Subgroups — #62490

Order 256.

806 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3565	C₂	1	2	yes	maximal, complemented
2	#3388	C₂	1	2	yes	maximal, complemented
3	#3383	C₂	1	1	yes	maximal, characteristic, complemented
4	#3380	C₂	1	1	yes	maximal, characteristic, complemented
5	#3351	C₂	1	2	yes	maximal, complemented
6	#3350	C₂	1	2	yes	maximal, complemented
7	#3348	C₂	1	2	yes	maximal, complemented
8	#3342	C₂	1	1	yes	maximal, characteristic, complemented
9	#3341	C₂	1	1	yes	maximal, characteristic, complemented
10	#3339	C₂	1	1	yes	maximal, characteristic, complemented
11	#3339	C₂	1	1	yes	maximal, characteristic, complemented
12	#3336	C₂	1	1	yes	maximal, characteristic, complemented
13	#3336	C₂	1	1	yes	maximal, characteristic, complemented
14	#3244	C₂	1	2	yes	maximal, complemented
15	#3244	C₂	1	2	yes	maximal, complemented
16	#3240	C₂	1	2	yes	maximal, complemented
17	#3175	C₂	1	1	yes	maximal, characteristic, complemented
18	#3175	C₂	1	1	yes	maximal, characteristic, complemented
19	#3168	C₂	1	1	yes	maximal, characteristic, complemented
20	#3164	C₂	1	1	yes	maximal, characteristic, complemented
21	#3164	C₂	1	1	yes	maximal, characteristic, complemented
22	#3160	C₂	1	1	yes	maximal, characteristic, complemented
23	#2966	C₂	1	1	yes	maximal, characteristic, complemented
24	#563	—	2	2	no	—
25	#562	—	2	2	no	—
26	#557	C₂²	1	2	yes	—
27	#556	—	2	2	no	—
28	#556	C₂²	1	2	yes	—
29	#555	C₂²	1	2	yes	—
30	#554	C₂²	1	2	yes	—
31	#553	C₂²	1	2	yes	—
32	#553	C₂²	1	2	yes	—
33	#552	—	2	2	no	—
34	#552	C₂²	1	2	yes	—
35	#552	C₂²	1	2	yes	—
36	#544	C₂²	1	2	yes	—
37	#544	C₂²	1	2	yes	—
38	#542	—	2	2	no	—
39	#542	—	2	2	no	—
40	#542	C₂²	1	2	yes	—
41	#542	C₂²	1	2	yes	—
42	#541	—	2	2	no	—
43	#539	—	2	2	no	—
44	#533	C₂²	1	2	yes	—
45	#529	C₂²	1	2	yes	—
46	#529	C₂²	1	1	yes	characteristic
47	#501	C₂²	1	2	yes	—
48	#501	C₂²	1	2	yes	—
49	#501	C₂²	1	2	yes	—
50	#501	C₂²	1	2	yes	—
51	#500	C₂²	1	1	yes	characteristic
52	#500	C₂²	1	1	yes	characteristic
53	#500	C₂²	1	1	yes	characteristic
54	#500	C₂²	1	1	yes	characteristic
55	#499	C₂²	1	1	yes	characteristic
56	#499	C₂²	1	1	yes	characteristic
57	#499	C₂²	1	1	yes	characteristic
58	#499	C₂²	1	1	yes	characteristic
59	#499	C₂²	1	2	yes	—
60	#499	C₂²	1	1	yes	characteristic
