	1	1	yes	characteristic, complemented
133	#460	C₂²	1	1	yes	characteristic, complemented
134	#460	C₂²	1	1	yes	characteristic, complemented
135	#460	C₂²	1	1	yes	characteristic, complemented
136	#459	C₂²	1	1	yes	characteristic, complemented
137	#452	C₂²	1	1	yes	characteristic, complemented
138	#452	C₂²	1	1	yes	characteristic, complemented
139	#452	C₂²	1	1	yes	characteristic, complemented
140	#452	C₂²	1	1	yes	characteristic, complemented
141	#452	C₂²	1	1	yes	characteristic, complemented
142	#452	C₂²	1	1	yes	characteristic, complemented
143	#452	C₂²	1	1	yes	characteristic, complemented
144	#451	C₂²	1	1	yes	characteristic, complemented
145	#450	C₂²	1	1	yes	characteristic
146	#450	C₂²	1	1	yes	characteristic
147	#450	C₂²	1	1	yes	characteristic
148	#450	C₂²	1	1	yes	characteristic, complemented
149	#450	C₂²	1	1	yes	characteristic, complemented
150	#450	C₂²	1	1	yes	characteristic, complemented
151	#450	C₂²	1	1	yes	characteristic, complemented
152	#450	C₂²	1	1	yes	characteristic, complemented
153	#450	C₂²	1	1	yes	characteristic, complemented
154	#450	C₂²	1	1	yes	characteristic, complemented
155	#450	C₂²	1	1	yes	characteristic, complemented
156	#450	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	#449	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	#448	C₂²	1	1	yes	characteristic, complemented
166	#448	C₂²	1	1	yes	characteristic, complemented
167	#448	C₂²	1	1	yes	characteristic, complemented
168	#447	C₂²	1	1	yes	characteristic
169	#447	C₂²	1	1	yes	characteristic, complemented
170	#447	C₂²	1	1	yes	characteristic, complemented
171	#447	C₂²	1	1	yes	characteristic, complemented
172	#447	C₂²	1	1	yes	characteristic, complemented
173	#442	C₂²	1	1	yes	characteristic, complemented
174	#440	C₂²	1	1	yes	characteristic, complemented
175	#440	C₂²	1	1	yes	characteristic, complemented
176	#440	C₂²	1	1	yes	characteristic, complemented
177	C₄×SD₁₆	C₂²	1	1	yes	characteristic, complemented
178	C₄×SD₁₆	C₂²	1	1	yes	characteristic, complemented
179	C₄×SD₁₆	C₂²	1	1	yes	characteristic, complemented
180	C₄×D₈	C₂²	1	1	yes	characteristic, complemented
181	#436	C₂²	1	1	yes	characteristic, complemented
182	#436	C₂²	1	1	yes	characteristic, complemented
183	#435	C₂²	1	1	yes	characteristic, complemented
184	#435	C₂²	1	1	yes	characteristic, complemented
185	#435	C₂²	1	1	yes	characteristic, complemented
186	#435	C₂²	1	1	yes	characteristic, complemented
187	C₈×D₄	C₂²	1	1	yes	characteristic, complemented
188	C₈×D₄	C₂²	1	1	yes	characteristic, complemented
189	#433	C₂²	1	1	yes	characteristic, complemented
190	#433	C₂²	1	1	yes	characteristic, complemented
191	#418	C₂²	1	1	yes	characteristic, complemented
192	#418	C₂²	1	1	yes	characteristic, complemented
193	#418	C₂²	1	1	yes	characteristic, complemented
194	#417	C₂²	1	1	yes	characteristic, complemented
195	#416	C₂²	1	1	yes	characteristic, complemented
196	C₂×#102	C₂²	1	1	yes	characteristic, complemented
197	C₂×#102	C₂²	1	1	yes	characteristic, complemented
198	C₂×#102	C₂²	1	1	yes	characteristic, complemented
199	#408	C₂²	1	1	yes	characteristic, complemented
200	#408	C₂²	1	1	yes	characteristic, complemented
201	#407	C₂²	1	1	yes	characteristic, complemented
202	C₂×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
203	C₂⁵	—	2	1	no	—
204	H(5,𝔽₂)	—	4	2	no	—
205	H(5,𝔽₂)	—	4	2	no	—
206	C₂×#41	—	2	1	no	—
207	C₂×#41	C₂³	1	1	yes	characteristic
208	C₂×#41	C₂³	1	1	yes	characteristic
209	C₂×#41	C₂³	1	1	yes	characteristic
210	C₂×#41	C₂³	1	1	yes	characteristic
211	C₂×#41	C₂³	1	1	yes	characteristic
212	C₂×#41	C₂³	1	1	yes	characteristic, complemented
213	C₂²×Q₈	C₂³	1	1	yes	characteristic
214	C₂²×Q₈	C₂³	1	1	yes	characteristic, complemented
215	C₂²×D₄	—	2	1	no	—
216	C₂²×D₄	—	2	1	no	—
