Subgroups — #61609

Order 256.

1145 conjugacy classes of subgroups.

The subgroup lattice has 996 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3542	C₂	1	1	yes	maximal, characteristic, complemented
2	#3484	C₂	1	1	yes	maximal, characteristic, complemented
3	#3325	C₂	1	1	yes	maximal, characteristic, complemented
4	#3322	C₂	1	1	yes	maximal, characteristic, complemented
5	#3319	C₂	1	1	yes	maximal, characteristic, complemented
6	#3318	C₂	1	1	yes	maximal, characteristic, complemented
7	#3310	C₂	1	1	yes	maximal, characteristic, complemented
8	#3306	C₂	1	1	yes	maximal, characteristic, complemented
9	#3296	C₂	1	1	yes	maximal, characteristic, complemented
10	#3294	C₂	1	1	yes	maximal, characteristic, complemented
11	#3280	C₂	1	1	yes	maximal, characteristic, complemented
12	D₄×D₈	C₂	1	1	yes	maximal, characteristic, complemented
13	#3274	C₂	1	1	yes	maximal, characteristic, complemented
14	#3273	C₂	1	1	yes	maximal, characteristic, complemented
15	#3268	C₂	1	1	yes	maximal, characteristic, complemented
16	#3264	C₂	1	1	yes	maximal, characteristic, complemented
17	#3264	C₂	1	1	yes	maximal, characteristic, complemented
18	#3264	C₂	1	1	yes	maximal, characteristic, complemented
19	#3224	C₂	1	1	yes	maximal, characteristic, complemented
20	#3220	C₂	1	1	yes	maximal, characteristic, complemented
21	#3199	C₂	1	1	yes	maximal, characteristic, complemented
22	#3198	C₂	1	1	yes	maximal, characteristic, complemented
23	#3194	C₂	1	1	yes	maximal, characteristic, complemented
24	#3191	C₂	1	1	yes	maximal, characteristic, complemented
25	#3122	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	#3008	C₂	1	1	yes	maximal, characteristic, complemented
29	#3003	C₂	1	1	yes	maximal, characteristic, complemented
30	C₂×#447	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, complemented
33	C₂³×D₄	C₂²	1	1	yes	characteristic, complemented
34	C₂×AGL(1,ℤ/8)	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×D₈	C₂²	1	1	yes	characteristic, complemented
40	C₂²×D₈	C₂²	1	1	yes	characteristic, complemented
41	C₂²×D₈	C₂²	1	1	yes	characteristic, complemented
42	#562	—	2	1	no	—
43	#560	—	2	1	no	—
44	#555	C₂²	1	1	yes	characteristic, complemented
45	#553	C₂²	1	1	yes	characteristic, complemented
46	#552	C₂²	1	1	yes	characteristic, complemented
47	#551	—	2	1	no	—
48	#550	C₂²	1	1	yes	characteristic, complemented
49	#547	C₂²	1	1	yes	characteristic, complemented
50	#546	—	2	1	no	—
51	#546	—	2	1	no	—
52	#546	—	2	1	no	—
53	#546	C₂²	1	1	yes	characteristic
54	#546	C₂²	1	1	yes	characteristic, complemented
55	#546	C₂²	1	1	yes	characteristic, complemented
56	#546	C₂²	1	1	yes	characteristic, complemented
57	#546	C₂²	1	1	yes	characteristic, complemented
58	#546	C₂²	1	1	yes	characteristic, complemented
59	D₄²	—	2	1	no	—
60	D₄²	—	2	1	no	—
61	D₄²	C₂²	1	1	yes	characteristic
62	D₄²	C₂²	1	1	yes	characteristic, complemented
63	D₄²	C₂²	1	1	yes	characteristic, complemented
64	D₄²	C₂²	1	1	yes	characteristic, complemented
65	D₄²	C₂²	1	1	yes	characteristic, complemented
66	#542	C₂²	1	1	yes	characteristic, complemented
67	#540	—	2	1	no	—
68	#540	C₂²	1	1	yes	characteristic, complemented
69	#538	—	2	1	no	—
70	#537	C₂²	1	1	yes	characteristic, complemented
71	#535	—	2	1	no	—
72	#535	C₂²	1	1	yes	characteristic, complemented
73	#535	C₂²	1	1	yes	characteristic, complemented
