Subgroups — #62055

Order 256.

945 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3543	C₂	1	1	yes	maximal, characteristic
2	#3523	C₂	1	1	yes	maximal, characteristic, complemented
3	#3400	C₂	1	1	yes	maximal, characteristic, complemented
4	#3392	C₂	1	1	yes	maximal, characteristic, complemented
5	#3368	C₂	1	1	yes	maximal, characteristic, complemented
6	#3365	C₂	1	1	yes	maximal, characteristic, complemented
7	#3324	C₂	1	1	yes	maximal, characteristic, complemented
8	#3310	C₂	1	2	yes	maximal, complemented
9	#3304	C₂	1	1	yes	maximal, characteristic, complemented
10	#3296	C₂	1	2	yes	maximal, complemented
11	D₄×SD₁₆	C₂	1	2	yes	maximal, complemented
12	D₄×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
13	#3278	C₂	1	1	yes	maximal, characteristic, complemented
14	#3266	C₂	1	2	yes	maximal, complemented
15	#3260	C₂	1	2	yes	maximal, complemented
16	#3248	C₂	1	1	yes	maximal, characteristic, complemented
17	#3222	C₂	1	2	yes	maximal, complemented
18	#3208	C₂	1	1	yes	maximal, characteristic, complemented
19	#3126	C₂	1	2	yes	maximal, complemented
20	#3108	C₂	1	1	yes	maximal, characteristic, complemented
21	#3043	C₂	1	2	yes	maximal, complemented
22	C₂×#460	C₂	1	1	yes	maximal, characteristic, complemented
23	#2994	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#137	C₂²	1	2	yes	complemented
25	C₂²×SD₁₆	C₂²	1	2	yes	complemented
26	C₂²×SD₁₆	C₂²	1	2	yes	complemented
27	#560	—	2	2	no	—
28	#559	C₂²	1	1	yes	characteristic
29	#557	—	2	1	no	—
30	#557	C₂²	1	1	yes	characteristic, complemented
31	#557	C₂²	1	1	yes	characteristic, complemented
32	#556	—	2	1	no	—
33	#556	C₂²	1	1	yes	characteristic, complemented
34	#552	—	2	2	no	—
35	#552	C₂²	1	2	yes	complemented
36	#550	C₂²	1	1	yes	characteristic
37	#550	C₂²	1	1	yes	characteristic
38	D₄×Q₈	C₂²	1	2	yes	complemented
39	D₄×Q₈	C₂²	1	1	yes	characteristic, complemented
40	#546	—	2	1	no	—
41	#546	C₂²	1	2	yes	—
42	D₄²	—	2	1	no	—
43	D₄²	C₂²	1	2	yes	—
44	D₄²	C₂²	1	1	yes	characteristic
45	#541	—	2	2	no	—
46	#541	C₂²	1	2	yes	complemented
47	#540	—	2	1	no	—
48	#540	C₂²	1	2	yes	—
49	#535	—	2	1	no	—
50	#535	C₂²	1	2	yes	—
51	#534	—	2	2	no	—
52	#533	—	2	1	no	—
53	#533	C₂²	1	1	yes	characteristic, complemented
54	C₂×#127	C₂²	1	1	yes	characteristic
55	#529	—	2	1	no	—
56	#529	C₂²	1	1	yes	characteristic
57	#529	C₂²	1	1	yes	characteristic
58	#519	C₂²	1	2	yes	complemented
59	C₂×C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
60	#497	C₂²	1	2	yes	complemented