61	#498	C₂²	1	2	yes	—
62	#495	C₂²	1	1	yes	characteristic
63	#489	C₂²	1	2	yes	—
64	#489	C₂²	1	2	yes	—
65	#488	C₂²	1	2	yes	—
66	#485	C₂²	1	2	yes	—
67	#485	C₂²	1	2	yes	—
68	#485	C₂²	1	2	yes	—
69	#485	C₂²	1	2	yes	—
70	#483	C₂²	1	2	yes	—
71	#483	C₂²	1	2	yes	—
72	#482	C₂²	1	2	yes	—
73	#482	C₂²	1	2	yes	—
74	#482	C₂²	1	2	yes	—
75	#482	C₂²	1	2	yes	—
76	#481	C₂²	1	2	yes	—
77	#481	C₂²	1	2	yes	—
78	#479	C₂²	1	2	yes	—
79	#479	C₂²	1	2	yes	—
80	#479	C₂²	1	2	yes	—
81	#479	C₂²	1	2	yes	—
82	#478	C₂²	1	2	yes	—
83	#478	C₂²	1	2	yes	—
84	#478	C₂²	1	2	yes	—
85	#478	C₂²	1	2	yes	—
86	#476	C₂²	1	2	yes	—
87	#476	C₂²	1	2	yes	—
88	#475	C₂²	1	2	yes	—
89	#475	C₂²	1	2	yes	—
90	#468	C₂²	1	2	yes	—
91	#468	C₂²	1	2	yes	—
92	#467	C₂²	1	1	yes	characteristic
93	#467	C₂²	1	1	yes	characteristic
94	#467	C₂²	1	1	yes	characteristic
95	#466	C₂²	1	1	yes	characteristic
96	#466	C₂²	1	1	yes	characteristic
97	#466	C₂²	1	1	yes	characteristic
98	#465	C₂²	1	2	yes	—
99	#446	C₂²	1	1	yes	characteristic
100	C₈×Q₈	C₂²	1	1	yes	characteristic
101	#440	C₂²	1	2	yes	—
102	#440	C₂²	1	2	yes	—
103	C₄×Q₁₆	C₂²	1	1	yes	characteristic
104	C₄×Q₁₆	C₂²	1	1	yes	characteristic
105	C₄×Q₁₆	C₂²	1	1	yes	characteristic
106	C₄×SD₁₆	C₂²	1	2	yes	—
107	C₄×D₈	C₂²	1	1	yes	characteristic
108	C₄×D₈	C₂²	1	1	yes	characteristic
109	C₄×D₈	C₂²	1	1	yes	characteristic
110	#436	C₂²	1	1	yes	characteristic
111	#435	C₂²	1	1	yes	characteristic
112	#435	C₂²	1	1	yes	characteristic
113	C₈×D₄	C₂²	1	1	yes	characteristic
114	C₈×D₄	C₂²	1	1	yes	characteristic
115	C₈×D₄	C₂²	1	1	yes	characteristic
116	#433	C₂²	1	1	yes	characteristic
117	#433	C₂²	1	1	yes	characteristic
118	#432	C₂²	1	1	yes	characteristic
119	#428	C₂²	1	2	yes	—
120	#428	C₂²	1	2	yes	—
121	#427	C₂²	1	1	yes	characteristic
122	#427	C₂²	1	1	yes	characteristic
123	#427	C₂²	1	1	yes	characteristic
124	#427	C₂²	1	1	yes	characteristic
125	#427	C₂²	1	2	yes	—
126	C₂×#107	C₂²	1	1	yes	characteristic
127	C₂×#107	C₂²	1	1	yes	characteristic
128	#405	C₂²	1	1	yes	characteristic
129	#405	C₂²	1	1	yes	characteristic
130	C₂×C₄×C₈	C₂²	1	1	yes	characteristic
131	C₂×Q₁₆	C₂³	1	1	yes	characteristic
132	C₂×SD₁₆	C₂³	1	2	yes	—
133	C₂×D₈	C₂³	1	1	yes	characteristic
134	C₂×M₁₆	C₂³	1	1	yes	characteristic
135	C₂×M₁₆	C₂³	1	1	yes	characteristic