74	#535	C₂²	1	1	yes	characteristic, complemented
75	#534	—	2	1	no	—
76	#534	—	2	1	no	—
77	#534	—	2	1	no	—
78	#525	C₂²	1	1	yes	characteristic
79	#525	C₂²	1	1	yes	characteristic, complemented
80	#525	C₂²	1	1	yes	characteristic, complemented
81	C₂×#121	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, complemented
85	#496	C₂²	1	1	yes	characteristic, complemented
86	#496	C₂²	1	1	yes	characteristic, complemented
87	#495	C₂²	1	1	yes	characteristic, complemented
88	#493	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	#483	C₂²	1	1	yes	characteristic, complemented
96	#482	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	#481	C₂²	1	1	yes	characteristic, complemented
103	#480	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	#469	C₂²	1	1	yes	characteristic, complemented
110	#469	C₂²	1	1	yes	characteristic, complemented
111	#469	C₂²	1	1	yes	characteristic, complemented
112	#469	C₂²	1	1	yes	characteristic, complemented
113	#469	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	#466	C₂²	1	1	yes	characteristic, complemented
121	#466	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	#463	C₂²	1	1	yes	characteristic, complemented
127	#463	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	#460	C₂²	1	1	yes	characteristic, complemented
132	#459	C₂²	1	1	yes	characteristic, complemented
133	#459	C₂²	1	1	yes	characteristic, complemented
134	#459	C₂²	1	1	yes	characteristic, complemented
135	#459	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	#450	C₂²	1	1	yes	characteristic, complemented
141	#450	C₂²	1	1	yes	characteristic, complemented
142	#450	C₂²	1	1	yes	characteristic, complemented
143	#450	C₂²	1	1	yes	characteristic, complemented
144	#450	C₂²	1	1	yes	characteristic, complemented
145	#450	C₂²	1	1	yes	characteristic, complemented
146	#449	C₂²	1	1	yes	characteristic, complemented
147	#449	C₂²	1	1	yes	characteristic, complemented
148	#449	C₂²	1	1	yes	characteristic, complemented
149	#449	C₂²	1	1	yes	characteristic, complemented
150	#449	C₂²	1	1	yes	characteristic, complemented
151	#449	C₂²	1	1	yes	characteristic, complemented
152	#449	C₂²	1	1	yes	characteristic, complemented
153	#449	C₂²	1	1	yes	characteristic, complemented
154	#449	C₂²	1	1	yes	characteristic, complemented
155	#447	C₂²	1	1	yes	characteristic
156	#447	C₂²	1	1	yes	characteristic, complemented
157	#447	C₂²	1	1	yes	characteristic, complemented
158	#447	C₂²	1	1	yes	characteristic, complemented
159	#447	C₂²	1	1	yes	characteristic, complemented
160	#447	C₂²	1	1	yes	characteristic, complemented
161	#447	C₂²	1	1	yes	characteristic, complemented
162	#447	C₂²	1	1	yes	characteristic, complemented
163	#447	C₂²	1	1	yes	characteristic, complemented
164	#447	C₂²	1	1	yes	characteristic, complemented
165	#447	C₂²	1	1	yes	characteristic, complemented
166	#447	C₂²	1	1	yes	characteristic, complemented
167	#447	C₂²	1	1	yes	characteristic, complemented
168	#447	C₂²	1	1	yes	characteristic, complemented
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	#442	C₂²	1	1	yes	characteristic, complemented
175	#442	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×D₈	C₂²	1	1	yes	characteristic, complemented
179	C₄×D₈	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	—	2	1	no	—