61	#492	C₂²	1	1	yes	characteristic
62	#492	C₂²	1	1	yes	characteristic, complemented
63	#492	C₂²	1	2	yes	complemented
64	#490	C₂²	1	2	yes	complemented
65	#488	C₂²	1	2	yes	complemented
66	#486	C₂²	1	1	yes	characteristic
67	#486	C₂²	1	1	yes	characteristic, complemented
68	#483	C₂²	1	1	yes	characteristic, complemented
69	#482	C₂²	1	2	yes	complemented
70	#482	C₂²	1	2	yes	complemented
71	#480	C₂²	1	1	yes	characteristic
72	#479	C₂²	1	1	yes	characteristic, complemented
73	#479	C₂²	1	1	yes	characteristic, complemented
74	#479	C₂²	1	2	yes	complemented
75	#478	C₂²	1	2	yes	complemented
76	#478	C₂²	1	2	yes	complemented
77	#475	C₂²	1	1	yes	characteristic, complemented
78	#474	C₂²	1	1	yes	characteristic, complemented
79	#468	C₂²	1	2	yes	complemented
80	#468	C₂²	1	2	yes	complemented
81	#467	C₂²	1	2	yes	complemented
82	#465	C₂²	1	2	yes	—
83	#465	C₂²	1	2	yes	complemented
84	#465	C₂²	1	2	yes	complemented
85	#464	C₂²	1	1	yes	characteristic, complemented
86	#464	C₂²	1	1	yes	characteristic, complemented
87	#464	C₂²	1	2	yes	complemented
88	#464	C₂²	1	2	yes	complemented
89	#464	C₂²	1	2	yes	complemented
90	#462	C₂²	1	1	yes	characteristic, complemented
91	#461	C₂²	1	1	yes	characteristic, complemented
92	#461	C₂²	1	2	yes	complemented
93	#461	C₂²	1	2	yes	complemented
94	#460	C₂²	1	1	yes	characteristic
95	#460	C₂²	1	1	yes	characteristic
96	#460	C₂²	1	1	yes	characteristic, complemented
97	#460	C₂²	1	2	yes	complemented
98	#460	C₂²	1	2	yes	complemented
99	#460	C₂²	1	2	yes	complemented
100	#460	C₂²	1	1	yes	characteristic, complemented
101	#460	C₂²	1	2	yes	complemented
102	#460	C₂²	1	2	yes	complemented
103	#460	C₂²	1	2	yes	complemented
104	#452	C₂²	1	2	yes	complemented
105	#452	C₂²	1	2	yes	complemented
106	#451	C₂²	1	1	yes	characteristic, complemented
107	#450	C₂²	1	2	yes	complemented
108	#450	C₂²	1	2	yes	complemented
109	#450	C₂²	1	2	yes	complemented
110	#450	C₂²	1	2	yes	complemented
111	#448	C₂²	1	1	yes	characteristic
112	#448	C₂²	1	2	yes	complemented
113	#448	C₂²	1	2	yes	complemented
114	#446	C₂²	1	1	yes	characteristic, complemented
115	C₈×Q₈	C₂²	1	1	yes	characteristic, complemented
116	#440	C₂²	1	2	yes	complemented
117	#440	C₂²	1	2	yes	complemented
118	C₄×Q₁₆	C₂²	1	1	yes	characteristic, complemented
119	C₄×Q₁₆	C₂²	1	1	yes	characteristic, complemented
120	C₄×SD₁₆	C₂²	1	1	yes	characteristic, complemented
121	C₄×SD₁₆	C₂²	1	1	yes	characteristic, complemented
122	C₄×SD₁₆	C₂²	1	2	yes	complemented
123	C₄×SD₁₆	C₂²	1	2	yes	complemented