217	C₂²×D₄	—	2	1	no	—
218	C₂²×D₄	—	2	1	no	—
219	C₂²×D₄	—	2	1	no	—
220	C₂²×D₄	—	2	1	no	—
221	C₂²×D₄	—	2	1	no	—
222	C₂²×D₄	—	2	1	no	—
223	C₂²×D₄	—	2	1	no	—
224	C₂²×D₄	—	2	1	no	—
225	C₂²×D₄	—	4	2	no	—
226	C₂²×D₄	—	4	2	no	—
227	C₂²×D₄	C₂³	1	1	yes	characteristic
228	C₂²×D₄	C₂³	1	1	yes	characteristic
229	C₂²×D₄	C₂³	1	1	yes	characteristic
230	C₂²×D₄	C₂³	1	1	yes	characteristic
231	C₂²×D₄	C₂³	1	1	yes	characteristic
232	C₂²×D₄	C₂³	1	1	yes	characteristic
233	C₂²×D₄	C₂³	1	1	yes	characteristic
234	C₂²×D₄	C₂³	1	1	yes	characteristic
235	C₂³×C₄	C₂³	1	1	yes	characteristic
236	#137	—	4	2	no	—
237	AGL(1,ℤ/8)	—	4	2	no	—
238	AGL(1,ℤ/8)	—	4	2	no	—
239	AGL(1,ℤ/8)	—	4	2	no	—
240	#135	—	4	2	no	—
241	C₂×Q₁₆	C₂³	1	1	yes	characteristic, complemented
242	C₂×Q₁₆	C₂³	1	1	yes	characteristic, complemented
243	C₂×Q₁₆	C₂³	1	1	yes	characteristic, complemented
244	C₂×SD₁₆	—	4	2	no	—
245	C₂×SD₁₆	—	4	2	no	—
246	C₂×SD₁₆	—	4	2	no	—
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×SD₁₆	C₂³	1	1	yes	characteristic
258	C₂×SD₁₆	C₂³	1	1	yes	characteristic
259	C₂×SD₁₆	C₂³	1	1	yes	characteristic, complemented
260	C₂×SD₁₆	C₂³	1	1	yes	characteristic, complemented
261	C₂×SD₁₆	C₂³	1	1	yes	characteristic, complemented
262	C₂×SD₁₆	C₂³	1	1	yes	characteristic, complemented
263	C₂×D₈	C₂³	1	1	yes	characteristic
264	C₂×D₈	C₂³	1	1	yes	characteristic
265	C₂×D₈	C₂³	1	1	yes	characteristic
266	C₂×D₈	C₂³	1	1	yes	characteristic
267	C₂×D₈	C₂³	1	1	yes	characteristic, complemented
268	C₂×M₁₆	C₂³	1	1	yes	characteristic
269	C₂×M₁₆	C₂³	1	1	yes	characteristic
270	C₂×M₁₆	C₂³	1	1	yes	characteristic, complemented
271	C₂×M₁₆	C₂³	1	1	yes	characteristic, complemented
272	C₂²×C₈	C₂³	1	1	yes	characteristic
273	C₂²×C₈	C₂³	1	1	yes	characteristic
274	C₂²×C₈	C₂³	1	1	yes	characteristic, complemented
275	C₂²×C₈	C₂³	1	1	yes	characteristic, complemented
276	C₄⋊Q₈	—	2	1	no	—
277	C₄⋊Q₈	—	2	1	no	—
278	C₄⋊Q₈	C₂³	1	1	yes	characteristic, complemented
279	C₄⋊Q₈	C₂³	1	1	yes	characteristic, complemented
280	#127	—	2	1	no	—
281	#127	C₂³	1	1	yes	characteristic
282	#127	C₂³	1	1	yes	characteristic
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	#125	—	2	1	no	—
291	#125	—	2	1	no	—
292	#125	—	2	1	no	—
293	#125	—	2	1	no	—
294	#125	C₂³	1	1	yes	characteristic, complemented
295	#124	—	2	1	no	—
296	#124	—	2	1	no	—
297	#124	—	2	1	no	—
298	#124	—	2	1	no	—
299	#124	—	2	1	no	—
300	#124	—	2	1	no	—
301	#124	C₂³	1	1	yes	characteristic
302	#124	C₂³	1	1	yes	characteristic
303	#124	C₂³	1	1	yes	characteristic, complemented
304	#123	—	2	1	no	—
305	#123	—	2	1	no	—
306	#123	—	2	1	no	—
307	#123	—	2	1	no	—
308	#123	—	2	1	no	—
309	#123	—	2	1	no	—
310	#123	—	2	1	no	—
311	#123	—	2	1	no	—
312	#123	—	2	1	no	—
313	#123	—	2	1	no	—
314	#123	—	2	1	no	—
315	#123	—	2	1	no	—
316	#123	—	2	1	no	—
317	#123	D₄	1	1	yes	characteristic
318	#123	D₄	1	1	yes	characteristic
319	C₂²⋊Q₈	—	2	1	no	—
320	C₂²⋊Q₈	—	2	1	no	—
321	C₂²⋊Q₈	—	2	1	no	—
322	C₂²⋊Q₈	—	2	1	no	—
323	C₂²⋊Q₈	—	2	1	no	—
324	C₂²⋊Q₈	—	2	1	no	—
325	C₂²⋊Q₈	—	2	1	no	—
326	C₂²⋊Q₈	—	2	1	no	—
327	C₂²⋊Q₈	—	2	1	no	—
328	C₂²⋊Q₈	—	2	1	no	—
329	C₂²⋊Q₈	D₄	1	1	yes	characteristic
330	C₂²⋊Q₈	D₄	1	1	yes	characteristic
331	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
332	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
333	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
334	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
335	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
336	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
337	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
338	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
339	C₂²⋊Q₈	C₂³	1	1	yes	characteristic, complemented
340	C₂²⋊Q₈	C₂³	1	1	yes	characteristic, complemented
