Subgroups — #62830

Order 256.

3632 conjugacy classes of subgroups.

The subgroup lattice has 914 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3562	C₂	1	4	yes	maximal, complemented
2	#3560	C₂	1	4	yes	maximal, complemented
3	#3552	C₂	1	2	yes	maximal, complemented
4	#3551	C₂	1	4	yes	maximal, complemented
5	#3547	C₂	1	2	yes	maximal, complemented
6	#3546	C₂	1	2	yes	maximal, complemented
7	#3543	C₂	1	2	yes	maximal, complemented
8	#3534	C₂	1	4	yes	maximal, complemented
9	#3520	C₂	1	2	yes	maximal, complemented
10	#3519	C₂	1	4	yes	maximal, complemented
11	#3519	C₂	1	2	yes	maximal, complemented
12	#3517	C₂	1	2	yes	maximal, complemented
13	#3514	C₂	1	4	yes	maximal, complemented
14	#3514	C₂	1	2	yes	maximal, complemented
15	#3512	C₂	1	2	yes	maximal, complemented
16	#3507	C₂	1	1	yes	maximal, characteristic, complemented
17	#3506	C₂	1	1	yes	maximal, characteristic, complemented
18	#3505	C₂	1	4	yes	maximal, complemented
19	#3500	C₂	1	2	yes	maximal, complemented
20	#3497	C₂	1	1	yes	maximal, characteristic, complemented
21	#3496	C₂	1	1	yes	maximal, characteristic, complemented
22	#3494	C₂	1	4	yes	maximal, complemented
23	#3489	C₂	1	2	yes	maximal, complemented
24	#3488	C₂	1	2	yes	maximal, complemented
25	#3444	C₂	1	1	yes	maximal, characteristic, complemented
26	C₂×#532	C₂	1	1	yes	maximal, characteristic, complemented
27	C₂×#529	C₂	1	1	yes	maximal, characteristic, complemented
28	C₂×2₋¹⁺⁴	C₂²	1	2	yes	complemented
29	C₂×H(5,𝔽₂)	C₂²	1	2	yes	complemented
30	C₂²×#41	C₂²	1	2	yes	complemented
31	#563	C₂²	1	8	yes	complemented
32	#562	C₂²	1	8	yes	complemented
33	#560	C₂²	1	8	yes	complemented
34	#560	C₂²	1	8	yes	complemented
35	#559	C₂²	1	4	yes	complemented
36	#559	C₂²	1	2	yes	complemented
37	#557	C₂²	1	2	yes	complemented
38	#556	C₂²	1	2	yes	complemented
39	#556	C₂²	1	4	yes	complemented
40	#556	C₂²	1	2	yes	complemented
41	#555	C₂²	1	8	yes	complemented
42	#555	C₂²	1	2	yes	complemented
43	#555	C₂²	1	4	yes	complemented
44	#554	C₂²	1	2	yes	complemented
45	#554	C₂²	1	4	yes	complemented
46	#553	C₂²	1	8	yes	complemented
47	#553	C₂²	1	8	yes	complemented
48	#553	C₂²	1	4	yes	complemented
49	#553	C₂²	1	4	yes	complemented
50	#553	C₂²	1	8	yes	complemented
51	#553	C₂²	1	4	yes	complemented
52	#553	C₂²	1	8	yes	complemented
53	#553	C₂²	1	4	yes	complemented
54	#553	C₂²	1	4	yes	complemented
55	#552	C₂²	1	4	yes	complemented
56	#552	C₂²	1	4	yes	complemented
57	#552	C₂²	1	4	yes	complemented
58	#551	C₂²	1	8	yes	complemented
59	#551	C₂²	1	8	yes	complemented
60	#551	C₂²	1	8	yes	complemented
61	#551	C₂²	1	8	yes	complemented
62	#550	C₂²	1	4	yes	complemented
63	#550	C₂²	1	2	yes	complemented
64	#550	C₂²	1	2	yes	complemented
65	#550	C₂²	1	2	yes	complemented
66	#550	C₂²	1	4	yes	complemented
67	D₄×Q₈	C₂²	1	4	yes	complemented
68	D₄×Q₈	C₂²	1	2	yes	complemented
69	D₄×Q₈	C₂²	1	2	yes	complemented
70	#548	C₂²	1	4	yes	complemented
71	#548	C₂²	1	4	yes	complemented
72	#548	C₂²	1	4	yes	complemented
73	#548	C₂²	1	4	yes	complemented
74	#548	C₂²	1	4	yes	complemented
75	#548	C₂²	1	4	yes	complemented
76	#547	C₂²	1	8	yes	complemented
77	#547	C₂²	1	4	yes	complemented
78	#547	C₂²	1	2	yes	complemented
79	#547	C₂²	1	2	yes	complemented
80	#547	C₂²	1	2	yes	complemented
81	#546	C₂²	1	8	yes	complemented
82	#546	C₂²	1	4	yes	complemented
83	#546	C₂²	1	4	yes	complemented
84	#546	C₂²	1	8	yes	complemented
85	#546	C₂²	1	8	yes	complemented
86	#546	C₂²	1	4	yes	complemented
87	#546	C₂²	1	4	yes	complemented
88	#546	C₂²	1	4	yes	complemented
89	#546	C₂²	1	4	yes	complemented
90	#546	C₂²	1	8	yes	complemented
91	#546	C₂²	1	8	yes	complemented
92	#546	C₂²	1	4	yes	complemented
93	#546	C₂²	1	4	yes	complemented
94	D₄²	C₂²	1	4	yes	complemented
95	D₄²	C₂²	1	8	yes	complemented
96	D₄²	C₂²	1	2	yes	complemented
97	D₄²	C₂²	1	2	yes	complemented
98	D₄²	C₂²	1	4	yes	complemented
99	#544	C₂²	1	4	yes	complemented