124	#436	C₂²	1	1	yes	characteristic, complemented
125	#435	C₂²	1	2	yes	complemented
126	C₈×D₄	C₂²	1	2	yes	complemented
127	C₈×D₄	C₂²	1	1	yes	characteristic, complemented
128	#433	C₂²	1	2	yes	complemented
129	#431	C₂²	1	1	yes	characteristic, complemented
130	#424	C₂²	1	2	yes	complemented
131	C₂×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
132	#418	C₂²	1	2	yes	complemented
133	#416	C₂²	1	2	yes	complemented
134	C₂×#102	C₂²	1	2	yes	complemented
135	C₂×#41	—	2	1	no	—
136	C₂×#41	C₂³	1	2	yes	—
137	C₂²×Q₈	C₂³	1	1	yes	characteristic
138	C₂²×Q₈	C₂³	1	2	yes	—
139	C₂²×D₄	—	2	2	no	—
140	C₂²×D₄	—	2	1	no	—
141	C₂²×D₄	—	2	1	no	—
142	C₂²×D₄	—	2	1	no	—
143	C₂²×D₄	C₂³	1	2	yes	—
144	C₂²×D₄	C₂³	1	2	yes	—
145	#137	—	4	4	no	—
146	C₂×Q₁₆	C₂³	1	1	yes	characteristic
147	C₂×Q₁₆	C₂³	1	2	yes	—
148	C₂×Q₁₆	C₂³	1	1	yes	characteristic
149	C₂×SD₁₆	—	4	4	no	—
150	C₂×SD₁₆	—	4	4	no	—
151	C₂×SD₁₆	C₂³	1	1	yes	characteristic
152	C₂×SD₁₆	C₂³	1	2	yes	—
153	C₂×SD₁₆	C₂³	1	2	yes	—
154	C₂×SD₁₆	C₂³	1	2	yes	—
155	C₂×SD₁₆	C₂³	1	2	yes	—
156	C₂×SD₁₆	C₂³	1	2	yes	—
157	C₂×SD₁₆	C₂³	1	2	yes	—
158	C₂×SD₁₆	C₂³	1	2	yes	—
159	C₂×SD₁₆	C₂³	1	1	yes	characteristic
160	C₂×SD₁₆	C₂³	1	2	yes	—
161	C₂×SD₁₆	C₂³	1	2	yes	—
162	C₂×M₁₆	C₂³	1	2	yes	—
163	C₂²×C₈	C₂³	1	2	yes	—
164	C₂²×C₈	C₂³	1	2	yes	—
165	C₄⋊Q₈	—	2	1	no	—
166	C₄⋊Q₈	—	2	1	no	—
167	C₄⋊Q₈	—	2	2	no	—
168	C₄⋊Q₈	C₂³	1	1	yes	characteristic
169	C₄⋊Q₈	C₂³	1	2	yes	—
170	C₄⋊Q₈	C₂³	1	1	yes	characteristic
171	#127	—	2	1	no	—
172	#127	—	2	1	no	—
173	#127	—	2	1	no	—
174	#127	C₂³	1	2	yes	—
175	#127	C₂³	1	1	yes	characteristic
176	#127	C₂³	1	1	yes	characteristic
177	#127	C₂³	1	2	yes	—
178	#126	—	2	2	no	—
179	#126	—	2	2	no	—
180	#126	—	2	2	no	—
181	#126	—	2	2	no	—
182	#126	—	2	1	no	—
183	#126	D₄	1	2	yes	—
184	#125	—	2	1	no	—
185	#125	—	2	2	no	—
186	#125	—	2	2	no	—
187	#125	—	2	2	no	—
188	#125	—	2	2	no	—
189	#125	—	2	2	no	—
190	#125	—	2	1	no	—
191	#125	D₄	1	1	yes	characteristic
192	#125	C₂³	1	1	yes	characteristic
193	#125	C₂³	1	2	yes	—
194	#124	—	2	1	no	—
195	#124	—	2	1	no	—
196	#124	D₄	1	1	yes	characteristic
197	#124	C₂³	1	1	yes	characteristic
198	#124	C₂³	1	2	yes	—
199	#123	—	2	2	no	—
200	#123	—	2	1	no	—
201	#123	—	2	2	no	—
202	#123	—	2	2	no	—
203	#123	—	2	2	no	—
204	#123	—	2	2	no	—
205	#123	D₄	1	2	yes	—
206	C₂²⋊Q₈	—	2	1	no	—
207	C₂²⋊Q₈	—	2	2	no	—
208	C₂²⋊Q₈	—	2	2	no	—
209	C₂²⋊Q₈	—	2	2	no	—
210	C₂²⋊Q₈	D₄	1	1	yes	characteristic
211	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
212	C₂²⋊Q₈	C₂³	1	2	yes	—