341	C₂²⋊Q₈	C₂³	1	1	yes	characteristic, complemented
342	#121	—	2	1	no	—
343	#121	—	2	1	no	—
344	#121	—	2	1	no	—
345	#121	—	2	1	no	—
346	#121	—	2	1	no	—
347	#121	—	2	1	no	—
348	#121	—	2	1	no	—
349	#121	—	2	1	no	—
350	#121	—	2	1	no	—
351	#121	—	2	1	no	—
352	#121	—	2	1	no	—
353	#121	—	2	1	no	—
354	#121	—	2	1	no	—
355	#121	—	2	1	no	—
356	#121	—	2	1	no	—
357	#121	—	2	1	no	—
358	#121	—	2	1	no	—
359	#121	D₄	1	1	yes	characteristic
360	#121	D₄	1	1	yes	characteristic
361	#121	C₂³	1	1	yes	characteristic
362	#121	C₂³	1	1	yes	characteristic
363	#121	C₂³	1	1	yes	characteristic
364	#121	C₂³	1	1	yes	characteristic
365	#121	C₂³	1	1	yes	characteristic
366	#121	C₂³	1	1	yes	characteristic
367	#121	C₂³	1	1	yes	characteristic
368	#121	C₂³	1	1	yes	characteristic
369	#121	C₂³	1	1	yes	characteristic, complemented
370	#120	—	2	1	no	—
371	#120	—	2	1	no	—
372	#120	—	2	1	no	—
373	#120	—	2	1	no	—
374	#120	—	2	1	no	—
375	#120	—	2	1	no	—
376	#120	—	2	1	no	—
377	#120	—	2	1	no	—
378	#120	—	2	1	no	—
379	#120	—	2	1	no	—
380	#120	—	2	1	no	—
381	#120	—	2	1	no	—
382	#120	—	2	1	no	—
383	#120	—	2	1	no	—
384	#120	—	2	1	no	—
385	#120	—	2	1	no	—
386	#120	—	2	1	no	—
387	#120	—	2	1	no	—
388	#120	D₄	1	1	yes	characteristic
389	#120	D₄	1	1	yes	characteristic
390	C₄×Q₈	—	2	1	no	—
391	C₄×Q₈	C₂³	1	1	yes	characteristic, complemented
392	C₄×Q₈	C₂³	1	1	yes	characteristic, complemented
393	C₄×Q₈	C₂³	1	1	yes	characteristic, complemented
394	C₄×D₄	—	2	1	no	—
395	C₄×D₄	—	2	1	no	—
396	C₄×D₄	—	2	1	no	—
397	C₄×D₄	—	2	1	no	—
398	C₄×D₄	—	2	1	no	—
399	C₄×D₄	—	2	1	no	—
400	C₄×D₄	—	2	1	no	—
401	C₄×D₄	—	2	1	no	—
402	C₄×D₄	—	2	1	no	—
403	C₄×D₄	—	2	1	no	—
404	C₄×D₄	—	2	1	no	—
405	C₄×D₄	C₂³	1	1	yes	characteristic
406	C₄×D₄	C₂³	1	1	yes	characteristic
407	C₄×D₄	C₂³	1	1	yes	characteristic
408	C₄×D₄	C₂³	1	1	yes	characteristic
409	C₄×D₄	C₂³	1	1	yes	characteristic
410	C₄×D₄	C₂³	1	1	yes	characteristic
411	C₄×D₄	C₂³	1	1	yes	characteristic
412	C₄×D₄	C₂³	1	1	yes	characteristic
413	C₄×D₄	C₂³	1	1	yes	characteristic, complemented
414	#117	—	2	1	no	—
415	#117	C₂³	1	1	yes	characteristic
416	#117	C₂³	1	1	yes	characteristic
417	#117	C₂³	1	1	yes	characteristic
418	#117	C₂³	1	1	yes	characteristic, complemented
419	C₂×C₄⋊C₄	—	2	1	no	—
420	C₂×C₄⋊C₄	—	2	1	no	—
421	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
422	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic, complemented
423	C₂×C₂²⋊C₄	—	2	1	no	—
424	C₂×C₂²⋊C₄	—	2	1	no	—
425	C₂×C₂²⋊C₄	—	2	1	no	—
426	C₂×C₂²⋊C₄	—	2	1	no	—
427	C₂×C₂²⋊C₄	—	2	1	no	—
428	C₂×C₂²⋊C₄	—	2	1	no	—
429	C₂×C₂²⋊C₄	—	2	1	no	—
430	#107	C₂³	1	1	yes	characteristic, complemented
431	#107	C₂³	1	1	yes	characteristic, complemented
432	#107	C₂³	1	1	yes	characteristic, complemented
433	#107	C₂³	1	1	yes	characteristic, complemented
434	#106	C₂³	1	1	yes	characteristic, complemented
435	#106	C₂³	1	1	yes	characteristic, complemented
436	#106	C₂³	1	1	yes	characteristic, complemented
437	#106	C₂³	1	1	yes	characteristic, complemented
438	C₄⋊C₈	C₂³	1	1	yes	characteristic, complemented
439	C₄⋊C₈	C₂³	1	1	yes	characteristic, complemented
440	C₄⋊C₈	C₂³	1	1	yes	characteristic, complemented
441	C₄⋊C₈	C₂³	1	1	yes	characteristic, complemented
442	#103	C₂³	1	1	yes	characteristic, complemented
443	#103	C₂³	1	1	yes	characteristic, complemented
444	#103	C₂³	1	1	yes	characteristic, complemented
445	#103	C₂³	1	1	yes	characteristic, complemented
446	#103	C₂³	1	1	yes	characteristic, complemented
447	#103	C₂³	1	1	yes	characteristic, complemented
448	#103	C₂³	1	1	yes	characteristic, complemented
449	#103	C₂³	1	1	yes	characteristic, complemented
450	#103	C₂³	1	1	yes	characteristic, complemented
451	#103	C₂³	1	1	yes	characteristic, complemented