100	#542	C₂²	1	4	yes	complemented
101	#542	C₂²	1	4	yes	complemented
102	#542	C₂²	1	8	yes	complemented
103	#541	C₂²	1	4	yes	complemented
104	#540	C₂²	1	4	yes	complemented
105	#540	C₂²	1	4	yes	complemented
106	#540	C₂²	1	4	yes	complemented
107	#540	C₂²	1	8	yes	complemented
108	#540	C₂²	1	8	yes	complemented
109	#539	C₂²	1	8	yes	complemented
110	#539	C₂²	1	4	yes	complemented
111	#539	C₂²	1	8	yes	complemented
112	#538	C₂²	1	8	yes	complemented
113	#538	C₂²	1	4	yes	complemented
114	#538	C₂²	1	8	yes	complemented
115	#538	C₂²	1	8	yes	complemented
116	#538	C₂²	1	8	yes	complemented
117	#538	C₂²	1	8	yes	complemented
118	#537	C₂²	1	2	yes	complemented
119	#537	C₂²	1	4	yes	complemented
120	#537	C₂²	1	2	yes	complemented
121	#537	C₂²	1	4	yes	complemented
122	#537	C₂²	1	4	yes	complemented
123	#536	C₂²	1	2	yes	complemented
124	#536	C₂²	1	4	yes	complemented
125	#536	C₂²	1	4	yes	complemented
126	#535	C₂²	1	2	yes	complemented
127	#535	C₂²	1	4	yes	complemented
128	#535	C₂²	1	4	yes	complemented
129	#535	C₂²	1	4	yes	complemented
130	#534	C₂²	1	4	yes	complemented
131	#534	C₂²	1	8	yes	complemented
132	#533	C₂²	1	1	yes	characteristic, complemented
133	#533	C₂²	1	1	yes	characteristic, complemented
134	#533	C₂²	1	1	yes	characteristic, complemented
135	#532	C₂²	1	1	yes	characteristic
136	#532	C₂²	1	2	yes	complemented
137	#532	C₂²	1	1	yes	characteristic, complemented
138	#532	C₂²	1	2	yes	complemented
139	#532	C₂²	1	1	yes	characteristic, complemented
140	#532	C₂²	1	1	yes	characteristic, complemented
141	#532	C₂²	1	2	yes	complemented
142	#532	C₂²	1	2	yes	complemented
143	#532	C₂²	1	2	yes	complemented
144	#532	C₂²	1	2	yes	complemented
145	#532	C₂²	1	1	yes	characteristic, complemented
146	#532	C₂²	1	1	yes	characteristic, complemented
147	#532	C₂²	1	1	yes	characteristic, complemented
148	#532	C₂²	1	4	yes	complemented
149	#532	C₂²	1	4	yes	complemented
150	C₂×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
151	C₂×#127	C₂²	1	1	yes	characteristic, complemented
152	#529	C₂²	1	2	yes	complemented
153	#529	C₂²	1	2	yes	complemented
154	#529	C₂²	1	2	yes	complemented
155	#529	C₂²	1	2	yes	complemented
156	#529	C₂²	1	2	yes	complemented
157	#529	C₂²	1	2	yes	complemented
158	#529	C₂²	1	2	yes	complemented
159	#529	C₂²	1	2	yes	complemented
160	#529	C₂²	1	2	yes	complemented
161	#529	C₂²	1	2	yes	complemented
162	#529	C₂²	1	2	yes	complemented
163	#529	C₂²	1	2	yes	complemented
164	#529	C₂²	1	2	yes	complemented
165	#529	C₂²	1	2	yes	complemented
166	#529	C₂²	1	4	yes	complemented
167	#529	C₂²	1	4	yes	complemented
168	#529	C₂²	1	4	yes	complemented
169	C₂×#126	C₂²	1	2	yes	complemented
170	C₂×#125	C₂²	1	1	yes	characteristic, complemented
171	C₂×#124	C₂²	1	1	yes	characteristic, complemented
172	C₂×#124	C₂²	1	2	yes	complemented
173	C₂×#124	C₂²	1	4	yes	complemented
174	#525	C₂²	1	2	yes	complemented
175	#525	C₂²	1	2	yes	complemented
176	#525	C₂²	1	2	yes	complemented
177	#525	C₂²	1	4	yes	complemented
178	#525	C₂²	1	4	yes	complemented
179	#525	C₂²	1	4	yes	complemented
180	C₂×#123	C₂²	1	2	yes	complemented
181	C₂×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
182	C₂×C₂²⋊Q₈	C₂²	1	4	yes	complemented
183	C₂×#121	C₂²	1	1	yes	characteristic
184	C₂×#121	C₂²	1	2	yes	complemented
185	C₂×#121	C₂²	1	2	yes	complemented
186	C₂×#121	C₂²	1	4	yes	complemented
187	C₂×#121	C₂²	1	4	yes	complemented
188	#520	C₂²	1	2	yes	complemented
189	#520	C₂²	1	2	yes	complemented
190	#520	C₂²	1	4	yes	complemented
191	#518	C₂²	1	4	yes	complemented
192	#518	C₂²	1	8	yes	complemented
193	C₄×#41	C₂²	1	2	yes	complemented
194	C₄×#41	C₂²	1	2	yes	complemented
195	C₄×#41	C₂²	1	2	yes	complemented
196	C₂×C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
197	C₂×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
198	C₂×C₄×D₄	C₂²	1	2	yes	complemented
199	C₂×C₄×D₄	C₂²	1	2	yes	complemented
200	C₂×C₄×D₄	C₂²	1	2	yes	complemented