213	C₂²⋊Q₈	C₂³	1	2	yes	—
214	C₂²⋊Q₈	C₂³	1	2	yes	—
215	#121	—	2	2	no	—
216	#121	—	2	2	no	—
217	#121	—	2	2	no	—
218	#121	—	2	1	no	—
219	#121	—	2	1	no	—
220	#121	—	2	2	no	—
221	#121	—	2	2	no	—
222	#121	—	2	2	no	—
223	#121	—	2	2	no	—
224	#121	—	2	2	no	—
225	#121	D₄	1	1	yes	characteristic
226	#121	C₂³	1	1	yes	characteristic
227	#121	C₂³	1	2	yes	—
228	#121	C₂³	1	2	yes	—
229	#120	—	2	2	no	—
230	#120	—	2	2	no	—
231	#120	—	2	2	no	—
232	#120	—	2	2	no	—
233	#120	—	2	2	no	—
234	#120	—	2	2	no	—
235	C₄×Q₈	—	2	1	no	—
236	C₄×Q₈	—	2	2	no	—
237	C₄×Q₈	—	2	2	no	—
238	C₄×Q₈	—	2	1	no	—
239	C₄×Q₈	—	2	1	no	—
240	C₄×Q₈	—	2	1	no	—
241	C₄×Q₈	—	2	1	no	—
242	C₄×Q₈	—	2	1	no	—
243	C₄×Q₈	C₂³	1	1	yes	characteristic
244	C₄×Q₈	C₂³	1	1	yes	characteristic
245	C₄×Q₈	C₂³	1	1	yes	characteristic
246	C₄×Q₈	C₂³	1	1	yes	characteristic
247	C₄×Q₈	C₂³	1	2	yes	—
248	C₄×Q₈	C₂³	1	2	yes	—
249	C₄×Q₈	C₂³	1	2	yes	—
250	C₄×Q₈	C₂³	1	1	yes	characteristic
251	C₄×Q₈	C₂³	1	1	yes	characteristic
252	C₄×D₄	—	2	2	no	—
253	C₄×D₄	—	2	1	no	—
254	C₄×D₄	—	2	1	no	—
255	C₄×D₄	—	2	1	no	—
256	C₄×D₄	—	2	1	no	—
257	C₄×D₄	C₂³	1	1	yes	characteristic
258	C₄×D₄	C₂³	1	2	yes	—
259	C₄×D₄	C₂³	1	2	yes	—
260	C₄×D₄	C₂³	1	2	yes	—
261	C₄×D₄	C₂³	1	1	yes	characteristic
262	#117	—	2	1	no	—
263	#117	—	2	2	no	—
264	#117	—	2	2	no	—
265	#117	—	2	2	no	—
266	#117	—	2	1	no	—
267	#117	C₂³	1	2	yes	—
268	#117	C₂³	1	2	yes	—
269	C₂×C₄⋊C₄	—	2	1	no	—
270	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
271	C₂×C₂²⋊C₄	—	2	2	no	—
272	C₂×C₄²	—	2	1	no	—
273	C₂×C₄²	C₂³	1	1	yes	characteristic
274	#107	C₂³	1	1	yes	characteristic
275	#107	C₂³	1	1	yes	characteristic
276	#107	C₂³	1	2	yes	—
277	#106	C₂³	1	1	yes	characteristic
278	#106	C₂³	1	2	yes	—
279	#106	C₂³	1	1	yes	characteristic
280	C₄⋊C₈	C₂³	1	2	yes	—
281	C₄⋊C₈	C₂³	1	1	yes	characteristic
282	C₄⋊C₈	C₂³	1	1	yes	characteristic
283	C₄⋊C₈	C₂³	1	1	yes	characteristic
284	C₄⋊C₈	C₂³	1	2	yes	—
285	C₄⋊C₈	C₂³	1	2	yes	—
286	C₄⋊C₈	C₂³	1	1	yes	characteristic
287	#103	C₂³	1	1	yes	characteristic
288	#103	C₂³	1	2	yes	—
289	#103	C₂³	1	1	yes	characteristic
290	#103	C₂³	1	1	yes	characteristic
291	#103	C₂³	1	2	yes	—
292	#103	C₂³	1	1	yes	characteristic
293	#103	C₂³	1	1	yes	characteristic
294	#103	C₂³	1	1	yes	characteristic
295	#103	C₂³	1	2	yes	—
296	#102	C₂³	1	2	yes	—
297	#102	C₂³	1	2	yes	—
298	#102	C₂³	1	2	yes	—
299	#102	C₂³	1	2	yes	—
300	#102	C₂³	1	2	yes	—
301	#102	C₂³	1	1	yes	characteristic
302	#102	C₂³	1	2	yes	—
303	#102	C₂³	1	2	yes	—
304	#102	C₂³	1	2	yes	—