136	C₂²×C₈	C₂³	1	1	yes	characteristic
137	C₂²×C₈	C₂³	1	1	yes	characteristic
138	C₂²×C₈	C₂³	1	1	yes	characteristic
139	C₂²×C₈	C₂³	1	1	yes	characteristic
140	C₄⋊Q₈	—	2	2	no	—
141	C₄⋊Q₈	—	2	2	no	—
142	C₄⋊Q₈	—	2	2	no	—
143	C₄⋊Q₈	C₂³	1	2	yes	—
144	C₄⋊Q₈	C₂³	1	2	yes	—
145	C₄⋊Q₈	C₂³	1	2	yes	—
146	C₄⋊Q₈	C₂³	1	2	yes	—
147	#126	—	2	2	no	—
148	#126	—	2	2	no	—
149	#126	—	2	2	no	—
150	#126	—	2	2	no	—
151	#126	—	2	2	no	—
152	#126	—	2	2	no	—
153	#126	—	2	2	no	—
154	#126	—	2	2	no	—
155	#126	—	2	2	no	—
156	#126	D₄	1	1	yes	characteristic
157	#126	D₄	1	1	yes	characteristic
158	#125	—	2	2	no	—
159	#125	—	2	2	no	—
160	#125	—	2	2	no	—
161	#125	—	2	2	no	—
162	#125	—	2	2	no	—
163	#125	—	2	2	no	—
164	#125	D₄	1	1	yes	characteristic
165	#125	C₂³	1	2	yes	—
166	#125	C₂³	1	2	yes	—
167	#125	C₂³	1	2	yes	—
168	#125	C₂³	1	2	yes	—
169	#125	C₂³	1	2	yes	—
170	#124	—	2	2	no	—
171	#124	—	2	2	no	—
172	#124	—	2	2	no	—
173	#124	—	2	2	no	—
174	#124	—	2	2	no	—
175	#124	D₄	1	1	yes	characteristic
176	#124	C₂³	1	2	yes	—
177	#123	—	2	2	no	—
178	#123	—	2	2	no	—
179	#123	—	2	2	no	—
180	#123	—	2	2	no	—
181	#123	—	2	2	no	—
182	#123	—	2	2	no	—
183	#123	—	2	2	no	—
184	#123	D₄	1	1	yes	characteristic
185	#123	D₄	1	1	yes	characteristic
186	C₂²⋊Q₈	—	2	2	no	—
187	C₂²⋊Q₈	—	2	2	no	—
188	C₂²⋊Q₈	—	2	2	no	—
189	C₂²⋊Q₈	—	2	2	no	—
190	C₂²⋊Q₈	—	2	2	no	—
191	C₂²⋊Q₈	—	2	2	no	—
192	C₂²⋊Q₈	—	2	2	no	—
193	C₂²⋊Q₈	—	2	2	no	—
194	C₂²⋊Q₈	—	2	2	no	—
195	C₂²⋊Q₈	—	2	2	no	—
196	C₂²⋊Q₈	—	2	2	no	—
197	C₂²⋊Q₈	D₄	1	1	yes	characteristic
198	C₂²⋊Q₈	C₂³	1	2	yes	—
199	C₂²⋊Q₈	C₂³	1	2	yes	—
200	C₂²⋊Q₈	C₂³	1	2	yes	—
201	#121	—	2	2	no	—
202	#121	—	2	2	no	—
203	#121	—	2	2	no	—
204	#121	D₄	1	1	yes	characteristic
205	#121	C₂³	1	2	yes	—
206	#121	C₂³	1	2	yes	—
207	#121	C₂³	1	2	yes	—
208	C₄×Q₈	—	2	2	no	—
209	C₄×Q₈	—	2	2	no	—
210	C₄×Q₈	—	2	2	no	—
211	C₄×Q₈	—	2	2	no	—
212	C₄×Q₈	C₂³	1	2	yes	—
213	C₄×Q₈	C₂³	1	2	yes	—
214	C₄×Q₈	C₂³	1	2	yes	—
215	C₄×Q₈	C₂³	1	1	yes	characteristic
216	C₄×D₄	—	2	2	no	—
217	C₄×D₄	—	2	2	no	—
218	C₄×D₄	—	2	2	no	—
219	C₄×D₄	C₂³	1	2	yes	—
220	C₄×D₄	C₂³	1	2	yes	—
221	C₄×D₄	C₂³	1	2	yes	—
222	C₄×D₄	C₂³	1	1	yes	characteristic
223	C₄×D₄	C₂³	1	1	yes	characteristic
224	C₄×D₄	C₂³	1	1	yes	characteristic
225	#117	—	2	2	no	—
226	#117	—	2	2	no	—
227	#117	—	2	2	no	—
228	#117	—	2	2	no	—