201	C₂×#117	C₂²	1	2	yes	complemented
202	C₂²×C₄²	C₂²	1	1	yes	characteristic, complemented
203	2₋¹⁺⁴	—	4	8	no	—
204	H(5,𝔽₂)	—	4	8	no	—
205	C₂×#41	—	4	8	no	—
206	C₂×#41	C₂³	1	2	yes	—
207	C₂×#41	C₂³	1	2	yes	—
208	C₂×#41	C₂³	1	2	yes	—
209	C₂×#41	C₂³	1	2	yes	—
210	C₂×#41	C₂³	1	2	yes	—
211	C₂×#41	C₂³	1	4	yes	—
212	C₂×#41	C₂³	1	4	yes	—
213	C₂×#41	C₂³	1	4	yes	—
214	C₂×#41	C₂³	1	4	yes	—
215	C₂×#41	C₂³	1	4	yes	—
216	C₂×#41	C₂³	1	2	yes	—
217	C₂×#41	C₂³	1	2	yes	—
218	C₂×#41	C₂³	1	4	yes	—
219	C₂×#41	C₂³	1	4	yes	—
220	C₂×#41	C₂³	1	8	yes	—
221	C₂²×Q₈	C₂³	1	1	yes	characteristic
222	C₂²×Q₈	C₂³	1	4	yes	—
223	C₂²×Q₈	C₂³	1	2	yes	—
224	C₂²×Q₈	C₂³	1	4	yes	—
225	C₂²×D₄	C₂³	1	1	yes	characteristic
226	C₂²×D₄	C₂³	1	2	yes	—
227	C₂²×D₄	C₂³	1	2	yes	—
228	C₂²×D₄	C₂³	1	2	yes	—
229	C₂²×D₄	C₂³	1	8	yes	—
230	C₂²×D₄	C₂³	1	4	yes	—
231	C₂²×D₄	C₂³	1	4	yes	—
232	C₂²×D₄	C₂³	1	8	yes	—
233	C₂²×D₄	C₂³	1	4	yes	—
234	C₂²×D₄	C₂³	1	2	yes	—
235	C₂²×D₄	C₂³	1	4	yes	—
236	C₂³×C₄	C₂³	1	1	yes	characteristic
237	C₂³×C₄	C₂³	1	2	yes	—
238	C₂³×C₄	C₂³	1	1	yes	characteristic
239	C₂³×C₄	C₂³	1	4	yes	—
240	C₂³×C₄	C₂³	1	1	yes	characteristic
241	C₄⋊Q₈	C₂³	1	1	yes	characteristic
242	C₄⋊Q₈	C₂³	1	2	yes	—
243	C₄⋊Q₈	C₂³	1	2	yes	—
244	C₄⋊Q₈	C₂³	1	1	yes	characteristic
245	C₄⋊Q₈	C₂³	1	2	yes	—
246	C₄⋊Q₈	C₂³	1	1	yes	characteristic
247	C₄⋊Q₈	C₂³	1	1	yes	characteristic
248	C₄⋊Q₈	C₂³	1	1	yes	characteristic
249	C₄⋊Q₈	C₂³	1	4	yes	—
250	C₄⋊Q₈	C₂³	1	4	yes	—
251	C₄⋊Q₈	C₂³	1	8	yes	—
252	#127	C₂³	1	1	yes	characteristic
253	#127	C₂³	1	2	yes	—
254	#127	C₂³	1	2	yes	—
255	#127	C₂³	1	1	yes	characteristic
256	#127	C₂³	1	2	yes	—
257	#127	C₂³	1	1	yes	characteristic
258	#127	C₂³	1	4	yes	—
259	#127	C₂³	1	4	yes	—
260	#127	C₂³	1	8	yes	—
261	#126	C₂³	1	4	yes	—
262	#126	C₂³	1	4	yes	—
263	#126	C₂³	1	4	yes	—
264	#126	C₂³	1	4	yes	—
265	#126	C₂³	1	4	yes	—
266	#126	C₂³	1	4	yes	—
267	#126	C₂³	1	8	yes	—
268	#126	C₂³	1	8	yes	—
269	#126	C₂³	1	8	yes	—
270	#126	C₂³	1	8	yes	—
271	#126	C₂³	1	8	yes	—
272	#126	C₂³	1	8	yes	—
273	#126	C₂³	1	8	yes	—
274	#125	C₂³	1	2	yes	—
275	#125	C₂³	1	2	yes	—
276	#125	C₂³	1	2	yes	—
277	#125	C₂³	1	2	yes	—
278	#125	C₂³	1	2	yes	—
279	#125	C₂³	1	2	yes	—
280	#125	C₂³	1	2	yes	—
281	#125	C₂³	1	4	yes	—
282	#125	C₂³	1	8	yes	—
283	#125	C₂³	1	8	yes	—
284	#125	C₂³	1	8	yes	—
285	#124	C₂³	1	2	yes	—
286	#124	C₂³	1	2	yes	—
287	#124	C₂³	1	2	yes	—
288	#124	C₂³	1	2	yes	—
289	#124	C₂³	1	2	yes	—
290	#124	C₂³	1	2	yes	—
291	#124	C₂³	1	2	yes	—
292	#124	C₂³	1	4	yes	—
293	#124	C₂³	1	2	yes	—
294	#124	C₂³	1	4	yes	—
295	#124	C₂³	1	4	yes	—
296	#124	C₂³	1	4	yes	—
297	#124	C₂³	1	8	yes	—
298	#124	C₂³	1	8	yes	—
299	#124	C₂³	1	2	yes	—
300	#124	C₂³	1	2	yes	—
301	#124	C₂³	1	2	yes	—
302	#124	C₂³	1	4	yes	—
303	#124	C₂³	1	8	yes	—
304	#124	C₂³	1	8	yes	—
305	#124	C₂³	1	8	yes	—
306	#124	C₂³	1	8	yes	—
307	#123	C₂³	1	4	yes	—
308	#123	C₂³	1	4	yes	—
309	#123	C₂³	1	4	yes	—
310	#123	C₂³	1	4	yes	—
311	#123	C₂³	1	4	yes	—
312	#123	C₂³	1	4	yes	—
313	#123	C₂³	1	4	yes	—
314	#123	C₂³	1	8	yes	—
315	#123	C₂³	1	8	yes	—
316	#123	C₂³	1	8	yes	—
317	#123	C₂³	1	8	yes	—
318	#123	C₂³	1	8	yes	—
319	#123	C₂³	1	8	yes	—
320	#123	C₂³	1	8	yes	—
321	#123	C₂³	1	8	yes	—
322	#123	C₂³	1	8	yes	—
323	#123	C₂³	1	8	yes	—
324	#123	C₂³	1	8	yes	—
325	#123	C₂³	1	8	yes	—
326	#123	C₂³	1	8	yes	—
327	#123	C₂³	1	8	yes	—
328	#123	C₂³	1	8	yes	—
329	#123	C₂³	1	8	yes	—
330	C₂²⋊Q₈	C₂³	1	2	yes	—
331	C₂²⋊Q₈	C₂³	1	2	yes	—
332	C₂²⋊Q₈	C₂³	1	2	yes	—
333	C₂²⋊Q₈	C₂³	1	2	yes	—
334	C₂²⋊Q₈	C₂³	1	2	yes	—
335	C₂²⋊Q₈	C₂³	1	4	yes	—
336	C₂²⋊Q₈	C₂³	1	4	yes	—
337	C₂²⋊Q₈	C₂³	1	8	yes	—
338	C₂²⋊Q₈	C₂³	1	8	yes	—
339	C₂²⋊Q₈	C₂³	1	2	yes	—
340	C₂²⋊Q₈	C₂³	1	2	yes	—
341	C₂²⋊Q₈	C₂³	1	2	yes	—
342	C₂²⋊Q₈	C₂³	1	2	yes	—
343	C₂²⋊Q₈	C₂³	1	2	yes	—
344	C₂²⋊Q₈	C₂³	1	4	yes	—
345	C₂²⋊Q₈	C₂³	1	4	yes	—
346	C₂²⋊Q₈	C₂³	1	4	yes	—
347	C₂²⋊Q₈	C₂³	1	4	yes	—
348	C₂²⋊Q₈	C₂³	1	4	yes	—
349	C₂²⋊Q₈	C₂³	1	8	yes	—
350	C₂²⋊Q₈	C₂³	1	8	yes	—