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
213	C₂×#41	C₂³	1	1	yes	characteristic, complemented
214	C₂²×D₄	—	2	1	no	—
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	—	2	1	no	—
226	C₂²×D₄	—	4	2	no	—
227	C₂²×D₄	—	4	2	no	—
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	C₂²×D₄	C₂³	1	1	yes	characteristic
236	C₂²×D₄	C₂³	1	1	yes	characteristic
237	C₂²×D₄	C₂³	1	1	yes	characteristic, complemented
238	C₂³×C₄	C₂³	1	1	yes	characteristic
239	AGL(1,ℤ/8)	—	4	2	no	—
240	AGL(1,ℤ/8)	—	4	2	no	—
241	AGL(1,ℤ/8)	—	4	2	no	—
242	AGL(1,ℤ/8)	—	4	2	no	—
243	#135	—	4	2	no	—
244	C₂×Q₁₆	C₂³	1	1	yes	characteristic, complemented
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, complemented
250	C₂×SD₁₆	C₂³	1	1	yes	characteristic, complemented
251	C₂×SD₁₆	C₂³	1	1	yes	characteristic, complemented
252	C₂×SD₁₆	C₂³	1	1	yes	characteristic, complemented
253	C₂×D₈	—	4	2	no	—
254	C₂×D₈	—	4	2	no	—
255	C₂×D₈	—	4	2	no	—
256	C₂×D₈	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×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
268	C₂×D₈	C₂³	1	1	yes	characteristic, complemented
269	C₂×D₈	C₂³	1	1	yes	characteristic, complemented
270	C₂×D₈	C₂³	1	1	yes	characteristic, complemented
271	C₂×M₁₆	C₂³	1	1	yes	characteristic
272	C₂×M₁₆	C₂³	1	1	yes	characteristic
273	C₂×M₁₆	C₂³	1	1	yes	characteristic, complemented
274	C₂×M₁₆	C₂³	1	1	yes	characteristic, complemented
275	C₂²×C₈	C₂³	1	1	yes	characteristic
276	C₂²×C₈	C₂³	1	1	yes	characteristic
277	C₂²×C₈	C₂³	1	1	yes	characteristic, complemented
278	C₂²×C₈	C₂³	1	1	yes	characteristic, complemented
279	C₄⋊Q₈	C₂³	1	1	yes	characteristic, complemented
280	#127	—	2	1	no	—
281	#127	—	2	1	no	—
282	#127	—	2	1	no	—
283	#127	C₂³	1	1	yes	characteristic
284	#127	C₂³	1	1	yes	characteristic
285	#127	C₂³	1	1	yes	characteristic, complemented
286	#126	—	2	1	no	—
287	#126	—	2	1	no	—
288	#126	—	2	1	no	—
289	#125	—	2	1	no	—
290	#125	C₂³	1	1	yes	characteristic, complemented
291	#124	—	2	1	no	—
292	#124	—	2	1	no	—
293	#124	—	2	1	no	—
294	#124	—	2	1	no	—
295	#124	—	2	1	no	—
296	#124	C₂³	1	1	yes	characteristic
297	#124	C₂³	1	1	yes	characteristic
298	#124	C₂³	1	1	yes	characteristic, complemented
299	#123	—	2	1	no	—
300	#123	—	2	1	no	—
301	#123	—	2	1	no	—
302	#123	—	2	1	no	—
303	#123	—	2	1	no	—
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	D₄	1	1	yes	characteristic
315	#123	D₄	1	1	yes	characteristic
316	C₂²⋊Q₈	—	2	1	no	—
317	C₂²⋊Q₈	—	2	1	no	—
318	C₂²⋊Q₈	—	2	1	no	—
319	C₂²⋊Q₈	D₄	1	1	yes	characteristic
320	C₂²⋊Q₈	D₄	1	1	yes	characteristic
321	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
322	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
323	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
324	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
325	C₂²⋊Q₈	C₂³	1	1	yes	characteristic, complemented
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	—	2	1	no	—
333	#121	—	2	1	no	—
334	#121	—	2	1	no	—
335	#121	—	2	1	no	—
336	#121	—	2	1	no	—
337	#121	—	2	1	no	—
338	#121	—	2	1	no	—
339	#121	—	2	1	no	—
340	#121	—	2	1	no	—
341	#121	—	2	1	no	—
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	D₄	1	1	yes	characteristic
351	#121	D₄	1	1	yes	characteristic
352	#121	C₂³	1	1	yes	characteristic
353	#121	C₂³	1	1	yes	characteristic
354	#121	C₂³	1	1	yes	characteristic