229	#117	C₂³	1	2	yes	—
230	#117	C₂³	1	2	yes	—
231	#117	C₂³	1	2	yes	—
232	#117	C₂³	1	2	yes	—
233	#117	C₂³	1	1	yes	characteristic
234	#117	C₂³	1	1	yes	characteristic
235	C₂×C₄⋊C₄	—	2	2	no	—
236	C₂×C₄⋊C₄	C₂³	1	2	yes	—
237	C₂×C₄⋊C₄	C₂³	1	2	yes	—
238	C₂×C₄²	C₂³	1	1	yes	characteristic
239	#107	C₂³	1	1	yes	characteristic
240	#107	C₂³	1	1	yes	characteristic
241	#107	C₂³	1	1	yes	characteristic
242	#107	C₂³	1	1	yes	characteristic
243	#107	C₂³	1	2	yes	—
244	#107	C₂³	1	2	yes	—
245	#107	C₂³	1	1	yes	characteristic
246	#107	C₂³	1	1	yes	characteristic
247	#107	C₂³	1	2	yes	—
248	#107	C₂³	1	2	yes	—
249	#107	C₂³	1	2	yes	—
250	#107	C₂³	1	2	yes	—
251	#106	C₂³	1	2	yes	—
252	#106	C₂³	1	2	yes	—
253	#106	C₂³	1	2	yes	—
254	#106	C₂³	1	2	yes	—
255	#106	C₂³	1	2	yes	—
256	#106	C₂³	1	2	yes	—
257	#106	C₂³	1	2	yes	—
258	#106	C₂³	1	2	yes	—
259	#106	C₂³	1	2	yes	—
260	C₄⋊C₈	C₂³	1	1	yes	characteristic
261	C₄⋊C₈	C₂³	1	1	yes	characteristic
262	C₄⋊C₈	C₂³	1	1	yes	characteristic
263	C₄⋊C₈	C₂³	1	1	yes	characteristic
264	C₄⋊C₈	C₂³	1	1	yes	characteristic
265	C₄⋊C₈	C₂³	1	1	yes	characteristic
266	#103	C₂³	1	2	yes	—
267	#103	C₂³	1	2	yes	—
268	#103	C₂³	1	2	yes	—
269	#103	C₂³	1	2	yes	—
270	#103	C₂³	1	2	yes	—
271	#103	C₂³	1	2	yes	—
272	#102	C₂³	1	2	yes	—
273	#102	C₂³	1	2	yes	—
274	#102	C₂³	1	2	yes	—
275	#102	C₂³	1	2	yes	—
276	#102	C₂³	1	2	yes	—
277	#102	C₂³	1	2	yes	—
278	C₂²⋊C₈	C₂³	1	1	yes	characteristic
279	C₂²⋊C₈	C₂³	1	1	yes	characteristic
280	C₂²⋊C₈	C₂³	1	1	yes	characteristic
281	C₂²⋊C₈	C₂³	1	1	yes	characteristic
282	C₂²⋊C₈	C₂³	1	1	yes	characteristic
283	C₂²⋊C₈	C₂³	1	1	yes	characteristic
284	#97	C₂³	1	1	yes	characteristic
285	#97	C₂³	1	1	yes	characteristic
286	#97	C₂³	1	1	yes	characteristic
287	#97	C₂³	1	1	yes	characteristic
288	C₄×C₈	C₂³	1	1	yes	characteristic
289	C₄×C₈	C₂³	1	1	yes	characteristic
290	C₄×C₈	C₂³	1	1	yes	characteristic
291	C₄×C₈	C₂³	1	1	yes	characteristic
292	C₄×C₈	C₂³	1	1	yes	characteristic
293	C₄×C₈	C₂³	1	1	yes	characteristic
294	C₂×Q₈	—	2	2	no	—
295	C₂×Q₈	—	2	2	no	—
296	C₂×Q₈	—	2	2	no	—
297	C₂×Q₈	—	2	2	no	—
298	C₂×Q₈	C₂×D₄	1	1	yes	characteristic
299	C₂×Q₈	C₂⁴	1	2	yes	—
300	C₂×D₄	—	2	2	no	—
301	C₂×D₄	—	2	2	no	—
302	C₂×D₄	—	2	2	no	—
303	C₂×D₄	C₂×D₄	1	1	yes	characteristic
304	C₂×D₄	C₂×D₄	1	1	yes	characteristic
