Subgroups — #60876

Order 256.

820 conjugacy classes of subgroups.

The subgroup lattice has 543 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3495	C₂	1	1	yes	maximal, characteristic
2	#3458	C₂	1	1	yes	maximal, characteristic, complemented
3	#3244	C₂	1	2	yes	maximal, complemented
4	#3243	C₂	1	2	yes	maximal, complemented
5	#3242	C₂	1	2	yes	maximal, complemented
6	#3242	C₂	1	2	yes	maximal, complemented
7	#3240	C₂	1	2	yes	maximal, complemented
8	#3237	C₂	1	2	yes	maximal, complemented
9	#3233	C₂	1	2	yes	maximal, complemented
10	#3231	C₂	1	2	yes	maximal, complemented
11	#3164	C₂	1	1	yes	maximal, characteristic, complemented
12	#3163	C₂	1	1	yes	maximal, characteristic, complemented
13	#3137	C₂	1	1	yes	maximal, characteristic, complemented
14	#3137	C₂	1	1	yes	maximal, characteristic, complemented
15	#3095	C₂	1	1	yes	maximal, characteristic, complemented
16	#3093	C₂	1	1	yes	maximal, characteristic
17	#3091	C₂	1	1	yes	maximal, characteristic
18	C₂×#485	C₂	1	1	yes	maximal, characteristic, complemented
19	#3084	C₂	1	1	yes	maximal, characteristic, complemented
20	#3083	C₂	1	1	yes	maximal, characteristic, complemented
21	#3082	C₂	1	1	yes	maximal, characteristic, complemented
22	#3082	C₂	1	1	yes	maximal, characteristic, complemented
23	#2924	C₂	1	1	yes	maximal, characteristic, complemented
24	#556	—	2	1	no	—
25	#554	—	2	1	no	—
26	#552	—	2	2	no	—
27	#552	—	2	1	no	—
28	#552	—	2	1	no	—
29	#551	—	2	2	no	—
30	#544	—	2	1	no	—
31	#544	—	2	1	no	—
32	#544	C₂²	1	1	yes	characteristic
33	#544	C₂²	1	1	yes	characteristic
34	#544	C₂²	1	1	yes	characteristic
35	#544	C₂²	1	1	yes	characteristic
36	#544	C₂²	1	1	yes	characteristic
37	#544	C₂²	1	2	yes	—
38	#544	C₂²	1	2	yes	—
39	#543	—	2	2	no	—
40	#542	C₂²	1	2	yes	—
41	#541	C₂²	1	2	yes	—
42	#536	C₂²	1	1	yes	characteristic
43	#533	—	2	2	no	—
44	#533	—	2	1	no	—
45	#533	—	2	1	no	—
46	#533	C₂²	1	2	yes	—
47	#533	C₂²	1	2	yes	—
48	#533	C₂²	1	2	yes	—
49	#529	C₂²	1	2	yes	—
50	#525	C₂²	1	1	yes	characteristic
51	C₂×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
52	#520	C₂²	1	1	yes	characteristic
53	#519	C₂²	1	1	yes	characteristic
54	C₂×#117	C₂²	1	1	yes	characteristic
55	C₂×#117	C₂²	1	1	yes	characteristic
56	C₂×#117	C₂²	1	1	yes	characteristic
57	#501	C₂²	1	2	yes	complemented
58	#501	C₂²	1	2	yes	complemented
59	#501	C₂²	1	2	yes	complemented
60	#501	C₂²	1	2	yes	complemented
61	#500	C₂²	1	2	yes	complemented
62	#499	C₂²	1	2	yes	complemented
63	#499	C₂²	1	2	yes	complemented
64	#498	C₂²	1	2	yes	complemented
65	#491	C₂²	1	2	yes	complemented