355	#121	C₂³	1	1	yes	characteristic
356	#121	C₂³	1	1	yes	characteristic
357	#121	C₂³	1	1	yes	characteristic
358	#121	C₂³	1	1	yes	characteristic
359	#121	C₂³	1	1	yes	characteristic
360	#121	C₂³	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, complemented
365	#121	C₂³	1	1	yes	characteristic, complemented
366	#121	C₂³	1	1	yes	characteristic, complemented
367	#120	—	2	1	no	—
368	#120	—	2	1	no	—
369	#120	—	2	1	no	—
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	—	2	1	no	—
389	#120	—	2	1	no	—
390	#120	—	2	1	no	—
391	#120	D₄	1	1	yes	characteristic
392	#120	D₄	1	1	yes	characteristic
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	C₂³	1	1	yes	characteristic
403	C₄×D₄	C₂³	1	1	yes	characteristic
404	C₄×D₄	C₂³	1	1	yes	characteristic
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, complemented
411	C₄×D₄	C₂³	1	1	yes	characteristic, complemented
412	C₄×D₄	C₂³	1	1	yes	characteristic, complemented
413	#117	—	2	1	no	—
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	C₂³	1	1	yes	characteristic
420	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic, complemented
421	C₂×C₂²⋊C₄	—	2	1	no	—
422	C₂×C₂²⋊C₄	—	2	1	no	—
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	#102	C₂³	1	1	yes	characteristic
449	#102	C₂³	1	1	yes	characteristic
450	#102	C₂³	1	1	yes	characteristic
451	#102	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, complemented
465	#102	C₂³	1	1	yes	characteristic, complemented
466	#102	C₂³	1	1	yes	characteristic, complemented
467	#102	C₂³	1	1	yes	characteristic, complemented
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	—	2	1	no	—
499	C₂⁴	—	2	1	no	—
500	C₂⁴	—	4	4	no	—
501	C₂⁴	—	8	2	no	—
502	C₂⁴	—	8	2	no	—
503	C₂⁴	C₂×D₄	1	1	yes	characteristic
504	#41	—	2	2	no	—
505	#41	—	2	2	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	1	no	—
515	#41	—	4	1	no	—
516	#41	—	4	4	no	—
517	#41	—	8	2	no	—
518	C₂×Q₈	—	2	1	no	—
519	C₂×Q₈	C₂×D₄	1	1	yes	characteristic
520	C₂×Q₈	C₂⁴	1	1	yes	characteristic
521	C₂×Q₈	C₂⁴	1	1	yes	characteristic
522	C₂×D₄	—	2	2	no	—
523	C₂×D₄	—	2	2	no	—
524	C₂×D₄	—	2	2	no	—
525	C₂×D₄	—	2	2	no	—
526	C₂×D₄	—	2	2	no	—
527	C₂×D₄	—	2	2	no	—
528	C₂×D₄	—	2	2	no	—
529	C₂×D₄	—	2	2	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	—	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	—	2	1	no	—
562	C₂×D₄	—	2	1	no	—
563	C₂×D₄	—	2	1	no	—
564	C₂×D₄	—	2	1	no	—
565	C₂×D₄	—	2	1	no	—
566	C₂×D₄	—	4	1	no	—
567	C₂×D₄	—	4	1	no	—
568	C₂×D₄	—	4	1	no	—
569	C₂×D₄	—	4	1	no	—
570	C₂×D₄	—	4	1	no	—
571	C₂×D₄	—	4	1	no	—
572	C₂×D₄	—	4	1	no	—
573	C₂×D₄	—	4	1	no	—
574	C₂×D₄	—	4	1	no	—
575	C₂×D₄	—	4	1	no	—
576	C₂×D₄	—	4	1	no	—
577	C₂×D₄	—	4	1	no	—
578	C₂×D₄	—	4	4	no	—
579	C₂×D₄	—	4	4	no	—
580	C₂×D₄	—	4	4	no	—
581	C₂×D₄	—	4	4	no	—
582	C₂×D₄	—	4	4	no	—
583	C₂×D₄	—	4	4	no	—
584	C₂×D₄	—	8	2	no	—
585	C₂×D₄	—	8	2	no	—
586	C₂×D₄	—	8	2	no	—
587	C₂×D₄	—	8	2	no	—
588	C₂×D₄	—	8	2	no	—
589	C₂×D₄	—	8	2	no	—
590	C₂×D₄	C₂×D₄	1	1	yes	characteristic
591	C₂×D₄	C₂×D₄	1	1	yes	characteristic
592	C₂×D₄	C₂×D₄	1	1	yes	characteristic
593	C₂×D₄	C₂×D₄	1	1	yes	characteristic
594	C₂×D₄	C₂×D₄	1	1	yes	characteristic
595	C₂×D₄	C₂×D₄	1	1	yes	characteristic
596	C₂×D₄	C₂×D₄	1	1	yes	characteristic
597	C₂×D₄	C₂⁴	1	1	yes	characteristic
598	C₂×D₄	C₂⁴	1	1	yes	characteristic
599	C₂×D₄	C₂⁴	1	1	yes	characteristic