305	C₂×D₄	C₂×D₄	1	1	yes	characteristic
306	C₂×D₄	C₂⁴	1	2	yes	—
307	C₂²×C₄	—	2	2	no	—
308	C₂²×C₄	—	2	2	no	—
309	C₂²×C₄	—	2	2	no	—
310	C₂²×C₄	—	2	2	no	—
311	C₂²×C₄	—	2	2	no	—
312	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
313	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
314	C₂²×C₄	C₂⁴	1	1	yes	characteristic
315	C₂²×C₄	C₂⁴	1	1	yes	characteristic
316	C₂²×C₄	C₂⁴	1	1	yes	characteristic
317	Q₁₆	—	2	2	no	—
318	SD₁₆	—	2	4	no	—
319	D₈	—	2	2	no	—
320	M₁₆	—	2	2	no	—
321	M₁₆	—	2	2	no	—
322	C₂×C₈	—	2	2	no	—
323	C₂×C₈	—	2	2	no	—
324	C₂×C₈	—	2	2	no	—
325	C₂×C₈	—	2	2	no	—
326	C₂×C₈	C₂⁴	1	1	yes	characteristic
327	C₂×C₈	C₂⁴	1	1	yes	characteristic
328	C₂×C₈	C₂⁴	1	1	yes	characteristic
329	C₂×C₈	C₂⁴	1	1	yes	characteristic
330	C₂×C₈	C₂⁴	1	1	yes	characteristic
331	C₂×C₈	C₂⁴	1	1	yes	characteristic
332	C₂×C₈	C₂⁴	1	1	yes	characteristic
333	C₂×C₈	C₂⁴	1	1	yes	characteristic
334	C₄⋊C₄	—	2	2	no	—
335	C₄⋊C₄	—	2	2	no	—
336	C₄⋊C₄	—	2	2	no	—
337	C₄⋊C₄	—	2	2	no	—
338	C₄⋊C₄	—	2	2	no	—
339	C₄⋊C₄	—	2	2	no	—
340	C₄⋊C₄	—	2	2	no	—
341	C₄⋊C₄	—	2	2	no	—
342	C₄⋊C₄	—	2	2	no	—
343	C₄⋊C₄	—	2	2	no	—
344	C₄⋊C₄	—	2	2	no	—
345	C₄⋊C₄	—	2	2	no	—
346	C₄⋊C₄	—	2	2	no	—
347	C₄⋊C₄	—	2	2	no	—
348	C₄⋊C₄	—	2	2	no	—
349	C₄⋊C₄	—	2	2	no	—
350	C₄⋊C₄	—	2	2	no	—
351	C₄⋊C₄	—	2	2	no	—
352	C₄⋊C₄	—	2	2	no	—
353	C₄⋊C₄	—	2	2	no	—
354	C₄⋊C₄	—	2	2	no	—
355	C₄⋊C₄	—	2	2	no	—
356	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
357	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
358	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
359	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
360	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
361	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
362	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
363	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
364	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
365	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
366	C₄⋊C₄	C₂⁴	1	2	yes	—
367	C₄⋊C₄	C₂⁴	1	2	yes	—
368	C₄⋊C₄	C₂⁴	1	2	yes	—
369	C₄⋊C₄	C₂⁴	1	2	yes	—
370	C₄⋊C₄	C₂⁴	1	2	yes	—
371	C₄⋊C₄	C₂⁴	1	2	yes	—
372	C₂²⋊C₄	—	2	2	no	—
373	C₂²⋊C₄	—	2	2	no	—
374	C₂²⋊C₄	—	2	2	no	—
375	C₂²⋊C₄	—	2	2	no	—
376	C₂²⋊C₄	—	2	2	no	—
377	C₂²⋊C₄	—	2	2	no	—