66	#491	C₂²	1	2	yes	complemented
67	#489	C₂²	1	2	yes	complemented
68	#489	C₂²	1	2	yes	complemented
69	#488	C₂²	1	2	yes	complemented
70	#488	C₂²	1	2	yes	complemented
71	#487	C₂²	1	2	yes	complemented
72	#487	C₂²	1	2	yes	complemented
73	#485	C₂²	1	2	yes	—
74	#485	C₂²	1	2	yes	—
75	#485	C₂²	1	2	yes	—
76	#485	C₂²	1	2	yes	—
77	#485	C₂²	1	1	yes	characteristic
78	#485	C₂²	1	1	yes	characteristic
79	#485	C₂²	1	2	yes	—
80	#485	C₂²	1	2	yes	—
81	#485	C₂²	1	2	yes	—
82	#485	C₂²	1	2	yes	—
83	#484	C₂²	1	1	yes	characteristic
84	#484	C₂²	1	2	yes	—
85	#483	C₂²	1	1	yes	characteristic
86	#483	C₂²	1	2	yes	—
87	#482	C₂²	1	1	yes	characteristic
88	#482	C₂²	1	1	yes	characteristic
89	#482	C₂²	1	2	yes	—
90	#482	C₂²	1	2	yes	—
91	#481	C₂²	1	1	yes	characteristic
92	#480	C₂²	1	1	yes	characteristic
93	#479	C₂²	1	2	yes	complemented
94	#479	C₂²	1	2	yes	complemented
95	#479	C₂²	1	2	yes	complemented
96	#479	C₂²	1	2	yes	complemented
97	#479	C₂²	1	2	yes	complemented
98	#479	C₂²	1	2	yes	complemented
99	#478	C₂²	1	2	yes	complemented
100	#478	C₂²	1	2	yes	complemented
101	#477	C₂²	1	2	yes	complemented
102	#477	C₂²	1	2	yes	complemented
103	#477	C₂²	1	2	yes	complemented
104	#476	C₂²	1	2	yes	complemented
105	#475	C₂²	1	2	yes	complemented
106	#475	C₂²	1	2	yes	complemented
107	#475	C₂²	1	2	yes	complemented
108	#474	C₂²	1	2	yes	complemented
109	#433	C₂²	1	2	yes	—
110	#433	C₂²	1	2	yes	—
111	#432	C₂²	1	2	yes	—
112	#431	C₂²	1	2	yes	—
113	#428	C₂²	1	1	yes	characteristic
114	#428	C₂²	1	1	yes	characteristic
115	#428	C₂²	1	1	yes	characteristic
116	#428	C₂²	1	1	yes	characteristic
117	#427	C₂²	1	1	yes	characteristic
118	#427	C₂²	1	1	yes	characteristic
119	C₂×#107	C₂²	1	1	yes	characteristic
120	C₂×#106	C₂²	1	1	yes	characteristic
121	#424	C₂²	1	1	yes	characteristic
122	#424	C₂²	1	1	yes	characteristic
123	#419	C₂²	1	1	yes	characteristic
124	#419	C₂²	1	1	yes	characteristic
125	#417	C₂²	1	1	yes	characteristic
126	#417	C₂²	1	1	yes	characteristic
127	#416	C₂²	1	1	yes	characteristic
128	#416	C₂²	1	1	yes	characteristic
129	C₂×#103	C₂²	1	1	yes	characteristic
130	C₂×#103	C₂²	1	1	yes	characteristic
131	#407	C₂²	1	1	yes	characteristic
132	C₂×C₂²⋊C₈	C₂²	1	1	yes	characteristic
133	#405	C₂²	1	1	yes	characteristic
134	#405	C₂²	1	1	yes	characteristic
135	C₂×#41	C₂³	1	1	yes	characteristic
136	C₂²×Q₈	C₂³	1	1	yes	characteristic
137	C₂³×C₄	C₂³	1	1	yes	characteristic
138	C₂×M₁₆	C₂³	1	1	yes	characteristic
139	C₂×M₁₆	C₂³	1	1	yes	characteristic
140	C₂²×C₈	C₂³	1	1	yes	characteristic
141	C₂²×C₈	C₂³	1	1	yes	characteristic