351	C₂²⋊Q₈	C₂³	1	8	yes	—
352	C₂²⋊Q₈	C₂³	1	8	yes	—
353	C₂²⋊Q₈	C₂³	1	8	yes	—
354	C₂²⋊Q₈	C₂³	1	8	yes	—
355	C₂²⋊Q₈	C₂³	1	8	yes	—
356	#121	C₂³	1	2	yes	—
357	#121	C₂³	1	2	yes	—
358	#121	C₂³	1	2	yes	—
359	#121	C₂³	1	2	yes	—
360	#121	C₂³	1	2	yes	—
361	#121	C₂³	1	2	yes	—
362	#121	C₂³	1	2	yes	—
363	#121	C₂³	1	2	yes	—
364	#121	C₂³	1	2	yes	—
365	#121	C₂³	1	2	yes	—
366	#121	C₂³	1	2	yes	—
367	#121	C₂³	1	4	yes	—
368	#121	C₂³	1	2	yes	—
369	#121	C₂³	1	4	yes	—
370	#121	C₂³	1	4	yes	—
371	#121	C₂³	1	2	yes	—
372	#121	C₂³	1	2	yes	—
373	#121	C₂³	1	4	yes	—
374	#121	C₂³	1	8	yes	—
375	#121	C₂³	1	4	yes	—
376	#121	C₂³	1	4	yes	—
377	#121	C₂³	1	8	yes	—
378	#121	C₂³	1	8	yes	—
379	#121	C₂³	1	8	yes	—
380	#121	C₂³	1	4	yes	—
381	#121	C₂³	1	4	yes	—
382	#121	C₂³	1	2	yes	—
383	#121	C₂³	1	2	yes	—
384	#121	C₂³	1	2	yes	—
385	#121	C₂³	1	2	yes	—
386	#121	C₂³	1	4	yes	—
387	#121	C₂³	1	4	yes	—
388	#121	C₂³	1	4	yes	—
389	#121	C₂³	1	4	yes	—
390	#121	C₂³	1	4	yes	—
391	#121	C₂³	1	8	yes	—
392	#121	C₂³	1	8	yes	—
393	#121	C₂³	1	8	yes	—
394	#121	C₂³	1	8	yes	—
395	#121	C₂³	1	8	yes	—
396	#121	C₂³	1	8	yes	—
397	#121	C₂³	1	8	yes	—
398	#121	C₂³	1	8	yes	—
399	#121	C₂³	1	8	yes	—
400	#121	C₂³	1	8	yes	—
401	#121	C₂³	1	8	yes	—
402	#121	C₂³	1	8	yes	—
403	#121	C₂³	1	8	yes	—
404	#121	C₂³	1	8	yes	—
405	#121	C₂³	1	8	yes	—
406	#121	C₂³	1	8	yes	—
407	#120	C₂³	1	4	yes	—
408	#120	C₂³	1	8	yes	—
409	#120	C₂³	1	8	yes	—
410	#120	C₂³	1	8	yes	—
411	#120	C₂³	1	8	yes	—
412	#120	C₂³	1	8	yes	—
413	#120	C₂³	1	8	yes	—
414	#120	C₂³	1	8	yes	—
415	#120	C₂³	1	8	yes	—
416	#120	C₂³	1	8	yes	—
417	C₄×Q₈	C₂³	1	2	yes	—
418	C₄×Q₈	C₂³	1	2	yes	—
419	C₄×Q₈	C₂³	1	2	yes	—
420	C₄×Q₈	C₂³	1	2	yes	—
421	C₄×Q₈	C₂³	1	2	yes	—
422	C₄×Q₈	C₂³	1	2	yes	—
423	C₄×Q₈	C₂³	1	2	yes	—
424	C₄×Q₈	C₂³	1	2	yes	—
425	C₄×Q₈	C₂³	1	2	yes	—
426	C₄×Q₈	C₂³	1	2	yes	—
427	C₄×Q₈	C₂³	1	4	yes	—
428	C₄×Q₈	C₂³	1	4	yes	—
429	C₄×Q₈	C₂³	1	4	yes	—
430	C₄×D₄	C₂³	1	4	yes	—
431	C₄×D₄	C₂³	1	2	yes	—
432	C₄×D₄	C₂³	1	2	yes	—
433	C₄×D₄	C₂³	1	4	yes	—
434	C₄×D₄	C₂³	1	4	yes	—
435	C₄×D₄	C₂³	1	2	yes	—
436	C₄×D₄	C₂³	1	2	yes	—
437	C₄×D₄	C₂³	1	2	yes	—
438	C₄×D₄	C₂³	1	2	yes	—
439	C₄×D₄	C₂³	1	4	yes	—
440	C₄×D₄	C₂³	1	2	yes	—
441	C₄×D₄	C₂³	1	2	yes	—
442	C₄×D₄	C₂³	1	4	yes	—
443	C₄×D₄	C₂³	1	4	yes	—
444	C₄×D₄	C₂³	1	4	yes	—
445	C₄×D₄	C₂³	1	2	yes	—
446	C₄×D₄	C₂³	1	2	yes	—
447	C₄×D₄	C₂³	1	2	yes	—
448	C₄×D₄	C₂³	1	4	yes	—
449	C₄×D₄	C₂³	1	2	yes	—
450	C₄×D₄	C₂³	1	4	yes	—
451	C₄×D₄	C₂³	1	2	yes	—
452	C₄×D₄	C₂³	1	4	yes	—
453	C₄×D₄	C₂³	1	4	yes	—
454	C₄×D₄	C₂³	1	4	yes	—
455	C₄×D₄	C₂³	1	4	yes	—
456	C₄×D₄	C₂³	1	4	yes	—
457	C₄×D₄	C₂³	1	2	yes	—
458	C₄×D₄	C₂³	1	2	yes	—
459	C₄×D₄	C₂³	1	2	yes	—
460	C₄×D₄	C₂³	1	2	yes	—
461	C₄×D₄	C₂³	1	2	yes	—
462	C₄×D₄	C₂³	1	8	yes	—
463	C₄×D₄	C₂³	1	8	yes	—
464	C₄×D₄	C₂³	1	8	yes	—
465	C₄×D₄	C₂³	1	8	yes	—
466	C₄×D₄	C₂³	1	8	yes	—
467	C₄×D₄	C₂³	1	8	yes	—
468	C₄×D₄	C₂³	1	4	yes	—
469	C₄×D₄	C₂³	1	8	yes	—
470	C₄×D₄	C₂³	1	8	yes	—
471	C₄×D₄	C₂³	1	4	yes	—
472	C₄×D₄	C₂³	1	8	yes	—
473	C₄×D₄	C₂³	1	8	yes	—
474	C₄×D₄	C₂³	1	8	yes	—
475	C₄×D₄	C₂³	1	4	yes	—
476	C₄×D₄	C₂³	1	4	yes	—
477	C₄×D₄	C₂³	1	8	yes	—
478	C₄×D₄	C₂³	1	4	yes	—
479	#117	C₂³	1	4	yes	—
480	#117	C₂³	1	4	yes	—
481	#117	C₂³	1	4	yes	—
482	#117	C₂³	1	4	yes	—
483	#117	C₂³	1	2	yes	—
484	#117	C₂³	1	2	yes	—
485	#117	C₂³	1	2	yes	—
486	#117	C₂³	1	4	yes	—
487	#117	C₂³	1	4	yes	—
488	#117	C₂³	1	4	yes	—
489	#117	C₂³	1	4	yes	—
490	#117	C₂³	1	8	yes	—
491	#117	C₂³	1	8	yes	—
492	#117	C₂³	1	4	yes	—
493	#117	C₂³	1	4	yes	—
494	#117	C₂³	1	8	yes	—
495	C₂×C₄⋊C₄	C₂³	1	2	yes	—
496	C₂×C₄⋊C₄	C₂³	1	2	yes	—
497	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
498	C₂×C₄⋊C₄	C₂³	1	2	yes	—
499	C₂×C₄⋊C₄	C₂³	1	2	yes	—
500	C₂×C₄⋊C₄	C₂³	1	2	yes	—
501	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
502	C₂×C₄⋊C₄	C₂³	1	2	yes	—
503	C₂×C₄⋊C₄	C₂³	1	4	yes	—
504	C₂×C₄⋊C₄	C₂³	1	4	yes	—
505	C₂×C₄⋊C₄	C₂³	1	4	yes	—
506	C₂×C₄⋊C₄	C₂³	1	8	yes	—