305	#102	C₂³	1	1	yes	characteristic
306	#102	C₂³	1	2	yes	—
307	C₂²⋊C₈	C₂³	1	1	yes	characteristic
308	C₂²⋊C₈	C₂³	1	1	yes	characteristic
309	C₂²⋊C₈	C₂³	1	2	yes	—
310	C₂²⋊C₈	C₂³	1	2	yes	—
311	#97	C₂³	1	2	yes	—
312	C₄×C₈	C₂³	1	1	yes	characteristic
313	C₄×C₈	C₂³	1	1	yes	characteristic
314	C₄×C₈	C₂³	1	2	yes	—
315	C₂⁴	—	2	2	no	—
316	C₂⁴	—	2	2	no	—
317	#41	—	4	2	no	—
318	#41	—	4	2	no	—
319	#41	—	8	2	no	—
320	C₂×Q₈	—	2	1	no	—
321	C₂×Q₈	—	2	2	no	—
322	C₂×Q₈	—	2	1	no	—
323	C₂×Q₈	—	2	2	no	—
324	C₂×Q₈	—	2	4	no	—
325	C₂×Q₈	—	4	1	no	—
326	C₂×Q₈	—	4	2	no	—
327	C₂×Q₈	C₂×D₄	1	1	yes	characteristic
328	C₂×Q₈	C₂⁴	1	1	yes	characteristic
329	C₂×Q₈	C₂⁴	1	1	yes	characteristic
330	C₂×Q₈	C₂⁴	1	2	yes	—
331	C₂×Q₈	C₂⁴	1	1	yes	characteristic
332	C₂×D₄	—	2	1	no	—
333	C₂×D₄	—	2	2	no	—
334	C₂×D₄	—	2	2	no	—
335	C₂×D₄	—	2	2	no	—
336	C₂×D₄	—	2	1	no	—
337	C₂×D₄	—	2	1	no	—
338	C₂×D₄	—	2	2	no	—
339	C₂×D₄	—	2	2	no	—
340	C₂×D₄	—	2	1	no	—
341	C₂×D₄	—	2	2	no	—
342	C₂×D₄	—	2	2	no	—
343	C₂×D₄	—	2	2	no	—
344	C₂×D₄	—	2	2	no	—
345	C₂×D₄	—	2	1	no	—
346	C₂×D₄	—	4	2	no	—
347	C₂×D₄	—	4	2	no	—
348	C₂×D₄	—	4	2	no	—
349	C₂×D₄	—	4	2	no	—
350	C₂×D₄	—	8	2	no	—
351	C₂×D₄	—	8	2	no	—
352	C₂×D₄	—	8	2	no	—
353	C₂×D₄	—	8	4	no	—
354	C₂×D₄	C₂×D₄	1	2	yes	—
355	C₂×D₄	C₂×D₄	1	1	yes	characteristic
356	C₂×D₄	C₂⁴	1	2	yes	—
357	C₂×D₄	C₂⁴	1	1	yes	characteristic
358	C₂×D₄	C₂⁴	1	2	yes	—
359	C₂²×C₄	—	2	1	no	—
360	C₂²×C₄	—	2	1	no	—
361	C₂²×C₄	—	2	2	no	—
362	C₂²×C₄	—	2	1	no	—
363	C₂²×C₄	—	2	2	no	—
364	C₂²×C₄	—	2	2	no	—
365	C₂²×C₄	—	2	2	no	—
366	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
367	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
368	C₂²×C₄	C₂⁴	1	1	yes	characteristic
369	C₂²×C₄	C₂⁴	1	2	yes	—
370	Q₁₆	—	2	2	no	—
371	Q₁₆	—	4	1	no	—
372	Q₁₆	—	4	2	no	—
373	SD₁₆	—	2	2	no	—
374	SD₁₆	—	2	4	no	—
375	SD₁₆	—	2	4	no	—
376	SD₁₆	—	4	2	no	—
377	SD₁₆	—	4	2	no	—
378	SD₁₆	—	4	2	no	—
379	SD₁₆	—	4	2	no	—
380	SD₁₆	—	4	1	no	—
381	SD₁₆	—	4	2	no	—
382	SD₁₆	—	4	2	no	—
383	SD₁₆	—	4	2	no	—
384	M₁₆	—	4	2	no	—
385	C₂×C₈	—	4	2	no	—
386	C₂×C₈	—	4	2	no	—
387	C₂×C₈	C₂⁴	1	1	yes	characteristic
388	C₂×C₈	C₂⁴	1	1	yes	characteristic
389	C₂×C₈	C₂⁴	1	1	yes	characteristic
390	C₂×C₈	C₂⁴	1	1	yes	characteristic
391	C₂×C₈	C₂⁴	1	2	yes	—
392	C₂×C₈	C₂⁴	1	2	yes	—
393	C₄⋊C₄	—	2	1	no	—
394	C₄⋊C₄	—	2	1	no	—
395	C₄⋊C₄	—	2	1	no	—
396	C₄⋊C₄	—	2	1	no	—
397	C₄⋊C₄	—	2	1	no	—
398	C₄⋊C₄	—	2	2	no	—
399	C₄⋊C₄	—	2	2	no	—
400	C₄⋊C₄	—	2	2	no	—
401	C₄⋊C₄	—	2	1	no	—
402	C₄⋊C₄	—	2	1	no	—
403	C₄⋊C₄	—	2	1	no	—