142	C₄⋊Q₈	—	2	1	no	—
143	C₄⋊Q₈	—	2	1	no	—
144	C₄⋊Q₈	—	2	1	no	—
145	C₄⋊Q₈	—	2	2	no	—
146	C₄⋊Q₈	—	2	1	no	—
147	C₄⋊Q₈	—	2	2	no	—
148	C₄⋊Q₈	—	2	1	no	—
149	C₄⋊Q₈	C₂³	1	2	yes	—
150	C₄⋊Q₈	C₂³	1	2	yes	—
151	C₄⋊Q₈	C₂³	1	2	yes	—
152	C₄⋊Q₈	C₂³	1	2	yes	—
153	C₄⋊Q₈	C₂³	1	2	yes	—
154	C₄⋊Q₈	C₂³	1	2	yes	—
155	#126	—	2	2	no	—
156	#126	—	2	2	no	—
157	#126	—	2	2	no	—
158	#126	—	2	2	no	—
159	#125	—	2	1	no	—
160	#125	—	2	1	no	—
161	#125	—	2	1	no	—
162	#125	—	2	2	no	—
163	#125	—	2	1	no	—
164	#125	—	2	2	no	—
165	#125	—	2	2	no	—
166	#125	—	2	2	no	—
167	#125	—	2	1	no	—
168	#125	—	2	2	no	—
169	#125	C₂³	1	2	yes	—
170	#125	C₂³	1	2	yes	—
171	#125	C₂³	1	2	yes	—
172	#125	C₂³	1	2	yes	—
173	#125	C₂³	1	2	yes	—
174	#124	—	2	2	no	—
175	#124	C₂³	1	2	yes	—
176	#123	—	2	1	no	—
177	#123	—	2	2	no	—
178	#123	—	2	2	no	—
179	#123	—	2	2	no	—
180	C₂²⋊Q₈	—	2	1	no	—
181	C₂²⋊Q₈	—	2	1	no	—
182	C₂²⋊Q₈	—	2	2	no	—
183	C₂²⋊Q₈	—	2	2	no	—
184	C₂²⋊Q₈	—	2	2	no	—
185	C₂²⋊Q₈	—	2	2	no	—
186	C₂²⋊Q₈	—	2	2	no	—
187	C₂²⋊Q₈	—	2	1	no	—
188	C₂²⋊Q₈	—	2	1	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	—	2	2	no	—
198	C₂²⋊Q₈	—	2	2	no	—
199	C₂²⋊Q₈	C₂³	1	2	yes	—
200	C₂²⋊Q₈	C₂³	1	2	yes	—
201	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
202	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
203	#121	C₂³	1	1	yes	characteristic
204	#121	C₂³	1	1	yes	characteristic
205	#120	—	2	1	no	—
206	C₄×Q₈	—	2	1	no	—
207	C₄×Q₈	—	2	1	no	—
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	—	2	2	no	—
213	C₄×Q₈	C₂³	1	2	yes	—
214	C₄×Q₈	C₂³	1	2	yes	—
215	C₄×Q₈	C₂³	1	2	yes	—
216	C₄×D₄	—	2	1	no	—
217	C₄×D₄	—	2	1	no	—
218	C₄×D₄	—	2	2	no	—
219	C₄×D₄	—	2	2	no	—
220	C₄×D₄	C₂³	1	2	yes	—
221	#117	—	2	1	no	—
222	#117	—	2	1	no	—
223	#117	—	2	1	no	—
224	#117	—	2	1	no	—
225	#117	—	2	2	no	—
226	#117	—	2	1	no	—
227	#117	—	2	2	no	—
228	#117	—	2	2	no	—
229	#117	D₄	1	1	yes	characteristic
230	#117	D₄	1	2	yes	—
231	#117	D₄	1	1	yes	characteristic
232	#117	C₂³	1	2	yes	—
233	#117	C₂³	1	1	yes	characteristic
234	#117	C₂³	1	1	yes	characteristic
235	#117	C₂³	1	1	yes	characteristic
236	#117	C₂³	1	1	yes	characteristic
237	#117	C₂³	1	2	yes	—
238	#117	C₂³	1	1	yes	characteristic
239	#117	C₂³	1	1	yes	characteristic
240	#117	C₂³	1	1	yes	characteristic
241	#117	C₂³	1	2	yes	—
242	C₂×C₄⋊C₄	—	2	1	no	—
243	C₂×C₄⋊C₄	—	2	1	no	—
244	C₂×C₄⋊C₄	D₄	1	1	yes	characteristic
245	C₂×C₄⋊C₄	D₄	1	1	yes	characteristic
246	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
247	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