378	C₂²⋊C₄	—	2	2	no	—
379	C₂²⋊C₄	—	2	2	no	—
380	C₂²⋊C₄	—	2	2	no	—
381	C₂²⋊C₄	—	2	2	no	—
382	C₂²⋊C₄	—	2	2	no	—
383	C₂²⋊C₄	—	2	2	no	—
384	C₂²⋊C₄	—	2	2	no	—
385	C₂²⋊C₄	—	2	2	no	—
386	C₂²⋊C₄	—	2	2	no	—
387	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
388	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
389	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
390	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
391	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
392	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
393	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
394	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
395	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
396	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
397	C₄²	—	2	2	no	—
398	C₄²	—	2	2	no	—
399	C₄²	—	2	2	no	—
400	C₄²	—	2	2	no	—
401	C₄²	—	2	2	no	—
402	C₄²	—	2	2	no	—
403	C₄²	—	2	2	no	—
404	C₄²	C₂×D₄	1	1	yes	characteristic
405	C₄²	C₂×D₄	1	1	yes	characteristic
406	C₄²	C₂⁴	1	1	yes	characteristic
407	C₄²	C₂⁴	1	1	yes	characteristic
408	C₄²	C₂⁴	1	1	yes	characteristic
409	C₄²	C₂⁴	1	1	yes	characteristic
410	C₂³	—	2	2	no	—
411	C₂³	C₂²×D₄	1	1	yes	characteristic
412	C₂³	C₂²×D₄	1	1	yes	characteristic
413	C₂³	C₂²×D₄	1	1	yes	characteristic
414	Q₈	—	2	2	no	—
415	Q₈	—	2	2	no	—
416	Q₈	—	4	1	no	—
417	Q₈	—	8	2	no	—
418	Q₈	—	8	2	no	—
419	Q₈	—	8	2	no	—
420	Q₈	—	8	2	no	—
421	D₄	—	2	2	no	—
422	D₄	—	2	2	no	—
423	D₄	—	4	1	no	—
424	D₄	—	4	1	no	—
425	D₄	—	4	1	no	—
426	D₄	—	8	2	no	—
427	D₄	—	8	2	no	—
428	D₄	—	8	2	no	—
429	C₂×C₄	—	2	1	no	—
430	C₂×C₄	—	2	1	no	—
431	C₂×C₄	—	2	1	no	—
432	C₂×C₄	—	2	1	no	—
433	C₂×C₄	—	2	1	no	—
434	C₂×C₄	—	2	1	no	—
435	C₂×C₄	—	2	2	no	—
436	C₂×C₄	—	2	2	no	—
437	C₂×C₄	—	2	2	no	—
438	C₂×C₄	—	2	2	no	—
439	C₂×C₄	—	2	2	no	—
440	C₂×C₄	—	2	2	no	—
441	C₂×C₄	—	2	2	no	—
442	C₂×C₄	—	4	1	no	—
443	C₂×C₄	—	4	1	no	—
444	C₂×C₄	—	8	2	no	—
445	C₂×C₄	—	8	2	no	—
446	C₂×C₄	—	8	2	no	—
447	C₂×C₄	—	8	2	no	—
448	C₂×C₄	—	8	2	no	—
449	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
450	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
451	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
452	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
453	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