404	C₄⋊C₄	—	2	2	no	—
405	C₄⋊C₄	—	2	1	no	—
406	C₄⋊C₄	—	2	2	no	—
407	C₄⋊C₄	—	2	1	no	—
408	C₄⋊C₄	—	2	1	no	—
409	C₄⋊C₄	—	2	2	no	—
410	C₄⋊C₄	—	2	2	no	—
411	C₄⋊C₄	—	2	2	no	—
412	C₄⋊C₄	—	2	2	no	—
413	C₄⋊C₄	—	2	2	no	—
414	C₄⋊C₄	—	2	1	no	—
415	C₄⋊C₄	C₂×D₄	1	2	yes	—
416	C₄⋊C₄	C₂×D₄	1	2	yes	—
417	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
418	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
419	C₄⋊C₄	C₂×D₄	1	2	yes	—
420	C₄⋊C₄	C₂×D₄	1	2	yes	—
421	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
422	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
423	C₄⋊C₄	C₂⁴	1	2	yes	—
424	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
425	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
426	C₂²⋊C₄	—	2	1	no	—
427	C₂²⋊C₄	—	2	2	no	—
428	C₂²⋊C₄	—	2	2	no	—
429	C₂²⋊C₄	—	2	2	no	—
430	C₂²⋊C₄	—	2	2	no	—
431	C₂²⋊C₄	—	2	2	no	—
432	C₂²⋊C₄	—	2	2	no	—
433	C₂²⋊C₄	—	2	1	no	—
434	C₂²⋊C₄	—	2	1	no	—
435	C₂²⋊C₄	—	2	1	no	—
436	C₂²⋊C₄	—	2	2	no	—
437	C₂²⋊C₄	—	2	2	no	—
438	C₂²⋊C₄	—	2	1	no	—
439	C₂²⋊C₄	—	2	2	no	—
440	C₂²⋊C₄	—	2	2	no	—
441	C₂²⋊C₄	C₂×D₄	1	2	yes	—
442	C₂²⋊C₄	C₂×D₄	1	2	yes	—
443	C₂²⋊C₄	C₂×D₄	1	2	yes	—
444	C₂²⋊C₄	C₂×D₄	1	2	yes	—
445	C₂²⋊C₄	C₂×D₄	1	2	yes	—
446	C₄²	—	2	1	no	—
447	C₄²	—	2	1	no	—
448	C₄²	—	2	1	no	—
449	C₄²	—	2	1	no	—
450	C₄²	—	2	2	no	—
451	C₄²	—	2	2	no	—
452	C₄²	—	2	2	no	—
453	C₄²	—	2	1	no	—
454	C₄²	—	2	2	no	—
455	C₄²	C₂×D₄	1	1	yes	characteristic
456	C₄²	C₂×D₄	1	1	yes	characteristic
457	C₄²	C₂⁴	1	1	yes	characteristic
458	C₄²	C₂⁴	1	2	yes	—
459	C₄²	C₂⁴	1	1	yes	characteristic
460	C₂³	—	2	1	no	—
461	C₂³	—	2	2	no	—
462	C₂³	—	2	2	no	—
463	C₂³	—	4	4	no	—
464	C₂³	—	8	2	no	—
465	C₂³	—	8	2	no	—
466	C₂³	—	8	2	no	—
467	C₂³	—	8	2	no	—
468	C₂³	—	8	2	no	—
469	C₂³	C₂²×D₄	1	2	yes	—
470	C₂³	C₂²×D₄	1	1	yes	characteristic
471	Q₈	—	2	2	no	—
472	Q₈	—	2	1	no	—
473	Q₈	—	2	1	no	—
474	Q₈	—	2	2	no	—
475	Q₈	—	2	1	no	—
476	Q₈	—	2	2	no	—
477	Q₈	—	2	1	no	—
478	Q₈	—	2	1	no	—
479	Q₈	—	4	4	no	—
480	Q₈	—	4	2	no	—
481	Q₈	—	4	2	no	—
482	Q₈	H(5,𝔽₂)	1	2	yes	—
483	D₄	—	2	4	no	—
484	D₄	—	2	2	no	—
485	D₄	—	2	1	no	—
486	D₄	—	2	2	no	—
487	D₄	—	2	2	no	—
488	D₄	—	2	1	no	—
489	D₄	—	2	2	no	—
490	D₄	—	2	2	no	—
491	D₄	—	4	2	no	—
492	D₄	—	4	2	no	—
493	D₄	—	4	2	no	—
494	D₄	—	8	2	no	—
495	D₄	—	8	2	no	—
496	D₄	—	8	2	no	—
497	D₄	—	8	1	no	—
498	D₄	—	8	2	no	—
499	D₄	—	8	1	no	—
500	D₄	—	8	2	no	—
501	D₄	—	8	2	no	—
502	D₄	—	8	2	no	—
503	D₄	—	8	2	no	—
504	D₄	—	8	2	no	—
505	C₂×C₄	—	2	2	no	—
506	C₂×C₄	—	2	1	no	—
507	C₂×C₄	—	2	2	no	—
508	C₂×C₄	—	2	1	no	—