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, complemented
469	#102	C₂³	1	1	yes	characteristic, complemented
470	#102	C₂³	1	1	yes	characteristic, complemented
471	#102	C₂³	1	1	yes	characteristic, complemented
472	#102	C₂³	1	1	yes	characteristic, complemented
473	#102	C₂³	1	1	yes	characteristic, complemented
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	C₂²⋊C₈	C₂³	1	1	yes	characteristic
481	C₂²⋊C₈	C₂³	1	1	yes	characteristic
482	C₂²⋊C₈	C₂³	1	1	yes	characteristic, complemented
483	C₂²⋊C₈	C₂³	1	1	yes	characteristic, complemented
484	C₂²⋊C₈	C₂³	1	1	yes	characteristic, complemented
485	C₂²⋊C₈	C₂³	1	1	yes	characteristic, complemented
486	#97	C₂³	1	1	yes	characteristic, complemented
487	#97	C₂³	1	1	yes	characteristic, complemented
488	C₄×C₈	C₂³	1	1	yes	characteristic, complemented
489	C₄×C₈	C₂³	1	1	yes	characteristic, complemented
490	C₂⁴	—	2	1	no	—
491	C₂⁴	—	2	1	no	—
492	C₂⁴	—	2	1	no	—
493	C₂⁴	—	2	1	no	—
494	C₂⁴	—	2	1	no	—
495	C₂⁴	—	2	1	no	—
496	C₂⁴	—	2	1	no	—
497	C₂⁴	—	2	1	no	—
498	C₂⁴	—	4	4	no	—
499	C₂⁴	—	8	2	no	—
500	C₂⁴	—	8	2	no	—
501	C₂⁴	C₂×D₄	1	1	yes	characteristic
502	#41	—	2	2	no	—
503	#41	—	2	2	no	—
504	#41	—	4	1	no	—
505	#41	—	4	1	no	—
506	#41	—	4	1	no	—
507	#41	—	4	1	no	—
508	#41	—	4	1	no	—
509	#41	—	4	1	no	—
510	#41	—	4	1	no	—
511	#41	—	4	1	no	—
512	#41	—	4	1	no	—
513	#41	—	4	1	no	—
514	#41	—	4	4	no	—
515	C₂×Q₈	—	2	1	no	—
516	C₂×Q₈	—	2	1	no	—
517	C₂×Q₈	—	2	1	no	—
518	C₂×Q₈	—	4	1	no	—
519	C₂×Q₈	—	4	1	no	—
520	C₂×Q₈	—	4	1	no	—
521	C₂×Q₈	—	4	1	no	—
522	C₂×Q₈	C₂×D₄	1	1	yes	characteristic
523	C₂×Q₈	C₂⁴	1	1	yes	characteristic
524	C₂×Q₈	C₂⁴	1	1	yes	characteristic
525	C₂×Q₈	C₂⁴	1	1	yes	characteristic
526	C₂×Q₈	C₂⁴	1	1	yes	characteristic
527	C₂×D₄	—	2	2	no	—
528	C₂×D₄	—	2	2	no	—
529	C₂×D₄	—	2	2	no	—
530	C₂×D₄	—	2	2	no	—
531	C₂×D₄	—	2	2	no	—
532	C₂×D₄	—	2	2	no	—
533	C₂×D₄	—	2	2	no	—
534	C₂×D₄	—	2	2	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	—	2	1	no	—
543	C₂×D₄	—	2	1	no	—
544	C₂×D₄	—	2	1	no	—
545	C₂×D₄	—	2	1	no	—
546	C₂×D₄	—	2	1	no	—
547	C₂×D₄	—	2	1	no	—
548	C₂×D₄	—	2	1	no	—
549	C₂×D₄	—	2	1	no	—
550	C₂×D₄	—	2	1	no	—
551	C₂×D₄	—	2	1	no	—
552	C₂×D₄	—	2	1	no	—
553	C₂×D₄	—	2	1	no	—
554	C₂×D₄	—	2	1	no	—
555	C₂×D₄	—	2	1	no	—
556	C₂×D₄	—	2	1	no	—
557	C₂×D₄	—	2	1	no	—
558	C₂×D₄	—	2	1	no	—
559	C₂×D₄	—	2	1	no	—
560	C₂×D₄	—	2	1	no	—
561	C₂×D₄	—	4	1	no	—
562	C₂×D₄	—	4	1	no	—
563	C₂×D₄	—	4	1	no	—
564	C₂×D₄	—	4	1	no	—
565	C₂×D₄	—	4	1	no	—
566	C₂×D₄	—	4	1	no	—
567	C₂×D₄	—	4	1	no	—
568	C₂×D₄	—	4	1	no	—
569	C₂×D₄	—	4	4	no	—
570	C₂×D₄	—	4	4	no	—
571	C₂×D₄	—	4	4	no	—
572	C₂×D₄	—	4	4	no	—
573	C₂×D₄	—	4	4	no	—
574	C₂×D₄	—	4	4	no	—
575	C₂×D₄	—	8	2	no	—
576	C₂×D₄	—	8	2	no	—
577	C₂×D₄	—	8	2	no	—
578	C₂×D₄	—	8	2	no	—
579	C₂×D₄	C₂×D₄	1	1	yes	characteristic
580	C₂×D₄	C₂×D₄	1	1	yes	characteristic
581	C₂×D₄	C₂×D₄	1	1	yes	characteristic
582	C₂×D₄	C₂×D₄	1	1	yes	characteristic
583	C₂×D₄	C₂×D₄	1	1	yes	characteristic
584	C₂×D₄	C₂×D₄	1	1	yes	characteristic
585	C₂×D₄	C₂×D₄	1	1	yes	characteristic
586	C₂×D₄	C₂⁴	1	1	yes	characteristic
587	C₂×D₄	C₂⁴	1	1	yes	characteristic
588	C₂×D₄	C₂⁴	1	1	yes	characteristic
589	C₂×D₄	C₂⁴	1	1	yes	characteristic
590	C₂×D₄	C₂⁴	1	1	yes	characteristic
591	C₂×D₄	C₂⁴	1	1	yes	characteristic
592	C₂²×C₄	—	2	1	no	—
593	C₂²×C₄	—	2	1	no	—
594	C₂²×C₄	—	2	1	no	—
595	C₂²×C₄	—	2	1	no	—
596	C₂²×C₄	—	2	1	no	—
597	C₂²×C₄	—	2	1	no	—
598	C₂²×C₄	—	2	1	no	—
599	C₂²×C₄	—	2	1	no	—
600	C₂²×C₄	—	2	1	no	—
601	C₂²×C₄	—	2	1	no	—
602	C₂²×C₄	—	2	1	no	—
603	C₂²×C₄	—	2	1	no	—
604	C₂²×C₄	—	2	1	no	—
605	C₂²×C₄	—	2	1	no	—
606	C₂²×C₄	—	4	1	no	—
607	C₂²×C₄	—	4	1	no	—
608	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
609	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
610	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