600	C₂×D₄	C₂⁴	1	1	yes	characteristic
601	C₂×D₄	C₂⁴	1	1	yes	characteristic
602	C₂×D₄	C₂⁴	1	1	yes	characteristic
603	C₂×D₄	C₂⁴	1	1	yes	characteristic
604	C₂×D₄	C₂⁴	1	1	yes	characteristic
605	C₂²×C₄	—	2	1	no	—
606	C₂²×C₄	—	2	1	no	—
607	C₂²×C₄	—	2	1	no	—
608	C₂²×C₄	—	2	1	no	—
609	C₂²×C₄	—	2	1	no	—
610	C₂²×C₄	—	2	1	no	—
611	C₂²×C₄	—	2	1	no	—
612	C₂²×C₄	—	2	1	no	—
613	C₂²×C₄	—	2	1	no	—
614	C₂²×C₄	—	2	1	no	—
615	C₂²×C₄	—	2	1	no	—
616	C₂²×C₄	—	2	1	no	—
617	C₂²×C₄	—	2	1	no	—
618	C₂²×C₄	—	2	1	no	—
619	C₂²×C₄	—	4	1	no	—
620	C₂²×C₄	—	4	1	no	—
621	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
622	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
623	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
624	C₂²×C₄	C₂⁴	1	1	yes	characteristic
625	C₂²×C₄	C₂⁴	1	1	yes	characteristic
626	C₂²×C₄	C₂⁴	1	1	yes	characteristic
627	C₂²×C₄	C₂⁴	1	1	yes	characteristic
628	C₂²×C₄	C₂⁴	1	1	yes	characteristic
629	Q₁₆	—	4	1	no	—
630	SD₁₆	—	2	2	no	—
631	SD₁₆	—	2	2	no	—
632	SD₁₆	—	4	1	no	—
633	SD₁₆	—	4	1	no	—
634	SD₁₆	—	4	1	no	—
635	SD₁₆	—	4	1	no	—
636	SD₁₆	—	4	1	no	—
637	SD₁₆	—	4	1	no	—
638	D₈	—	2	2	no	—
639	D₈	—	2	2	no	—
640	D₈	—	2	2	no	—
641	D₈	—	2	2	no	—
642	D₈	—	2	2	no	—
643	D₈	—	2	2	no	—
644	D₈	—	4	1	no	—
645	D₈	—	4	1	no	—
646	D₈	—	4	1	no	—
647	D₈	—	4	1	no	—
648	D₈	—	4	1	no	—
649	D₈	—	4	1	no	—
650	D₈	—	4	1	no	—
651	D₈	—	4	1	no	—
652	D₈	—	4	1	no	—
653	M₁₆	—	4	1	no	—
654	M₁₆	—	4	1	no	—
655	M₁₆	—	4	1	no	—
656	M₁₆	—	4	1	no	—
657	C₂×C₈	—	4	1	no	—
658	C₂×C₈	—	4	1	no	—
659	C₂×C₈	—	4	1	no	—
660	C₂×C₈	—	4	1	no	—
661	C₂×C₈	C₂⁴	1	1	yes	characteristic
662	C₂×C₈	C₂⁴	1	1	yes	characteristic
663	C₂×C₈	C₂⁴	1	1	yes	characteristic
664	C₂×C₈	C₂⁴	1	1	yes	characteristic
665	C₂×C₈	C₂⁴	1	1	yes	characteristic
666	C₂×C₈	C₂⁴	1	1	yes	characteristic
667	C₂×C₈	C₂⁴	1	1	yes	characteristic
668	C₂×C₈	C₂⁴	1	1	yes	characteristic
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	—	2	1	no	—
678	C₄⋊C₄	—	2	1	no	—
679	C₄⋊C₄	—	2	1	no	—
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	C₂×D₄	1	1	yes	characteristic
684	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
685	C₄⋊C₄	C₂×D₄	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	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
690	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
691	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
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	—	2	1	no	—
724	C₂²⋊C₄	—	2	1	no	—
725	C₂²⋊C₄	—	2	1	no	—
726	C₂²⋊C₄	—	2	1	no	—
727	C₂²⋊C₄	—	2	1	no	—
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	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
734	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
735	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
736	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
737	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
738	C₄²	—	2	1	no	—
739	C₄²	—	2	1	no	—
740	C₄²	—	2	1	no	—
741	C₄²	—	2	1	no	—
742	C₄²	C₂⁴	1	1	yes	characteristic
743	C₄²	C₂⁴	1	1	yes	characteristic
744	C₂³	—	2	4	no	—
745	C₂³	—	2	2	no	—
746	C₂³	—	2	1	no	—
747	C₂³	—	2	1	no	—
748	C₂³	—	2	1	no	—
749	C₂³	—	2	1	no	—
750	C₂³	—	2	1	no	—
751	C₂³	—	2	1	no	—
752	C₂³	—	2	1	no	—
753	C₂³	—	2	1	no	—
754	C₂³	—	4	1	no	—
755	C₂³	—	4	1	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	—	4	2	no	—
763	C₂³	—	4	2	no	—