507	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
508	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
509	C₂×C₂²⋊C₄	C₂³	1	4	yes	—
510	C₂×C₂²⋊C₄	C₂³	1	4	yes	—
511	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
512	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
513	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
514	C₂×C₂²⋊C₄	C₂³	1	8	yes	—
515	C₂×C₂²⋊C₄	C₂³	1	8	yes	—
516	C₂×C₂²⋊C₄	C₂³	1	8	yes	—
517	C₂×C₂²⋊C₄	C₂³	1	8	yes	—
518	C₂×C₂²⋊C₄	C₂³	1	8	yes	—
519	C₂×C₄²	C₂³	1	1	yes	characteristic
520	C₂×C₄²	C₂³	1	2	yes	—
521	C₂×C₄²	C₂³	1	1	yes	characteristic
522	C₂×C₄²	C₂³	1	1	yes	characteristic
523	C₂×C₄²	C₂³	1	1	yes	characteristic
524	C₂×C₄²	C₂³	1	4	yes	—
525	C₂×C₄²	C₂³	1	1	yes	characteristic
526	C₂×C₄²	C₂³	1	1	yes	characteristic
527	C₂×C₄²	C₂³	1	1	yes	characteristic
528	C₂×C₄²	C₂³	1	1	yes	characteristic
529	C₂×C₄²	C₂³	1	1	yes	characteristic
530	C₂×C₄²	C₂³	1	1	yes	characteristic
531	C₂×C₄²	C₂³	1	1	yes	characteristic
532	C₂×C₄²	C₂³	1	1	yes	characteristic
533	C₂⁴	C₂⁴	1	1	yes	characteristic
534	C₂⁴	C₂⁴	1	2	yes	—
535	C₂⁴	C₂⁴	1	4	yes	—
536	C₂⁴	C₂⁴	1	8	yes	—
537	#41	—	2	8	no	—
538	#41	—	2	8	no	—
539	#41	—	2	8	no	—
540	#41	—	4	8	no	—
541	#41	—	4	8	no	—
542	#41	—	4	4	no	—
543	#41	—	4	16	no	—
544	#41	—	4	4	no	—
545	#41	—	4	4	no	—
546	#41	—	4	8	no	—
547	#41	—	4	4	no	—
548	#41	—	4	8	no	—
549	#41	—	4	8	no	—
550	#41	—	4	8	no	—
551	#41	—	4	8	no	—
552	C₂×Q₈	—	2	4	no	—
553	C₂×Q₈	—	4	4	no	—
554	C₂×Q₈	—	4	8	no	—
555	C₂×Q₈	—	4	8	no	—
556	C₂×Q₈	C₂⁴	1	2	yes	—
557	C₂×Q₈	C₂⁴	1	2	yes	—
558	C₂×Q₈	C₂⁴	1	2	yes	—
559	C₂×Q₈	C₂⁴	1	2	yes	—
560	C₂×Q₈	C₂⁴	1	2	yes	—
561	C₂×Q₈	C₂⁴	1	2	yes	—
562	C₂×Q₈	C₂⁴	1	2	yes	—
563	C₂×Q₈	C₂⁴	1	8	yes	—
564	C₂×Q₈	C₂⁴	1	4	yes	—
565	C₂×D₄	—	2	4	no	—
566	C₂×D₄	—	4	4	no	—
567	C₂×D₄	—	4	8	no	—
568	C₂×D₄	—	4	4	no	—
569	C₂×D₄	—	4	8	no	—
570	C₂×D₄	—	4	8	no	—
571	C₂×D₄	—	4	4	no	—
572	C₂×D₄	—	4	4	no	—
573	C₂×D₄	—	4	16	no	—
574	C₂×D₄	—	4	8	no	—
575	C₂×D₄	—	4	16	no	—
576	C₂×D₄	C₂⁴	1	4	yes	—
577	C₂×D₄	C₂⁴	1	4	yes	—
578	C₂×D₄	C₂⁴	1	2	yes	—
579	C₂×D₄	C₂⁴	1	2	yes	—
580	C₂×D₄	C₂⁴	1	2	yes	—
581	C₂×D₄	C₂⁴	1	4	yes	—
582	C₂×D₄	C₂⁴	1	4	yes	—
583	C₂×D₄	C₂⁴	1	4	yes	—
584	C₂×D₄	C₂⁴	1	2	yes	—
585	C₂×D₄	C₂⁴	1	2	yes	—
586	C₂×D₄	C₂⁴	1	2	yes	—
587	C₂×D₄	C₂⁴	1	2	yes	—
588	C₂×D₄	C₂⁴	1	2	yes	—
589	C₂×D₄	C₂⁴	1	2	yes	—
590	C₂×D₄	C₂⁴	1	8	yes	—
591	C₂×D₄	C₂⁴	1	2	yes	—
592	C₂×D₄	C₂⁴	1	8	yes	—
593	C₂×D₄	C₂⁴	1	4	yes	—
594	C₂×D₄	C₂⁴	1	8	yes	—
595	C₂×D₄	C₂⁴	1	4	yes	—
596	C₂×D₄	C₂⁴	1	4	yes	—
597	C₂×D₄	C₂⁴	1	4	yes	—
598	C₂×D₄	C₂⁴	1	8	yes	—
599	C₂×D₄	C₂⁴	1	2	yes	—
600	C₂×D₄	C₂⁴	1	8	yes	—
601	C₂×D₄	C₂⁴	1	4	yes	—
602	C₂×D₄	C₂⁴	1	8	yes	—
603	C₂×D₄	C₂⁴	1	4	yes	—
604	C₂×D₄	C₂⁴	1	8	yes	—
605	C₂×D₄	C₂⁴	1	4	yes	—
606	C₂²×C₄	—	2	4	no	—
607	C₂²×C₄	—	4	2	no	—
608	C₂²×C₄	—	4	4	no	—
609	C₂²×C₄	—	4	8	no	—
610	C₂²×C₄	—	4	2	no	—
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	C₂²×C₄	C₂⁴	1	1	yes	characteristic
617	C₂²×C₄	C₂⁴	1	1	yes	characteristic
618	C₂²×C₄	C₂⁴	1	1	yes	characteristic
619	C₂²×C₄	C₂⁴	1	1	yes	characteristic
620	C₂²×C₄	C₂⁴	1	1	yes	characteristic
621	C₂²×C₄	C₂⁴	1	2	yes	—
622	C₂²×C₄	C₂⁴	1	4	yes	—
623	C₂²×C₄	C₂⁴	1	4	yes	—
624	C₂²×C₄	C₂⁴	1	4	yes	—
625	C₂²×C₄	C₂⁴	1	4	yes	—
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	C₂²×C₄	C₂⁴	1	1	yes	characteristic
630	C₂²×C₄	C₂⁴	1	1	yes	characteristic
631	C₂²×C₄	C₂⁴	1	1	yes	characteristic
632	C₂²×C₄	C₂⁴	1	1	yes	characteristic
633	C₂²×C₄	C₂⁴	1	4	yes	—
634	C₂²×C₄	C₂⁴	1	4	yes	—
635	C₂²×C₄	C₂⁴	1	2	yes	—
636	C₂²×C₄	C₂⁴	1	2	yes	—
637	C₂²×C₄	C₂⁴	1	4	yes	—
638	C₂²×C₄	C₂⁴	1	4	yes	—
639	C₂²×C₄	C₂⁴	1	4	yes	—
640	C₂²×C₄	C₂⁴	1	8	yes	—
641	C₂²×C₄	C₂⁴	1	8	yes	—
642	C₂²×C₄	C₂⁴	1	8	yes	—
643	C₂²×C₄	C₂⁴	1	8	yes	—
644	C₂²×C₄	C₂⁴	1	8	yes	—
645	C₂²×C₄	C₂⁴	1	4	yes	—
646	C₂²×C₄	C₂⁴	1	1	yes	characteristic
647	C₄⋊C₄	C₂⁴	1	2	yes	—
648	C₄⋊C₄	C₂⁴	1	4	yes	—
649	C₄⋊C₄	C₂⁴	1	2	yes	—
650	C₄⋊C₄	C₂⁴	1	2	yes	—
651	C₄⋊C₄	C₂⁴	1	2	yes	—
652	C₄⋊C₄	C₂⁴	1	2	yes	—