611	C₂²×C₄	C₂⁴	1	1	yes	characteristic
612	C₂²×C₄	C₂⁴	1	1	yes	characteristic
613	C₂²×C₄	C₂⁴	1	1	yes	characteristic
614	C₂²×C₄	C₂⁴	1	1	yes	characteristic
615	C₂²×C₄	C₂⁴	1	1	yes	characteristic
616	Q₁₆	—	4	1	no	—
617	Q₁₆	—	4	1	no	—
618	Q₁₆	—	4	1	no	—
619	SD₁₆	—	2	2	no	—
620	SD₁₆	—	2	2	no	—
621	SD₁₆	—	2	2	no	—
622	SD₁₆	—	2	2	no	—
623	SD₁₆	—	2	2	no	—
624	SD₁₆	—	2	2	no	—
625	SD₁₆	—	4	1	no	—
626	SD₁₆	—	4	1	no	—
627	SD₁₆	—	4	1	no	—
628	SD₁₆	—	4	1	no	—
629	SD₁₆	—	4	1	no	—
630	SD₁₆	—	4	1	no	—
631	SD₁₆	—	4	1	no	—
632	SD₁₆	—	4	1	no	—
633	SD₁₆	—	4	1	no	—
634	SD₁₆	—	4	1	no	—
635	D₈	—	2	2	no	—
636	D₈	—	2	2	no	—
637	D₈	—	4	1	no	—
638	D₈	—	4	1	no	—
639	D₈	—	4	1	no	—
640	M₁₆	—	4	1	no	—
641	M₁₆	—	4	1	no	—
642	M₁₆	—	4	1	no	—
643	M₁₆	—	4	1	no	—
644	C₂×C₈	—	4	1	no	—
645	C₂×C₈	—	4	1	no	—
646	C₂×C₈	—	4	1	no	—
647	C₂×C₈	—	4	1	no	—
648	C₂×C₈	C₂⁴	1	1	yes	characteristic
649	C₂×C₈	C₂⁴	1	1	yes	characteristic
650	C₂×C₈	C₂⁴	1	1	yes	characteristic
651	C₂×C₈	C₂⁴	1	1	yes	characteristic
652	C₂×C₈	C₂⁴	1	1	yes	characteristic
653	C₂×C₈	C₂⁴	1	1	yes	characteristic
654	C₂×C₈	C₂⁴	1	1	yes	characteristic
655	C₂×C₈	C₂⁴	1	1	yes	characteristic
656	C₄⋊C₄	—	2	1	no	—
657	C₄⋊C₄	—	2	1	no	—
658	C₄⋊C₄	—	2	1	no	—
659	C₄⋊C₄	—	2	1	no	—
660	C₄⋊C₄	—	2	1	no	—
661	C₄⋊C₄	—	2	1	no	—
662	C₄⋊C₄	—	2	1	no	—
663	C₄⋊C₄	—	2	1	no	—
664	C₄⋊C₄	—	2	1	no	—
665	C₄⋊C₄	—	2	1	no	—
666	C₄⋊C₄	—	2	1	no	—
667	C₄⋊C₄	—	2	1	no	—
668	C₄⋊C₄	—	2	1	no	—
669	C₄⋊C₄	—	2	1	no	—
670	C₄⋊C₄	—	2	1	no	—
671	C₄⋊C₄	—	2	1	no	—
672	C₄⋊C₄	—	2	1	no	—
673	C₄⋊C₄	—	2	1	no	—
674	C₄⋊C₄	—	2	1	no	—
675	C₄⋊C₄	—	2	1	no	—
676	C₄⋊C₄	—	2	1	no	—
677	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
678	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
679	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
680	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
681	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
682	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
683	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
684	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
685	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
686	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
687	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
688	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
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	—	2	1	no	—
705	C₂²⋊C₄	—	2	1	no	—
706	C₂²⋊C₄	—	2	1	no	—
707	C₂²⋊C₄	—	2	1	no	—
708	C₂²⋊C₄	—	2	1	no	—
709	C₂²⋊C₄	—	2	1	no	—
710	C₂²⋊C₄	—	2	1	no	—
711	C₂²⋊C₄	—	2	1	no	—
712	C₂²⋊C₄	—	2	1	no	—
713	C₂²⋊C₄	—	2	1	no	—
714	C₂²⋊C₄	—	2	1	no	—
715	C₂²⋊C₄	—	2	1	no	—
716	C₂²⋊C₄	—	2	1	no	—
717	C₂²⋊C₄	—	2	1	no	—
718	C₂²⋊C₄	—	2	1	no	—
719	C₂²⋊C₄	—	2	1	no	—
720	C₂²⋊C₄	—	2	1	no	—
721	C₂²⋊C₄	—	2	1	no	—
722	C₂²⋊C₄	—	2	1	no	—
723	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
724	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
725	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
726	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
727	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
728	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
729	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
730	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
731	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
732	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
733	C₄²	—	2	1	no	—
734	C₄²	—	2	1	no	—
735	C₄²	—	2	1	no	—
736	C₄²	—	2	1	no	—
737	C₄²	—	2	1	no	—
738	C₄²	—	2	1	no	—
739	C₄²	C₂⁴	1	1	yes	characteristic
740	C₄²	C₂⁴	1	1	yes	characteristic
741	C₂³	—	2	4	no	—
742	C₂³	—	2	2	no	—
743	C₂³	—	2	1	no	—
744	C₂³	—	2	1	no	—
745	C₂³	—	2	1	no	—
746	C₂³	—	2	1	no	—
747	C₂³	—	2	1	no	—
748	C₂³	—	2	1	no	—