764	C₂³	—	4	2	no	—
765	C₂³	—	4	2	no	—
766	C₂³	—	4	2	no	—
767	C₂³	—	4	2	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	1	no	—
775	C₂³	—	8	1	no	—
776	C₂³	—	8	1	no	—
777	C₂³	—	8	1	no	—
778	C₂³	—	8	1	no	—
779	C₂³	—	8	1	no	—
780	C₂³	—	8	1	no	—
781	C₂³	—	8	1	no	—
782	C₂³	—	8	1	no	—
783	C₂³	—	8	1	no	—
784	C₂³	—	8	1	no	—
785	C₂³	—	8	16	no	—
786	C₂³	C₂²×D₄	1	1	yes	characteristic
787	C₂³	C₂²×D₄	1	1	yes	characteristic
788	C₂³	C₂²×D₄	1	1	yes	characteristic
789	C₂³	C₂²×D₄	1	1	yes	characteristic
790	C₂³	C₂²×D₄	1	1	yes	characteristic
791	Q₈	—	2	1	no	—
792	Q₈	—	2	1	no	—
793	Q₈	—	2	1	no	—
794	Q₈	—	2	1	no	—
795	Q₈	—	4	1	no	—
796	Q₈	—	8	1	no	—
797	D₄	—	2	4	no	—
798	D₄	—	2	2	no	—
799	D₄	—	2	2	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	—	2	1	no	—
806	D₄	—	2	1	no	—
807	D₄	—	2	1	no	—
808	D₄	—	2	1	no	—
809	D₄	—	2	1	no	—
810	D₄	—	2	1	no	—
811	D₄	—	2	1	no	—
812	D₄	—	2	1	no	—
813	D₄	—	2	1	no	—
814	D₄	—	4	1	no	—
815	D₄	—	4	1	no	—
816	D₄	—	4	1	no	—
817	D₄	—	4	1	no	—
818	D₄	—	4	1	no	—
819	D₄	—	4	2	no	—
820	D₄	—	4	2	no	—
821	D₄	—	4	2	no	—
822	D₄	—	4	2	no	—
823	D₄	—	4	2	no	—
824	D₄	—	4	2	no	—
825	D₄	—	4	2	no	—
826	D₄	—	4	2	no	—
827	D₄	—	4	2	no	—
828	D₄	—	4	2	no	—
829	D₄	—	4	2	no	—
830	D₄	—	4	2	no	—
831	D₄	—	4	2	no	—
832	D₄	—	8	1	no	—
833	D₄	—	8	1	no	—
834	D₄	—	8	1	no	—
835	D₄	—	8	1	no	—
836	D₄	—	8	1	no	—
837	D₄	—	8	1	no	—
838	D₄	—	8	1	no	—
839	D₄	—	8	1	no	—
840	D₄	—	8	1	no	—
841	D₄	—	8	1	no	—
842	D₄	—	8	1	no	—
843	D₄	—	8	1	no	—
844	D₄	—	8	1	no	—
845	D₄	—	8	1	no	—
846	D₄	—	8	1	no	—
847	D₄	—	8	1	no	—
848	D₄	—	8	1	no	—
849	D₄	—	8	1	no	—
850	D₄	—	8	1	no	—
851	D₄	—	8	1	no	—
852	D₄	—	8	1	no	—
853	D₄	—	8	1	no	—
854	D₄	H(5,𝔽₂)	1	2	yes	—
855	D₄	H(5,𝔽₂)	1	2	yes	—
856	C₂×C₄	—	2	1	no	—
857	C₂×C₄	—	2	1	no	—
858	C₂×C₄	—	2	1	no	—
859	C₂×C₄	—	2	1	no	—
860	C₂×C₄	—	2	1	no	—
861	C₂×C₄	—	2	1	no	—
862	C₂×C₄	—	2	1	no	—
863	C₂×C₄	—	2	1	no	—
864	C₂×C₄	—	2	1	no	—
865	C₂×C₄	—	2	1	no	—
866	C₂×C₄	—	2	1	no	—
867	C₂×C₄	—	2	1	no	—
868	C₂×C₄	—	2	1	no	—
869	C₂×C₄	—	2	1	no	—
870	C₂×C₄	—	2	1	no	—
871	C₂×C₄	—	2	1	no	—
872	C₂×C₄	—	2	1	no	—
873	C₂×C₄	—	2	1	no	—
874	C₂×C₄	—	4	1	no	—
875	C₂×C₄	—	4	1	no	—
876	C₂×C₄	—	4	1	no	—
877	C₂×C₄	—	4	2	no	—
878	C₂×C₄	—	4	2	no	—
879	C₂×C₄	—	4	2	no	—
880	C₂×C₄	—	4	2	no	—
881	C₂×C₄	—	8	1	no	—
882	C₂×C₄	—	8	1	no	—
883	C₂×C₄	—	8	1	no	—
884	C₂×C₄	—	8	1	no	—
885	C₂×C₄	—	8	1	no	—
886	C₂×C₄	—	8	1	no	—
887	C₂×C₄	—	8	1	no	—
888	C₂×C₄	—	8	1	no	—
889	C₂×C₄	—	8	1	no	—
890	C₂×C₄	—	8	1	no	—
891	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
892	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
893	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
894	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
895	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
896	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
897	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
898	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
899	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
900	C₂×C₄	C₂⁵	1	1	yes	characteristic
901	C₈	—	2	1	no	—
902	C₈	—	2	1	no	—
903	C₈	—	2	1	no	—
904	C₈	—	2	1	no	—
905	C₈	—	2	1	no	—
906	C₈	—	2	1	no	—
907	C₈	—	2	1	no	—
908	C₈	—	2	1	no	—
909	C₂²	—	2	1	no	—
910	C₂²	—	2	1	no	—
911	C₂²	—	2	1	no	—
912	C₂²	—	2	1	no	—
913	C₂²	—	2	1	no	—
914	C₂²	—	2	1	no	—