509	C₂×C₄	—	2	2	no	—
510	C₂×C₄	—	2	1	no	—
511	C₂×C₄	—	2	2	no	—
512	C₂×C₄	—	2	1	no	—
513	C₂×C₄	—	2	2	no	—
514	C₂×C₄	—	2	1	no	—
515	C₂×C₄	—	2	1	no	—
516	C₂×C₄	—	2	2	no	—
517	C₂×C₄	—	2	1	no	—
518	C₂×C₄	—	2	1	no	—
519	C₂×C₄	—	2	1	no	—
520	C₂×C₄	—	4	2	no	—
521	C₂×C₄	—	4	4	no	—
522	C₂×C₄	—	4	2	no	—
523	C₂×C₄	—	4	2	no	—
524	C₂×C₄	—	8	2	no	—
525	C₂×C₄	—	8	2	no	—
526	C₂×C₄	—	8	2	no	—
527	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
528	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
529	C₂×C₄	C₂²×D₄	1	2	yes	—
530	C₂×C₄	C₂²×D₄	1	2	yes	—
531	C₂×C₄	C₂²×D₄	1	2	yes	—
532	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
533	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
534	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
535	C₂×C₄	C₂⁵	1	1	yes	characteristic
536	C₈	—	2	1	no	—
537	C₈	—	2	2	no	—
538	C₈	—	2	2	no	—
539	C₈	—	2	1	no	—
540	C₈	—	2	1	no	—
541	C₈	—	2	1	no	—
542	C₂²	—	2	1	no	—
543	C₂²	—	2	1	no	—
544	C₂²	—	2	2	no	—
545	C₂²	—	2	2	no	—
546	C₂²	—	2	2	no	—
547	C₂²	—	4	2	no	—
548	C₂²	—	4	1	no	—
549	C₂²	—	4	2	no	—
550	C₂²	—	4	1	no	—
551	C₂²	—	4	2	no	—
552	C₂²	—	4	2	no	—
553	C₂²	—	4	1	no	—
554	C₂²	—	4	2	no	—
555	C₂²	—	4	2	no	—
556	C₂²	—	16	4	no	—
557	C₂²	—	16	4	no	—
558	C₂²	#577	1	2	yes	—
559	C₂²	C₂³×D₄	1	1	yes	characteristic
560	C₄	—	2	2	no	—
561	C₄	—	2	1	no	—
562	C₄	—	2	2	no	—
563	C₄	—	2	1	no	—
564	C₄	—	2	1	no	—
565	C₄	—	2	1	no	—
566	C₄	—	2	2	no	—
567	C₄	—	2	2	no	—
568	C₄	—	4	1	no	—
569	C₄	—	4	2	no	—
570	C₄	—	4	1	no	—
571	C₄	—	4	1	no	—
572	C₄	—	4	1	no	—
573	C₄	—	4	1	no	—
574	C₄	—	4	1	no	—
575	C₄	—	4	2	no	—
576	C₄	#577	1	2	yes	—
577	C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
578	C₄	#585	1	1	yes	characteristic
579	C₂	—	2	2	no	—
580	C₂	—	4	2	no	—
581	C₂	—	8	2	no	—
582	C₂	—	8	1	no	—
583	C₂	—	8	2	no	—
584	C₂	#3488	1	1	yes	characteristic
585	C₂	C₂×#577	1	1	yes	characteristic
586	C₂	C₂×#577	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵
prime radical	#3543	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂² ◁ #529 ◁ G
LECS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
2. #3523	C₂	semidirect
3. #3400	C₂	semidirect
4. #3392	C₂	semidirect
5. #3368	C₂	semidirect
6. #3365	C₂	semidirect
7. #3324	C₂	semidirect
8. #3310	C₂	semidirect
9. #3304	C₂	semidirect
10. #3296	C₂	semidirect
11. D₄×SD₁₆	C₂	semidirect
12. D₄×SD₁₆	C₂	semidirect
13. #3278	C₂	semidirect
14. #3266	C₂	semidirect
15. #3260	C₂	semidirect
16. #3248	C₂	semidirect
17. #3222	C₂	semidirect