749	C₂³	—	4	1	no	—
750	C₂³	—	4	1	no	—
751	C₂³	—	4	2	no	—
752	C₂³	—	4	2	no	—
753	C₂³	—	4	2	no	—
754	C₂³	—	4	2	no	—
755	C₂³	—	4	2	no	—
756	C₂³	—	4	2	no	—
757	C₂³	—	4	2	no	—
758	C₂³	—	4	2	no	—
759	C₂³	—	4	2	no	—
760	C₂³	—	4	2	no	—
761	C₂³	—	4	2	no	—
762	C₂³	—	8	1	no	—
763	C₂³	—	8	1	no	—
764	C₂³	—	8	1	no	—
765	C₂³	—	8	1	no	—
766	C₂³	—	8	1	no	—
767	C₂³	—	8	1	no	—
768	C₂³	—	8	1	no	—
769	C₂³	—	8	1	no	—
770	C₂³	—	8	1	no	—
771	C₂³	—	8	1	no	—
772	C₂³	—	8	1	no	—
773	C₂³	—	8	1	no	—
774	C₂³	—	8	16	no	—
775	C₂³	C₂²×D₄	1	1	yes	characteristic
776	C₂³	C₂²×D₄	1	1	yes	characteristic
777	C₂³	C₂²×D₄	1	1	yes	characteristic
778	C₂³	C₂²×D₄	1	1	yes	characteristic
779	C₂³	C₂²×D₄	1	1	yes	characteristic
780	Q₈	—	2	1	no	—
781	Q₈	—	2	1	no	—
782	Q₈	—	2	1	no	—
783	Q₈	—	2	1	no	—
784	Q₈	—	2	1	no	—
785	Q₈	—	2	1	no	—
786	Q₈	—	2	1	no	—
787	Q₈	—	2	1	no	—
788	Q₈	—	4	1	no	—
789	Q₈	—	8	1	no	—
790	Q₈	—	8	1	no	—
791	Q₈	—	8	1	no	—
792	D₄	—	2	4	no	—
793	D₄	—	2	2	no	—
794	D₄	—	2	2	no	—
795	D₄	—	2	1	no	—
796	D₄	—	2	1	no	—
797	D₄	—	2	1	no	—
798	D₄	—	2	1	no	—
799	D₄	—	2	1	no	—
800	D₄	—	2	1	no	—
801	D₄	—	2	1	no	—
802	D₄	—	2	1	no	—
803	D₄	—	2	1	no	—
804	D₄	—	2	1	no	—
805	D₄	—	4	1	no	—
806	D₄	—	4	1	no	—
807	D₄	—	4	1	no	—
808	D₄	—	4	1	no	—
809	D₄	—	4	1	no	—
810	D₄	—	4	2	no	—
811	D₄	—	4	2	no	—
812	D₄	—	4	2	no	—
813	D₄	—	4	2	no	—
814	D₄	—	4	2	no	—
815	D₄	—	4	2	no	—
816	D₄	—	4	2	no	—
817	D₄	—	4	2	no	—
818	D₄	—	4	2	no	—
819	D₄	—	4	2	no	—
820	D₄	—	4	2	no	—
821	D₄	—	4	2	no	—
822	D₄	—	4	2	no	—
823	D₄	—	8	1	no	—
824	D₄	—	8	1	no	—
825	D₄	—	8	1	no	—
826	D₄	—	8	1	no	—
827	D₄	—	8	1	no	—
828	D₄	—	8	1	no	—
829	D₄	—	8	1	no	—
830	D₄	—	8	1	no	—
831	D₄	—	8	1	no	—
832	D₄	—	8	1	no	—
833	D₄	—	8	1	no	—
834	D₄	—	8	1	no	—
835	D₄	H(5,𝔽₂)	1	2	yes	—
836	D₄	H(5,𝔽₂)	1	2	yes	—
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	1	no	—
847	C₂×C₄	—	2	1	no	—
848	C₂×C₄	—	2	1	no	—
849	C₂×C₄	—	2	1	no	—
850	C₂×C₄	—	2	1	no	—
851	C₂×C₄	—	2	1	no	—
852	C₂×C₄	—	2	1	no	—
853	C₂×C₄	—	2	1	no	—
854	C₂×C₄	—	2	1	no	—
855	C₂×C₄	—	2	1	no	—
856	C₂×C₄	—	2	1	no	—
857	C₂×C₄	—	4	1	no	—
858	C₂×C₄	—	4	1	no	—
859	C₂×C₄	—	4	1	no	—
860	C₂×C₄	—	4	2	no	—
861	C₂×C₄	—	4	2	no	—
862	C₂×C₄	—	4	2	no	—
863	C₂×C₄	—	8	1	no	—
864	C₂×C₄	—	8	1	no	—
865	C₂×C₄	—	8	1	no	—
866	C₂×C₄	—	8	1	no	—
867	C₂×C₄	—	8	1	no	—
868	C₂×C₄	—	8	1	no	—
869	C₂×C₄	—	8	1	no	—
870	C₂×C₄	—	8	1	no	—
871	C₂×C₄	—	8	1	no	—
872	C₂×C₄	—	8	1	no	—
873	C₂×C₄	—	8	1	no	—
874	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
875	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
876	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
877	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
878	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
879	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
880	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
881	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
882	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
883	C₂×C₄	C₂⁵	1	1	yes	characteristic
884	C₈	—	2	1	no	—
885	C₈	—	2	1	no	—
886	C₈	—	2	1	no	—
887	C₈	—	2	1	no	—
888	C₈	—	2	1	no	—
889	C₈	—	2	1	no	—
890	C₈	—	2	1	no	—
891	C₈	—	2	1	no	—
892	C₂²	—	2	1	no	—
893	C₂²	—	2	1	no	—
894	C₂²	—	2	1	no	—
895	C₂²	—	2	1	no	—
896	C₂²	—	2	1	no	—
897	C₂²	—	2	1	no	—
898	C₂²	—	2	1	no	—
899	C₂²	—	2	1	no	—
900	C₂²	—	2	1	no	—
901	C₂²	—	2	1	no	—
902	C₂²	—	2	2	no	—
903	C₂²	—	2	2	no	—
904	C₂²	—	2	1	no	—
905	C₂²	—	2	1	no	—
906	C₂²	—	2	1	no	—
907	C₂²	—	2	1	no	—
908	C₂²	—	4	4	no	—
909	C₂²	—	4	1	no	—
910	C₂²	—	4	1	no	—
911	C₂²	—	4	1	no	—
912	C₂²	—	4	1	no	—
913	C₂²	—	4	1	no	—
914	C₂²	—	4	1	no	—
915	C₂²	—	4	1	no	—
916	C₂²	—	4	1	no	—
917	C₂²	—	4	1	no	—
918	C₂²	—	4	1	no	—
919	C₂²	—	4	1	no	—
920	C₂²	—	4	1	no	—
921	C₂²	—	4	1	no	—
922	C₂²	—	4	1	no	—