915	C₂²	—	2	1	no	—
916	C₂²	—	2	1	no	—
917	C₂²	—	2	1	no	—
918	C₂²	—	2	1	no	—
919	C₂²	—	2	2	no	—
920	C₂²	—	2	2	no	—
921	C₂²	—	2	1	no	—
922	C₂²	—	2	1	no	—
923	C₂²	—	2	1	no	—
924	C₂²	—	2	1	no	—
925	C₂²	—	4	4	no	—
926	C₂²	—	4	1	no	—
927	C₂²	—	4	1	no	—
928	C₂²	—	4	1	no	—
929	C₂²	—	4	1	no	—
930	C₂²	—	4	1	no	—
931	C₂²	—	4	1	no	—
932	C₂²	—	4	1	no	—
933	C₂²	—	4	1	no	—
934	C₂²	—	4	1	no	—
935	C₂²	—	4	1	no	—
936	C₂²	—	4	1	no	—
937	C₂²	—	4	1	no	—
938	C₂²	—	4	1	no	—
939	C₂²	—	4	1	no	—
940	C₂²	—	4	1	no	—
941	C₂²	—	4	1	no	—
942	C₂²	—	4	1	no	—
943	C₂²	—	4	1	no	—
944	C₂²	—	4	1	no	—
945	C₂²	—	4	1	no	—
946	C₂²	—	4	1	no	—
947	C₂²	—	4	1	no	—
948	C₂²	—	8	4	no	—
949	C₂²	—	8	4	no	—
950	C₂²	—	8	4	no	—
951	C₂²	—	8	4	no	—
952	C₂²	—	8	4	no	—
953	C₂²	—	8	4	no	—
954	C₂²	—	16	2	no	—
955	C₂²	—	16	2	no	—
956	C₂²	—	16	2	no	—
957	C₂²	—	16	2	no	—
958	C₂²	#576	1	2	yes	—
959	C₂²	C₂³×D₄	1	1	yes	characteristic
960	C₄	—	2	1	no	—
961	C₄	—	2	1	no	—
962	C₄	—	2	1	no	—
963	C₄	—	2	1	no	—
964	C₄	—	2	1	no	—
965	C₄	—	2	1	no	—
966	C₄	—	2	1	no	—
967	C₄	—	2	1	no	—
968	C₄	—	2	1	no	—
969	C₄	—	4	1	no	—
970	C₄	—	4	1	no	—
971	C₄	—	4	1	no	—
972	C₄	—	4	1	no	—
973	C₄	—	4	1	no	—
974	C₄	—	4	1	no	—
975	C₄	—	4	1	no	—
976	C₄	—	4	1	no	—
977	C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
978	C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
979	C₂	—	2	2	no	—
980	C₂	—	4	1	no	—
981	C₂	—	4	1	no	—
982	C₂	—	4	1	no	—
983	C₂	—	4	1	no	—
984	C₂	—	4	2	no	—
985	C₂	—	4	2	no	—
986	C₂	—	8	1	no	—
987	C₂	—	8	1	no	—
988	C₂	—	8	1	no	—
989	C₂	—	8	1	no	—
990	C₂	—	8	1	no	—
991	C₂	—	8	1	no	—
992	C₂	#3484	1	1	yes	characteristic
993	C₂	C₂×#576	1	1	yes	characteristic
994	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. #3542	C₂	semidirect
2. #3484	C₂	semidirect
3. #3325	C₂	semidirect
4. #3322	C₂	semidirect
5. #3319	C₂	semidirect
6. #3318	C₂	semidirect
7. #3310	C₂	semidirect
8. #3306	C₂	semidirect
9. #3296	C₂	semidirect
10. #3294	C₂	semidirect
11. #3280	C₂	semidirect
12. D₄×D₈	C₂	semidirect
13. #3274	C₂	semidirect
14. #3273	C₂	semidirect
15. #3268	C₂	semidirect
16. #3264	C₂	semidirect
17. #3264	C₂	semidirect
18. #3264	C₂	semidirect
19. #3224	C₂	semidirect
20. #3220	C₂	semidirect
21. #3199	C₂	semidirect
22. #3198	C₂	semidirect
23. #3194	C₂	semidirect
24. #3191	C₂	semidirect
25. #3122	C₂	semidirect
26. #3118	C₂	semidirect
27. #3012	C₂	semidirect
28. #3008	C₂	semidirect
29. #3003	C₂	semidirect
30. C₂×#447	C₂	semidirect
31. #2976	C₂	semidirect
32. C₂×H(5,𝔽₂)	C₂²	semidirect
33. C₂³×D₄	C₂²	semidirect
34. C₂×AGL(1,ℤ/8)	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×D₈	C₂²	semidirect
40. C₂²×D₈	C₂²	semidirect
41. C₂²×D₈	C₂²	semidirect
44. #555	C₂²	semidirect
45. #553	C₂²	semidirect
46. #552	C₂²	semidirect
48. #550	C₂²	semidirect
49. #547	C₂²	semidirect
54. #546	C₂²	semidirect
55. #546	C₂²	semidirect
56. #546	C₂²	semidirect
57. #546	C₂²	semidirect
58. #546	C₂²	semidirect
62. D₄²	C₂²	semidirect
63. D₄²	C₂²	semidirect
64. D₄²	C₂²	semidirect
65. D₄²	C₂²	semidirect
66. #542	C₂²	semidirect
68. #540	C₂²	semidirect
70. #537	C₂²	semidirect
72. #535	C₂²	semidirect
73. #535	C₂²	semidirect
74. #535	C₂²	semidirect
79. #525	C₂²	semidirect
80. #525	C₂²	semidirect
81. C₂×#121	C₂²	semidirect
84. #518	C₂²	semidirect
85. #496	C₂²	semidirect
86. #496	C₂²	semidirect
87. #495	C₂²	semidirect