18. #3208	C₂	semidirect
19. #3126	C₂	semidirect
20. #3108	C₂	semidirect
21. #3043	C₂	semidirect
22. C₂×#460	C₂	semidirect
23. #2994	C₂	semidirect
24. C₂×#137	C₂²	semidirect
25. C₂²×SD₁₆	C₂²	semidirect
26. C₂²×SD₁₆	C₂²	semidirect
30. #557	C₂²	semidirect
31. #557	C₂²	semidirect
33. #556	C₂²	semidirect
35. #552	C₂²	semidirect
38. D₄×Q₈	C₂²	semidirect
39. D₄×Q₈	C₂²	semidirect
46. #541	C₂²	semidirect
53. #533	C₂²	semidirect
58. #519	C₂²	semidirect
59. C₂×C₄×Q₈	C₂²	semidirect
60. #497	C₂²	semidirect
62. #492	C₂²	semidirect
63. #492	C₂²	semidirect
64. #490	C₂²	semidirect
65. #488	C₂²	semidirect
67. #486	C₂²	semidirect
68. #483	C₂²	semidirect
69. #482	C₂²	semidirect
70. #482	C₂²	semidirect
72. #479	C₂²	semidirect
73. #479	C₂²	semidirect
74. #479	C₂²	semidirect
75. #478	C₂²	semidirect
76. #478	C₂²	semidirect
77. #475	C₂²	semidirect
78. #474	C₂²	semidirect
79. #468	C₂²	semidirect
80. #468	C₂²	semidirect
81. #467	C₂²	semidirect
83. #465	C₂²	semidirect
84. #465	C₂²	semidirect
85. #464	C₂²	semidirect
86. #464	C₂²	semidirect
87. #464	C₂²	semidirect
88. #464	C₂²	semidirect
89. #464	C₂²	semidirect
90. #462	C₂²	semidirect
91. #461	C₂²	semidirect
92. #461	C₂²	semidirect
93. #461	C₂²	semidirect
96. #460	C₂²	semidirect
97. #460	C₂²	semidirect
98. #460	C₂²	semidirect
99. #460	C₂²	semidirect
100. #460	C₂²	semidirect
101. #460	C₂²	semidirect
102. #460	C₂²	semidirect
103. #460	C₂²	semidirect
104. #452	C₂²	semidirect
105. #452	C₂²	semidirect
106. #451	C₂²	semidirect
107. #450	C₂²	semidirect
108. #450	C₂²	semidirect
109. #450	C₂²	semidirect
110. #450	C₂²	semidirect
112. #448	C₂²	semidirect
113. #448	C₂²	semidirect
114. #446	C₂²	semidirect
115. C₈×Q₈	C₂²	semidirect
116. #440	C₂²	semidirect
117. #440	C₂²	semidirect
118. C₄×Q₁₆	C₂²	semidirect
119. C₄×Q₁₆	C₂²	semidirect
120. C₄×SD₁₆	C₂²	semidirect
121. C₄×SD₁₆	C₂²	semidirect
122. C₄×SD₁₆	C₂²	semidirect
123. C₄×SD₁₆	C₂²	semidirect
124. #436	C₂²	semidirect
125. #435	C₂²	semidirect
126. C₈×D₄	C₂²	semidirect
127. C₈×D₄	C₂²	semidirect
128. #433	C₂²	semidirect
129. #431	C₂²	semidirect
130. #424	C₂²	semidirect
131. C₂×C₄⋊C₈	C₂²	semidirect
132. #418	C₂²	semidirect
133. #416	C₂²	semidirect
134. C₂×#102	C₂²	semidirect

Maximal subgroups

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

subgroup	index
#3543	2
#3523	2
#3400	2
#3392	2
#3368	2
#3365	2
#3324	2
#3310	2
#3304	2
#3296	2
D₄×SD₁₆	2
#3278	2
#3266	2
#3260	2
#3248	2
#3222	2
#3208	2
#3126	2
#3108	2
#3043	2
C₂×#460	2
#2994	2