923	C₂²	—	4	1	no	—
924	C₂²	—	4	1	no	—
925	C₂²	—	8	4	no	—
926	C₂²	—	8	4	no	—
927	C₂²	—	8	4	no	—
928	C₂²	—	8	4	no	—
929	C₂²	—	8	4	no	—
930	C₂²	—	8	4	no	—
931	C₂²	—	16	2	no	—
932	C₂²	—	16	2	no	—
933	C₂²	#577	1	2	yes	—
934	C₂²	C₂³×D₄	1	1	yes	characteristic
935	C₄	—	2	1	no	—
936	C₄	—	2	1	no	—
937	C₄	—	2	1	no	—
938	C₄	—	2	1	no	—
939	C₄	—	2	1	no	—
940	C₄	—	2	1	no	—
941	C₄	—	2	1	no	—
942	C₄	—	2	1	no	—
943	C₄	—	2	1	no	—
944	C₄	—	4	1	no	—
945	C₄	—	4	1	no	—
946	C₄	—	4	1	no	—
947	C₄	—	4	1	no	—
948	C₄	—	4	1	no	—
949	C₄	—	4	1	no	—
950	C₄	—	4	1	no	—
951	C₄	—	4	1	no	—
952	C₄	—	4	1	no	—
953	C₄	—	4	1	no	—
954	C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
955	C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
956	C₂	—	2	2	no	—
957	C₂	—	4	1	no	—
958	C₂	—	4	1	no	—
959	C₂	—	4	1	no	—
960	C₂	—	4	1	no	—
961	C₂	—	4	2	no	—
962	C₂	—	4	2	no	—
963	C₂	—	8	1	no	—
964	C₂	—	8	1	no	—
965	C₂	—	8	1	no	—
966	C₂	—	8	1	no	—
967	C₂	#3484	1	1	yes	characteristic
968	C₂	C₂×#577	1	1	yes	characteristic
969	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 ◁ #525 ◁ G
LECS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #3541	C₂	semidirect
2. #3484	C₂	semidirect
3. #3324	C₂	semidirect
4. #3323	C₂	semidirect
5. #3318	C₂	semidirect
6. #3314	C₂	semidirect
7. #3311	C₂	semidirect
8. #3310	C₂	semidirect
9. #3297	C₂	semidirect
10. #3295	C₂	semidirect
11. #3282	C₂	semidirect
12. D₄×SD₁₆	C₂	semidirect
13. #3275	C₂	semidirect
14. #3272	C₂	semidirect
15. #3267	C₂	semidirect
16. #3266	C₂	semidirect
17. #3265	C₂	semidirect
18. #3265	C₂	semidirect
19. #3224	C₂	semidirect
20. #3222	C₂	semidirect
21. #3200	C₂	semidirect
22. #3198	C₂	semidirect
23. #3196	C₂	semidirect
24. #3191	C₂	semidirect
25. #3123	C₂	semidirect
26. #3118	C₂	semidirect
27. #3012	C₂	semidirect
28. #3009	C₂	semidirect
29. #3003	C₂	semidirect
30. C₂×#450	C₂	semidirect
31. #2976	C₂	semidirect
34. C₂×#137	C₂²	semidirect
35. C₂×AGL(1,ℤ/8)	C₂²	semidirect
36. C₂×AGL(1,ℤ/8)	C₂²	semidirect
37. C₂×AGL(1,ℤ/8)	C₂²	semidirect
38. C₂×#135	C₂²	semidirect
39. C₂²×SD₁₆	C₂²	semidirect
40. C₂²×SD₁₆	C₂²	semidirect
41. C₂²×SD₁₆	C₂²	semidirect
44. #556	C₂²	semidirect
46. #554	C₂²	semidirect
48. #553	C₂²	semidirect
49. #552	C₂²	semidirect
50. D₄×Q₈	C₂²	semidirect
51. #548	C₂²	semidirect
52. #548	C₂²	semidirect
53. #547	C₂²	semidirect
67. #542	C₂²	semidirect
68. #541	C₂²	semidirect
72. #537	C₂²	semidirect
73. #536	C₂²	semidirect
80. #525	C₂²	semidirect
81. C₂×C₂²⋊Q₈	C₂²	semidirect
85. #497	C₂²	semidirect
86. #496	C₂²	semidirect
87. #495	C₂²	semidirect
88. #492	C₂²	semidirect
89. #490	C₂²	semidirect
90. #489	C₂²	semidirect
91. #488	C₂²	semidirect
92. #486	C₂²	semidirect
93. #485	C₂²	semidirect
94. #485	C₂²	semidirect
95. #485	C₂²	semidirect
96. #485	C₂²	semidirect
97. #484	C₂²	semidirect
98. #482	C₂²	semidirect
99. #482	C₂²	semidirect
100. #482	C₂²	semidirect
101. #482	C₂²	semidirect
102. #481	C₂²	semidirect
103. #481	C₂²	semidirect
104. #480	C₂²	semidirect
105. #478	C₂²	semidirect
106. #478	C₂²	semidirect
107. #476	C₂²	semidirect
108. #474	C₂²	semidirect
109. #470	C₂²	semidirect
110. #470	C₂²	semidirect
111. #469	C₂²	semidirect
112. #468	C₂²	semidirect
113. #468	C₂²	semidirect
114. #468	C₂²	semidirect
115. #468	C₂²	semidirect
116. #468	C₂²	semidirect
117. #467	C₂²	semidirect
118. #466	C₂²	semidirect
119. #466	C₂²	semidirect
120. #465	C₂²	semidirect
121. #465	C₂²	semidirect
122. #465	C₂²	semidirect
123. #465	C₂²	semidirect
124. #465	C₂²	semidirect
125. #464	C₂²	semidirect
126. #464	C₂²	semidirect
127. #464	C₂²	semidirect
128. #463	C₂²	semidirect
129. #463	C₂²	semidirect
130. #463	C₂²	semidirect
131. #461	C₂²	semidirect
132. #461	C₂²	semidirect
133. #460	C₂²	semidirect