248	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
249	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
250	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
251	C₂×C₂²⋊C₄	—	2	1	no	—
252	C₂×C₂²⋊C₄	—	2	1	no	—
253	C₂×C₂²⋊C₄	—	2	1	no	—
254	C₂×C₂²⋊C₄	D₄	1	2	yes	—
255	C₂×C₄²	—	2	1	no	—
256	C₂×C₄²	—	2	1	no	—
257	C₂×C₄²	C₂³	1	2	yes	—
258	#107	C₂³	1	2	yes	—
259	#107	C₂³	1	2	yes	—
260	#107	C₂³	1	1	yes	characteristic
261	#107	C₂³	1	1	yes	characteristic
262	#107	C₂³	1	1	yes	characteristic
263	#107	C₂³	1	1	yes	characteristic
264	#107	C₂³	1	2	yes	—
265	#107	C₂³	1	2	yes	—
266	#107	C₂³	1	2	yes	—
267	#107	C₂³	1	2	yes	—
268	#106	C₂³	1	2	yes	—
269	#106	C₂³	1	2	yes	—
270	#106	C₂³	1	1	yes	characteristic
271	#106	C₂³	1	1	yes	characteristic
272	#106	C₂³	1	1	yes	characteristic
273	#106	C₂³	1	1	yes	characteristic
274	#106	C₂³	1	2	yes	—
275	#106	C₂³	1	2	yes	—
276	#106	C₂³	1	2	yes	—
277	#106	C₂³	1	2	yes	—
278	C₄⋊C₈	C₂³	1	2	yes	—
279	C₄⋊C₈	C₂³	1	2	yes	—
280	C₄⋊C₈	C₂³	1	2	yes	—
281	C₄⋊C₈	C₂³	1	2	yes	—
282	#103	C₂³	1	2	yes	—
283	#103	C₂³	1	2	yes	—
284	#103	C₂³	1	2	yes	—
285	#103	C₂³	1	2	yes	—
286	#103	C₂³	1	1	yes	characteristic
287	#103	C₂³	1	1	yes	characteristic
288	#103	C₂³	1	1	yes	characteristic
289	#103	C₂³	1	1	yes	characteristic
290	#103	C₂³	1	2	yes	—
291	#103	C₂³	1	2	yes	—
292	#103	C₂³	1	2	yes	—
293	#103	C₂³	1	2	yes	—
294	#103	C₂³	1	2	yes	—
295	#103	C₂³	1	2	yes	—
296	#102	C₂³	1	1	yes	characteristic
297	#102	C₂³	1	1	yes	characteristic
298	#102	C₂³	1	1	yes	characteristic
299	#102	C₂³	1	1	yes	characteristic
300	#102	C₂³	1	2	yes	—
301	#102	C₂³	1	2	yes	—
302	C₂²⋊C₈	C₂³	1	1	yes	characteristic
303	C₂²⋊C₈	C₂³	1	1	yes	characteristic
304	C₂²⋊C₈	C₂³	1	1	yes	characteristic
305	C₂²⋊C₈	C₂³	1	1	yes	characteristic
306	C₂²⋊C₈	C₂³	1	2	yes	—
307	C₂²⋊C₈	C₂³	1	2	yes	—
308	#97	C₂³	1	2	yes	—
309	#97	C₂³	1	2	yes	—
310	C₄×C₈	C₂³	1	2	yes	—
311	C₄×C₈	C₂³	1	2	yes	—
312	C₂⁴	C₂×D₄	1	1	yes	characteristic
313	#41	—	2	2	no	—
314	#41	—	2	2	no	—
315	C₂×Q₈	—	2	1	no	—
316	C₂×Q₈	—	2	2	no	—
317	C₂×Q₈	—	2	2	no	—
318	C₂×Q₈	—	2	2	no	—
319	C₂×Q₈	—	2	2	no	—
320	C₂×Q₈	—	2	2	no	—
321	C₂×Q₈	—	2	2	no	—
322	C₂×Q₈	—	2	2	no	—
323	C₂×Q₈	C₂⁴	1	2	yes	—
324	C₂×Q₈	C₂⁴	1	1	yes	characteristic
325	C₂×D₄	—	2	1	no	—
326	C₂×D₄	—	2	1	no	—
327	C₂×D₄	—	2	1	no	—
328	C₂×D₄	C₂⁴	1	1	yes	characteristic
329	C₂²×C₄	—	2	2	no	—
330	C₂²×C₄	—	2	2	no	—
331	C₂²×C₄	—	2	1	no	—
332	C₂²×C₄	—	2	1	no	—
333	C₂²×C₄	—	2	1	no	—
334	C₂²×C₄	—	2	1	no	—
335	C₂²×C₄	—	2	1	no	—
336	C₂²×C₄	—	2	1	no	—
337	C₂²×C₄	—	2	1	no	—
338	C₂²×C₄	—	2	2	no	—