653	C₄⋊C₄	C₂⁴	1	2	yes	—
654	C₄⋊C₄	C₂⁴	1	4	yes	—
655	C₄⋊C₄	C₂⁴	1	8	yes	—
656	C₄⋊C₄	C₂⁴	1	4	yes	—
657	C₄⋊C₄	C₂⁴	1	2	yes	—
658	C₄⋊C₄	C₂⁴	1	4	yes	—
659	C₄⋊C₄	C₂⁴	1	4	yes	—
660	C₄⋊C₄	C₂⁴	1	4	yes	—
661	C₄⋊C₄	C₂⁴	1	2	yes	—
662	C₄⋊C₄	C₂⁴	1	2	yes	—
663	C₄⋊C₄	C₂⁴	1	2	yes	—
664	C₄⋊C₄	C₂⁴	1	4	yes	—
665	C₄⋊C₄	C₂⁴	1	4	yes	—
666	C₄⋊C₄	C₂⁴	1	2	yes	—
667	C₄⋊C₄	C₂⁴	1	4	yes	—
668	C₄⋊C₄	C₂⁴	1	8	yes	—
669	C₄⋊C₄	C₂⁴	1	8	yes	—
670	C₄⋊C₄	C₂⁴	1	8	yes	—
671	C₄⋊C₄	C₂⁴	1	4	yes	—
672	C₄⋊C₄	C₂⁴	1	4	yes	—
673	C₄⋊C₄	C₂⁴	1	2	yes	—
674	C₄⋊C₄	C₂⁴	1	4	yes	—
675	C₄⋊C₄	C₂⁴	1	8	yes	—
676	C₄⋊C₄	C₂⁴	1	8	yes	—
677	C₄⋊C₄	C₂⁴	1	4	yes	—
678	C₄⋊C₄	C₂⁴	1	4	yes	—
679	C₄⋊C₄	C₂⁴	1	4	yes	—
680	C₄⋊C₄	C₂⁴	1	4	yes	—
681	C₄⋊C₄	C₂⁴	1	2	yes	—
682	C₄⋊C₄	C₂⁴	1	2	yes	—
683	C₂²⋊C₄	C₂⁴	1	4	yes	—
684	C₂²⋊C₄	C₂⁴	1	4	yes	—
685	C₂²⋊C₄	C₂⁴	1	4	yes	—
686	C₂²⋊C₄	C₂⁴	1	4	yes	—
687	C₂²⋊C₄	C₂⁴	1	4	yes	—
688	C₂²⋊C₄	C₂⁴	1	4	yes	—
689	C₂²⋊C₄	C₂⁴	1	4	yes	—
690	C₂²⋊C₄	C₂⁴	1	4	yes	—
691	C₂²⋊C₄	C₂⁴	1	4	yes	—
692	C₂²⋊C₄	C₂⁴	1	4	yes	—
693	C₂²⋊C₄	C₂⁴	1	8	yes	—
694	C₂²⋊C₄	C₂⁴	1	8	yes	—
695	C₂²⋊C₄	C₂⁴	1	8	yes	—
696	C₂²⋊C₄	C₂⁴	1	4	yes	—
697	C₂²⋊C₄	C₂⁴	1	4	yes	—
698	C₂²⋊C₄	C₂⁴	1	4	yes	—
699	C₂²⋊C₄	C₂⁴	1	4	yes	—
700	C₂²⋊C₄	C₂⁴	1	4	yes	—
701	C₂²⋊C₄	C₂⁴	1	4	yes	—
702	C₂²⋊C₄	C₂⁴	1	4	yes	—
703	C₂²⋊C₄	C₂⁴	1	4	yes	—
704	C₂²⋊C₄	C₂⁴	1	8	yes	—
705	C₂²⋊C₄	C₂⁴	1	8	yes	—
706	C₂²⋊C₄	C₂⁴	1	4	yes	—
707	C₂²⋊C₄	C₂⁴	1	8	yes	—
708	C₂²⋊C₄	C₂⁴	1	8	yes	—
709	C₂²⋊C₄	C₂⁴	1	4	yes	—
710	C₂²⋊C₄	C₂⁴	1	4	yes	—
711	C₂²⋊C₄	C₂⁴	1	4	yes	—
712	C₂²⋊C₄	C₂⁴	1	8	yes	—
713	C₂²⋊C₄	C₂⁴	1	4	yes	—
714	C₂²⋊C₄	C₂⁴	1	4	yes	—
715	C₂²⋊C₄	C₂⁴	1	4	yes	—
716	C₂²⋊C₄	C₂⁴	1	4	yes	—
717	C₂²⋊C₄	C₂⁴	1	8	yes	—
718	C₂²⋊C₄	C₂⁴	1	4	yes	—
719	C₂²⋊C₄	C₂⁴	1	8	yes	—
720	C₄²	C₂⁴	1	1	yes	characteristic
721	C₄²	C₂⁴	1	1	yes	characteristic
722	C₄²	C₂⁴	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	C₄²	C₂⁴	1	1	yes	characteristic
728	C₄²	C₂⁴	1	1	yes	characteristic
729	C₄²	C₂⁴	1	1	yes	characteristic
730	C₄²	C₂⁴	1	1	yes	characteristic
731	C₄²	C₂⁴	1	1	yes	characteristic
732	C₄²	C₂⁴	1	1	yes	characteristic
733	C₄²	C₂⁴	1	1	yes	characteristic
734	C₄²	C₂⁴	1	1	yes	characteristic
735	C₄²	C₂⁴	1	1	yes	characteristic
736	C₄²	C₂⁴	1	4	yes	—
737	C₄²	C₂⁴	1	4	yes	—
738	C₄²	C₂⁴	1	4	yes	—
739	C₄²	C₂⁴	1	4	yes	—
740	C₄²	C₂⁴	1	4	yes	—
741	C₄²	C₂⁴	1	8	yes	—
742	C₄²	C₂⁴	1	8	yes	—
743	C₂³	—	2	2	no	—
744	C₂³	—	2	2	no	—
745	C₂³	—	2	4	no	—
746	C₂³	—	2	8	no	—
747	C₂³	—	4	1	no	—
748	C₂³	—	4	4	no	—
749	C₂³	—	4	2	no	—
750	C₂³	—	4	4	no	—
751	C₂³	—	4	2	no	—
752	C₂³	—	4	8	no	—
753	C₂³	—	4	8	no	—
754	C₂³	—	4	8	no	—
755	C₂³	C₂⁵	1	4	yes	—
756	C₂³	C₂⁵	1	4	yes	—
757	C₂³	C₂⁵	1	4	yes	—
758	C₂³	C₂⁵	1	1	yes	characteristic
759	C₂³	C₂⁵	1	4	yes	—
760	C₂³	C₂⁵	1	1	yes	characteristic
761	C₂³	C₂⁵	1	1	yes	characteristic
762	Q₈	—	2	4	no	—
763	Q₈	—	2	4	no	—
764	Q₈	—	2	4	no	—
765	Q₈	—	2	4	no	—
766	Q₈	—	2	4	no	—
767	Q₈	—	2	4	no	—
768	Q₈	—	4	8	no	—
769	Q₈	—	4	4	no	—
770	Q₈	—	4	2	no	—
771	D₄	—	2	8	no	—
772	D₄	—	2	8	no	—
773	D₄	—	2	8	no	—
774	D₄	—	2	8	no	—
775	D₄	—	2	8	no	—
776	D₄	—	2	4	no	—
777	D₄	—	2	4	no	—
778	D₄	—	2	4	no	—
779	D₄	—	2	4	no	—
780	D₄	—	2	4	no	—
781	D₄	—	2	4	no	—
782	D₄	—	2	4	no	—
783	D₄	—	2	4	no	—
784	D₄	—	4	8	no	—
785	D₄	—	4	8	no	—
786	D₄	—	4	8	no	—
787	D₄	—	4	4	no	—
788	D₄	—	4	2	no	—
789	D₄	—	4	4	no	—
790	D₄	—	4	2	no	—
791	D₄	—	4	4	no	—
792	D₄	—	4	8	no	—
793	D₄	—	4	8	no	—
794	D₄	—	4	4	no	—
795	D₄	—	4	4	no	—
796	D₄	—	4	4	no	—
797	D₄	—	4	2	no	—
798	D₄	—	4	4	no	—
799	D₄	—	4	8	no	—
800	D₄	—	4	8	no	—
801	C₂×C₄	—	2	2	no	—
802	C₂×C₄	—	2	4	no	—
803	C₂×C₄	—	2	2	no	—
804	C₂×C₄	—	2	2	no	—
805	C₂×C₄	—	2	2	no	—
806	C₂×C₄	—	2	2	no	—
807	C₂×C₄	—	2	2	no	—
808	C₂×C₄	—	2	2	no	—
809	C₂×C₄	—	2	8	no	—
810	C₂×C₄	—	2	8	no	—
811	C₂×C₄	—	2	8	no	—
812	C₂×C₄	—	2	2	no	—
813	C₂×C₄	—	2	2	no	—
814	C₂×C₄	—	2	8	no	—
815	C₂×C₄	—	2	2	no	—
816	C₂×C₄	—	4	1	no	—
817	C₂×C₄	—	4	4	no	—
818	C₂×C₄	—	4	1	no	—
819	C₂×C₄	—	4	1	no	—