134. #460	C₂²	semidirect
135. #460	C₂²	semidirect
136. #459	C₂²	semidirect
137. #452	C₂²	semidirect
138. #452	C₂²	semidirect
139. #452	C₂²	semidirect
140. #452	C₂²	semidirect
141. #452	C₂²	semidirect
142. #452	C₂²	semidirect
143. #452	C₂²	semidirect
144. #451	C₂²	semidirect
148. #450	C₂²	semidirect
149. #450	C₂²	semidirect
150. #450	C₂²	semidirect
151. #450	C₂²	semidirect
152. #450	C₂²	semidirect
153. #450	C₂²	semidirect
154. #450	C₂²	semidirect
155. #450	C₂²	semidirect
156. #450	C₂²	semidirect
157. #450	C₂²	semidirect
158. #450	C₂²	semidirect
159. #450	C₂²	semidirect
160. #449	C₂²	semidirect
161. #449	C₂²	semidirect
162. #449	C₂²	semidirect
163. #449	C₂²	semidirect
164. #449	C₂²	semidirect
165. #448	C₂²	semidirect
166. #448	C₂²	semidirect
167. #448	C₂²	semidirect
169. #447	C₂²	semidirect
170. #447	C₂²	semidirect
171. #447	C₂²	semidirect
172. #447	C₂²	semidirect
173. #442	C₂²	semidirect
174. #440	C₂²	semidirect
175. #440	C₂²	semidirect
176. #440	C₂²	semidirect
177. C₄×SD₁₆	C₂²	semidirect
178. C₄×SD₁₆	C₂²	semidirect
179. C₄×SD₁₆	C₂²	semidirect
180. C₄×D₈	C₂²	semidirect
181. #436	C₂²	semidirect
182. #436	C₂²	semidirect
183. #435	C₂²	semidirect
184. #435	C₂²	semidirect
185. #435	C₂²	semidirect
186. #435	C₂²	semidirect
187. C₈×D₄	C₂²	semidirect
188. C₈×D₄	C₂²	semidirect
189. #433	C₂²	semidirect
190. #433	C₂²	semidirect
191. #418	C₂²	semidirect
192. #418	C₂²	semidirect
193. #418	C₂²	semidirect
194. #417	C₂²	semidirect
195. #416	C₂²	semidirect
196. C₂×#102	C₂²	semidirect
197. C₂×#102	C₂²	semidirect
198. C₂×#102	C₂²	semidirect
199. #408	C₂²	semidirect
200. #408	C₂²	semidirect
201. #407	C₂²	semidirect
202. C₂×C₂²⋊C₈	C₂²	semidirect
212. C₂×#41	C₂³	semidirect
214. C₂²×Q₈	C₂³	semidirect
241. C₂×Q₁₆	C₂³	semidirect
242. C₂×Q₁₆	C₂³	semidirect
243. C₂×Q₁₆	C₂³	semidirect
259. C₂×SD₁₆	C₂³	semidirect
260. C₂×SD₁₆	C₂³	semidirect
261. C₂×SD₁₆	C₂³	semidirect
262. C₂×SD₁₆	C₂³	semidirect
267. C₂×D₈	C₂³	semidirect
270. C₂×M₁₆	C₂³	semidirect
271. C₂×M₁₆	C₂³	semidirect
274. C₂²×C₈	C₂³	semidirect
275. C₂²×C₈	C₂³	semidirect
278. C₄⋊Q₈	C₂³	semidirect
279. C₄⋊Q₈	C₂³	semidirect
294. #125	C₂³	semidirect
303. #124	C₂³	semidirect
339. C₂²⋊Q₈	C₂³	semidirect
340. C₂²⋊Q₈	C₂³	semidirect
341. C₂²⋊Q₈	C₂³	semidirect
369. #121	C₂³	semidirect
391. C₄×Q₈	C₂³	semidirect
392. C₄×Q₈	C₂³	semidirect
393. C₄×Q₈	C₂³	semidirect
413. C₄×D₄	C₂³	semidirect
418. #117	C₂³	semidirect
422. C₂×C₄⋊C₄	C₂³	semidirect
430. #107	C₂³	semidirect
431. #107	C₂³	semidirect
432. #107	C₂³	semidirect
433. #107	C₂³	semidirect
434. #106	C₂³	semidirect
435. #106	C₂³	semidirect
436. #106	C₂³	semidirect
437. #106	C₂³	semidirect
438. C₄⋊C₈	C₂³	semidirect
439. C₄⋊C₈	C₂³	semidirect
440. C₄⋊C₈	C₂³	semidirect
441. C₄⋊C₈	C₂³	semidirect
442. #103	C₂³	semidirect
443. #103	C₂³	semidirect
444. #103	C₂³	semidirect
445. #103	C₂³	semidirect
446. #103	C₂³	semidirect
447. #103	C₂³	semidirect
448. #103	C₂³	semidirect
449. #103	C₂³	semidirect
450. #103	C₂³	semidirect
451. #103	C₂³	semidirect
468. #102	C₂³	semidirect
469. #102	C₂³	semidirect
470. #102	C₂³	semidirect
471. #102	C₂³	semidirect
472. #102	C₂³	semidirect
473. #102	C₂³	semidirect
482. C₂²⋊C₈	C₂³	semidirect
483. C₂²⋊C₈	C₂³	semidirect
484. C₂²⋊C₈	C₂³	semidirect
485. C₂²⋊C₈	C₂³	semidirect
486. #97	C₂³	semidirect
487. #97	C₂³	semidirect
488. C₄×C₈	C₂³	semidirect
489. C₄×C₈	C₂³	semidirect

Maximal subgroups

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

subgroup	index
#3541	2
#3484	2
#3324	2
#3323	2
#3318	2
#3314	2
#3311	2
#3310	2
#3297	2
#3295	2
#3282	2
D₄×SD₁₆	2
#3275	2
#3272	2
#3267	2
#3266	2
#3265	2
#3224	2
#3222	2
#3200	2
#3198	2
#3196	2
#3191	2
#3123	2
#3118	2
#3012	2
#3009	2
#3003	2
C₂×#450	2
#2976	2