454	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
455	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
456	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
457	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
458	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
459	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
460	C₂×C₄	C₂⁵	1	1	yes	characteristic
461	C₈	—	2	1	no	—
462	C₈	—	2	1	no	—
463	C₈	—	2	1	no	—
464	C₈	—	2	1	no	—
465	C₈	—	2	1	no	—
466	C₈	—	2	1	no	—
467	C₈	2₋¹⁺⁴	1	2	yes	—
468	C₈	2₋¹⁺⁴	1	2	yes	—
469	C₂²	—	2	1	no	—
470	C₂²	—	2	1	no	—
471	C₂²	—	2	1	no	—
472	C₂²	—	2	1	no	—
473	C₂²	—	2	1	no	—
474	C₂²	—	2	1	no	—
475	C₂²	—	2	1	no	—
476	C₂²	—	2	1	no	—
477	C₂²	—	2	1	no	—
478	C₂²	—	4	2	no	—
479	C₂²	—	4	2	no	—
480	C₂²	—	4	2	no	—
481	C₂²	C₂³×D₄	1	1	yes	characteristic
482	C₄	—	2	1	no	—
483	C₄	—	2	1	no	—
484	C₄	—	2	1	no	—
485	C₄	—	2	1	no	—
486	C₄	—	2	1	no	—
487	C₄	—	2	1	no	—
488	C₄	—	2	1	no	—
489	C₄	—	2	1	no	—
490	C₄	—	2	1	no	—
491	C₄	—	2	1	no	—
492	C₄	—	2	1	no	—
493	C₄	—	4	2	no	—
494	C₄	—	4	2	no	—
495	C₄	—	4	2	no	—
496	C₄	—	4	2	no	—
497	C₄	—	4	2	no	—
498	C₄	—	4	2	no	—
499	C₄	—	4	2	no	—
500	C₄	C₂×2₋¹⁺⁴	1	1	yes	characteristic
501	C₄	C₂×2₋¹⁺⁴	1	1	yes	characteristic
502	C₂	—	4	1	no	—
503	C₂	—	4	1	no	—
504	C₂	—	4	1	no	—
505	C₂	—	8	2	no	—
506	C₂	#3499	1	1	yes	characteristic
507	C₂	#3584	1	1	yes	characteristic
508	C₂	#3584	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. #3565	C₂	semidirect
2. #3388	C₂	semidirect
3. #3383	C₂	semidirect
4. #3380	C₂	semidirect
5. #3351	C₂	semidirect
6. #3350	C₂	semidirect
7. #3348	C₂	semidirect
8. #3342	C₂	semidirect
9. #3341	C₂	semidirect
10. #3339	C₂	semidirect
11. #3339	C₂	semidirect
12. #3336	C₂	semidirect
13. #3336	C₂	semidirect
14. #3244	C₂	semidirect
15. #3244	C₂	semidirect
16. #3240	C₂	semidirect
17. #3175	C₂	semidirect
18. #3175	C₂	semidirect
19. #3168	C₂	semidirect
20. #3164	C₂	semidirect
21. #3164	C₂	semidirect
22. #3160	C₂	semidirect
23. #2966	C₂	semidirect

Maximal subgroups

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

subgroup	index
#3565	2
#3388	2
#3383	2
#3380	2
#3351	2
#3350	2
#3348	2
#3342	2
#3341	2
#3339	2
#3336	2
#3244	2
#3240	2
#3175	2
#3168	2
#3164	2
#3160	2
#2966	2