820	C₂×C₄	—	4	1	no	—
821	C₂×C₄	—	4	1	no	—
822	C₂×C₄	—	4	2	no	—
823	C₂×C₄	—	4	1	no	—
824	C₂×C₄	—	4	1	no	—
825	C₂×C₄	—	4	4	no	—
826	C₂×C₄	—	4	4	no	—
827	C₂×C₄	—	4	4	no	—
828	C₂×C₄	—	4	2	no	—
829	C₂×C₄	—	4	8	no	—
830	C₂×C₄	—	4	8	no	—
831	C₂×C₄	—	4	8	no	—
832	C₂×C₄	—	4	8	no	—
833	C₂×C₄	—	4	4	no	—
834	C₂×C₄	—	4	4	no	—
835	C₂×C₄	—	4	8	no	—
836	C₂×C₄	H(5,𝔽₂)	1	4	yes	—
837	C₂×C₄	C₂⁵	1	1	yes	characteristic
838	C₂×C₄	C₂⁵	1	1	yes	characteristic
839	C₂×C₄	C₂⁵	1	1	yes	characteristic
840	C₂×C₄	C₂⁵	1	1	yes	characteristic
841	C₂×C₄	C₂⁵	1	4	yes	—
842	C₂×C₄	C₂⁵	1	4	yes	—
843	C₂×C₄	C₂⁵	1	1	yes	characteristic
844	C₂×C₄	C₂⁵	1	1	yes	characteristic
845	C₂×C₄	C₂⁵	1	1	yes	characteristic
846	C₂×C₄	C₂⁵	1	4	yes	—
847	C₂×C₄	C₂⁵	1	1	yes	characteristic
848	C₂×C₄	C₂⁵	1	1	yes	characteristic
849	C₂×C₄	C₂⁵	1	4	yes	—
850	C₂×C₄	C₂⁵	1	4	yes	—
851	C₂×C₄	C₂⁵	1	4	yes	—
852	C₂×C₄	C₂⁵	1	4	yes	—
853	C₂×C₄	C₂⁵	1	4	yes	—
854	C₂×C₄	C₂⁵	1	1	yes	characteristic
855	C₂×C₄	C₂⁵	1	1	yes	characteristic
856	C₂×C₄	C₂⁵	1	1	yes	characteristic
857	C₂²	—	2	1	no	—
858	C₂²	—	2	1	no	—
859	C₂²	—	2	1	no	—
860	C₂²	—	2	1	no	—
861	C₂²	—	2	1	no	—
862	C₂²	—	2	4	no	—
863	C₂²	—	2	4	no	—
864	C₂²	—	2	4	no	—
865	C₂²	—	2	4	no	—
866	C₂²	—	2	1	no	—
867	C₂²	—	2	4	no	—
868	C₂²	—	2	4	no	—
869	C₂²	—	2	1	no	—
870	C₂²	—	2	4	no	—
871	C₂²	—	2	4	no	—
872	C₂²	—	2	4	no	—
873	C₂²	—	2	4	no	—
874	C₂²	—	2	4	no	—
875	C₂²	—	2	4	no	—
876	C₂²	—	4	4	no	—
877	C₂²	—	8	8	no	—
878	C₂²	—	8	4	no	—
879	C₂²	—	16	8	no	—
880	C₂²	C₂×H(5,𝔽₂)	1	2	yes	—
881	C₂²	#585	1	2	yes	—
882	C₂²	C₂⁶	1	1	yes	characteristic
883	C₄	—	2	1	no	—
884	C₄	—	2	1	no	—
885	C₄	—	2	4	no	—
886	C₄	—	2	4	no	—
887	C₄	—	2	4	no	—
888	C₄	—	2	4	no	—
889	C₄	—	2	1	no	—
890	C₄	—	2	1	no	—
891	C₄	—	2	1	no	—
892	C₄	—	2	4	no	—
893	C₄	—	2	1	no	—
894	C₄	—	2	1	no	—
895	C₄	—	2	1	no	—
896	C₄	—	2	1	no	—
897	C₄	—	2	4	no	—
898	C₄	—	2	4	no	—
899	C₄	—	2	4	no	—
900	C₄	C₂×H(5,𝔽₂)	1	2	yes	—
901	C₄	C₂×H(5,𝔽₂)	1	2	yes	—
902	C₄	#585	1	2	yes	—
903	C₂	—	2	2	no	—
904	C₂	—	2	2	no	—
905	C₂	—	4	1	no	—
906	C₂	—	4	4	no	—
907	C₂	—	4	4	no	—
908	C₂	—	4	4	no	—
909	C₂	—	4	4	no	—
910	C₂	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
911	C₂	C₂×#585	1	1	yes	characteristic
912	C₂	C₂×#585	1	1	yes	characteristic

	subgroup	G/H
center, commutator, Frattini, socle, cosocle	C₂²	C₂⁶
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂² ◁ G
LECS	G ▷ C₂² ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #3562	C₂	semidirect
2. #3560	C₂	semidirect
3. #3552	C₂	semidirect
4. #3551	C₂	semidirect
5. #3547	C₂	semidirect
6. #3546	C₂	semidirect
7. #3543	C₂	semidirect
8. #3534	C₂	semidirect
9. #3520	C₂	semidirect
10. #3519	C₂	semidirect
11. #3519	C₂	semidirect
12. #3517	C₂	semidirect
13. #3514	C₂	semidirect
14. #3514	C₂	semidirect
15. #3512	C₂	semidirect
16. #3507	C₂	semidirect
17. #3506	C₂	semidirect
18. #3505	C₂	semidirect
19. #3500	C₂	semidirect
20. #3497	C₂	semidirect
21. #3496	C₂	semidirect
22. #3494	C₂	semidirect
23. #3489	C₂	semidirect
24. #3488	C₂	semidirect
25. #3444	C₂	semidirect
26. C₂×#532	C₂	semidirect
27. C₂×#529	C₂	semidirect
28. C₂×2₋¹⁺⁴	C₂²	semidirect
29. C₂×H(5,𝔽₂)	C₂²	semidirect
30. C₂²×#41	C₂²	semidirect
31. #563	C₂²	semidirect
32. #562	C₂²	semidirect
33. #560	C₂²	semidirect
34. #560	C₂²	semidirect
35. #559	C₂²	semidirect
36. #559	C₂²	semidirect
37. #557	C₂²	semidirect
38. #556	C₂²	semidirect
39. #556	C₂²	semidirect
40. #556	C₂²	semidirect
41. #555	C₂²	semidirect
42. #555	C₂²	semidirect
43. #555	C₂²	semidirect
44. #554	C₂²	semidirect
45. #554	C₂²	semidirect
46. #553	C₂²	semidirect
47. #553	C₂²	semidirect
48. #553	C₂²	semidirect
49. #553	C₂²	semidirect
50. #553	C₂²	semidirect
51. #553	C₂²	semidirect
52. #553	C₂²	semidirect
53. #553	C₂²	semidirect
54. #553	C₂²	semidirect
55. #552	C₂²	semidirect
56. #552	C₂²	semidirect
57. #552	C₂²	semidirect
58. #551	C₂²	semidirect
59. #551	C₂²	semidirect