88. #493	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. #483	C₂²	semidirect
96. #482	C₂²	semidirect
97. #482	C₂²	semidirect
98. #482	C₂²	semidirect
99. #482	C₂²	semidirect
100. #482	C₂²	semidirect
101. #482	C₂²	semidirect
102. #481	C₂²	semidirect
103. #480	C₂²	semidirect
104. #480	C₂²	semidirect
105. #478	C₂²	semidirect
106. #478	C₂²	semidirect
107. #476	C₂²	semidirect
108. #474	C₂²	semidirect
109. #469	C₂²	semidirect
110. #469	C₂²	semidirect
111. #469	C₂²	semidirect
112. #469	C₂²	semidirect
113. #469	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. #466	C₂²	semidirect
121. #466	C₂²	semidirect
122. #465	C₂²	semidirect
123. #465	C₂²	semidirect
124. #465	C₂²	semidirect
125. #464	C₂²	semidirect
126. #463	C₂²	semidirect
127. #463	C₂²	semidirect
128. #463	C₂²	semidirect
129. #463	C₂²	semidirect
130. #463	C₂²	semidirect
131. #460	C₂²	semidirect
132. #459	C₂²	semidirect
133. #459	C₂²	semidirect
134. #459	C₂²	semidirect
135. #459	C₂²	semidirect
136. #459	C₂²	semidirect
137. #452	C₂²	semidirect
138. #452	C₂²	semidirect
139. #452	C₂²	semidirect
140. #450	C₂²	semidirect
141. #450	C₂²	semidirect
142. #450	C₂²	semidirect
143. #450	C₂²	semidirect
144. #450	C₂²	semidirect
145. #450	C₂²	semidirect
146. #449	C₂²	semidirect
147. #449	C₂²	semidirect
148. #449	C₂²	semidirect
149. #449	C₂²	semidirect
150. #449	C₂²	semidirect
151. #449	C₂²	semidirect
152. #449	C₂²	semidirect
153. #449	C₂²	semidirect
154. #449	C₂²	semidirect
156. #447	C₂²	semidirect
157. #447	C₂²	semidirect
158. #447	C₂²	semidirect
159. #447	C₂²	semidirect
160. #447	C₂²	semidirect
161. #447	C₂²	semidirect
162. #447	C₂²	semidirect
163. #447	C₂²	semidirect
164. #447	C₂²	semidirect
165. #447	C₂²	semidirect
166. #447	C₂²	semidirect
167. #447	C₂²	semidirect
168. #447	C₂²	semidirect
169. #447	C₂²	semidirect
170. #447	C₂²	semidirect
171. #447	C₂²	semidirect
172. #447	C₂²	semidirect
173. #442	C₂²	semidirect
174. #442	C₂²	semidirect
175. #442	C₂²	semidirect
176. #440	C₂²	semidirect
177. C₄×SD₁₆	C₂²	semidirect
178. C₄×D₈	C₂²	semidirect
179. C₄×D₈	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
213. C₂×#41	C₂³	semidirect
237. C₂²×D₄	C₂³	semidirect
244. C₂×Q₁₆	C₂³	semidirect
249. C₂×SD₁₆	C₂³	semidirect
250. C₂×SD₁₆	C₂³	semidirect
251. C₂×SD₁₆	C₂³	semidirect
252. C₂×SD₁₆	C₂³	semidirect
268. C₂×D₈	C₂³	semidirect
269. C₂×D₈	C₂³	semidirect
270. C₂×D₈	C₂³	semidirect
273. C₂×M₁₆	C₂³	semidirect
274. C₂×M₁₆	C₂³	semidirect
277. C₂²×C₈	C₂³	semidirect
278. C₂²×C₈	C₂³	semidirect
279. C₄⋊Q₈	C₂³	semidirect
285. #127	C₂³	semidirect
290. #125	C₂³	semidirect
298. #124	C₂³	semidirect
325. C₂²⋊Q₈	C₂³	semidirect
364. #121	C₂³	semidirect
365. #121	C₂³	semidirect
366. #121	C₂³	semidirect
393. C₄×Q₈	C₂³	semidirect
410. C₄×D₄	C₂³	semidirect
411. C₄×D₄	C₂³	semidirect
412. C₄×D₄	C₂³	semidirect
418. #117	C₂³	semidirect
420. 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
464. #102	C₂³	semidirect
465. #102	C₂³	semidirect
466. #102	C₂³	semidirect
467. #102	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
#3542	2
#3484	2
#3325	2
#3322	2
#3319	2
#3318	2
#3310	2
#3306	2
#3296	2
#3294	2
#3280	2
D₄×D₈	2
#3274	2
#3273	2
#3268	2
#3264	2
#3224	2
#3220	2
#3199	2
#3198	2
#3194	2
#3191	2
#3122	2
#3118	2
#3012	2
#3008	2
#3003	2
C₂×#447	2
#2976	2