60. #551	C₂²	semidirect
61. #551	C₂²	semidirect
62. #550	C₂²	semidirect
63. #550	C₂²	semidirect
64. #550	C₂²	semidirect
65. #550	C₂²	semidirect
66. #550	C₂²	semidirect
67. D₄×Q₈	C₂²	semidirect
68. D₄×Q₈	C₂²	semidirect
69. D₄×Q₈	C₂²	semidirect
70. #548	C₂²	semidirect
71. #548	C₂²	semidirect
72. #548	C₂²	semidirect
73. #548	C₂²	semidirect
74. #548	C₂²	semidirect
75. #548	C₂²	semidirect
76. #547	C₂²	semidirect
77. #547	C₂²	semidirect
78. #547	C₂²	semidirect
79. #547	C₂²	semidirect
80. #547	C₂²	semidirect
81. #546	C₂²	semidirect
82. #546	C₂²	semidirect
83. #546	C₂²	semidirect
84. #546	C₂²	semidirect
85. #546	C₂²	semidirect
86. #546	C₂²	semidirect
87. #546	C₂²	semidirect
88. #546	C₂²	semidirect
89. #546	C₂²	semidirect
90. #546	C₂²	semidirect
91. #546	C₂²	semidirect
92. #546	C₂²	semidirect
93. #546	C₂²	semidirect
94. D₄²	C₂²	semidirect
95. D₄²	C₂²	semidirect
96. D₄²	C₂²	semidirect
97. D₄²	C₂²	semidirect
98. D₄²	C₂²	semidirect
99. #544	C₂²	semidirect
100. #542	C₂²	semidirect
101. #542	C₂²	semidirect
102. #542	C₂²	semidirect
103. #541	C₂²	semidirect
104. #540	C₂²	semidirect
105. #540	C₂²	semidirect
106. #540	C₂²	semidirect
107. #540	C₂²	semidirect
108. #540	C₂²	semidirect
109. #539	C₂²	semidirect
110. #539	C₂²	semidirect
111. #539	C₂²	semidirect
112. #538	C₂²	semidirect
113. #538	C₂²	semidirect
114. #538	C₂²	semidirect
115. #538	C₂²	semidirect
116. #538	C₂²	semidirect
117. #538	C₂²	semidirect
118. #537	C₂²	semidirect
119. #537	C₂²	semidirect
120. #537	C₂²	semidirect
121. #537	C₂²	semidirect
122. #537	C₂²	semidirect
123. #536	C₂²	semidirect
124. #536	C₂²	semidirect
125. #536	C₂²	semidirect
126. #535	C₂²	semidirect
127. #535	C₂²	semidirect
128. #535	C₂²	semidirect
129. #535	C₂²	semidirect
130. #534	C₂²	semidirect
131. #534	C₂²	semidirect
132. #533	C₂²	semidirect
133. #533	C₂²	semidirect
134. #533	C₂²	semidirect
136. #532	C₂²	semidirect
137. #532	C₂²	semidirect
138. #532	C₂²	semidirect
139. #532	C₂²	semidirect
140. #532	C₂²	semidirect
141. #532	C₂²	semidirect
142. #532	C₂²	semidirect
143. #532	C₂²	semidirect
144. #532	C₂²	semidirect
145. #532	C₂²	semidirect
146. #532	C₂²	semidirect
147. #532	C₂²	semidirect
148. #532	C₂²	semidirect
149. #532	C₂²	semidirect
150. C₂×C₄⋊Q₈	C₂²	semidirect
151. C₂×#127	C₂²	semidirect
152. #529	C₂²	semidirect
153. #529	C₂²	semidirect
154. #529	C₂²	semidirect
155. #529	C₂²	semidirect
156. #529	C₂²	semidirect
157. #529	C₂²	semidirect
158. #529	C₂²	semidirect
159. #529	C₂²	semidirect
160. #529	C₂²	semidirect
161. #529	C₂²	semidirect
162. #529	C₂²	semidirect
163. #529	C₂²	semidirect
164. #529	C₂²	semidirect
165. #529	C₂²	semidirect
166. #529	C₂²	semidirect
167. #529	C₂²	semidirect
168. #529	C₂²	semidirect
169. C₂×#126	C₂²	semidirect
170. C₂×#125	C₂²	semidirect
171. C₂×#124	C₂²	semidirect
172. C₂×#124	C₂²	semidirect
173. C₂×#124	C₂²	semidirect
174. #525	C₂²	semidirect
175. #525	C₂²	semidirect
176. #525	C₂²	semidirect
177. #525	C₂²	semidirect
178. #525	C₂²	semidirect
179. #525	C₂²	semidirect
180. C₂×#123	C₂²	semidirect
181. C₂×C₂²⋊Q₈	C₂²	semidirect
182. C₂×C₂²⋊Q₈	C₂²	semidirect
184. C₂×#121	C₂²	semidirect
185. C₂×#121	C₂²	semidirect
186. C₂×#121	C₂²	semidirect
187. C₂×#121	C₂²	semidirect
188. #520	C₂²	semidirect
189. #520	C₂²	semidirect
190. #520	C₂²	semidirect
191. #518	C₂²	semidirect
192. #518	C₂²	semidirect
193. C₄×#41	C₂²	semidirect
194. C₄×#41	C₂²	semidirect
195. C₄×#41	C₂²	semidirect
196. C₂×C₄×Q₈	C₂²	semidirect
197. C₂×C₄×D₄	C₂²	semidirect
198. C₂×C₄×D₄	C₂²	semidirect
199. C₂×C₄×D₄	C₂²	semidirect
200. C₂×C₄×D₄	C₂²	semidirect
201. C₂×#117	C₂²	semidirect
202. C₂²×C₄²	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
#3560	2
#3552	2
#3551	2
#3547	2
#3546	2
#3543	2
#3534	2
#3520	2
#3519	2
#3517	2
#3514	2
#3512	2
#3507	2
#3506	2
#3505	2
#3500	2
#3497	2
#3496	2
#3494	2
#3489	2
#3488	2
#3444	2
C₂×#532	2
C₂×#529	2