339	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
340	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
341	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
342	C₂²×C₄	C₂×D₄	1	2	yes	—
343	C₂²×C₄	C₂×D₄	1	2	yes	—
344	C₂²×C₄	C₂⁴	1	1	yes	characteristic
345	C₂²×C₄	C₂⁴	1	1	yes	characteristic
346	C₂²×C₄	C₂⁴	1	1	yes	characteristic
347	M₁₆	—	2	2	no	—
348	M₁₆	—	2	2	no	—
349	C₂×C₈	—	2	2	no	—
350	C₂×C₈	—	2	2	no	—
351	C₂×C₈	C₂⁴	1	1	yes	characteristic
352	C₂×C₈	C₂⁴	1	1	yes	characteristic
353	C₂×C₈	C₂⁴	1	2	yes	—
354	C₂×C₈	C₂⁴	1	2	yes	—
355	C₂×C₈	C₂⁴	1	1	yes	characteristic
356	C₂×C₈	C₂⁴	1	1	yes	characteristic
357	C₄⋊C₄	—	2	1	no	—
358	C₄⋊C₄	—	2	2	no	—
359	C₄⋊C₄	—	2	2	no	—
360	C₄⋊C₄	—	2	2	no	—
361	C₄⋊C₄	—	2	1	no	—
362	C₄⋊C₄	—	2	1	no	—
363	C₄⋊C₄	—	2	1	no	—
364	C₄⋊C₄	—	2	1	no	—
365	C₄⋊C₄	—	2	2	no	—
366	C₄⋊C₄	—	2	2	no	—
367	C₄⋊C₄	—	2	2	no	—
368	C₄⋊C₄	—	2	2	no	—
369	C₄⋊C₄	—	2	2	no	—
370	C₄⋊C₄	—	2	1	no	—
371	C₄⋊C₄	—	2	2	no	—
372	C₄⋊C₄	—	2	1	no	—
373	C₄⋊C₄	—	2	2	no	—
374	C₄⋊C₄	—	2	2	no	—
375	C₄⋊C₄	—	2	2	no	—
376	C₄⋊C₄	—	2	2	no	—
377	C₄⋊C₄	—	2	2	no	—
378	C₄⋊C₄	—	2	2	no	—
379	C₄⋊C₄	—	2	2	no	—
380	C₄⋊C₄	—	2	2	no	—
381	C₄⋊C₄	—	2	2	no	—
382	C₄⋊C₄	—	2	2	no	—
383	C₄⋊C₄	—	2	2	no	—
384	C₄⋊C₄	—	2	2	no	—
385	C₄⋊C₄	—	2	2	no	—
386	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
387	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
388	C₄⋊C₄	C₂×D₄	1	2	yes	—
389	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
390	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
391	C₄⋊C₄	C₂×D₄	1	2	yes	—
392	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
393	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
394	C₄⋊C₄	C₂⁴	1	2	yes	—
395	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
396	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
397	C₄⋊C₄	C₂⁴	1	2	yes	—
398	C₄⋊C₄	C₂⁴	1	2	yes	—
399	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
400	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
401	C₂²⋊C₄	—	2	2	no	—
402	C₂²⋊C₄	—	2	1	no	—
403	C₂²⋊C₄	—	2	1	no	—
404	C₂²⋊C₄	—	2	2	no	—
405	C₂²⋊C₄	—	2	1	no	—
406	C₂²⋊C₄	—	2	1	no	—
407	C₂²⋊C₄	—	2	2	no	—
408	C₂²⋊C₄	—	2	2	no	—
409	C₂²⋊C₄	—	2	1	no	—
410	C₂²⋊C₄	—	2	1	no	—
411	C₂²⋊C₄	—	2	1	no	—
412	C₂²⋊C₄	—	2	1	no	—
413	C₂²⋊C₄	—	2	2	no	—
414	C₂²⋊C₄	—	2	2	no	—
415	C₂²⋊C₄	—	2	1	no	—
416	C₂²⋊C₄	—	2	2	no	—
417	C₂²⋊C₄	C₂×D₄	1	2	yes	—
418	C₂²⋊C₄	C₂×D₄	1	2	yes	—
419	C₂²⋊C₄	C₂×D₄	1	2	yes	—
420	C₂²⋊C₄	C₂×D₄	1	2	yes	—
421	C₄²	—	2	2	no	—
422	C₄²	—	2	1	no	—
423	C₄²	—	2	1	no	—
424	C₄²	—	2	2	no	—
425	C₄²	—	2	1	no	—
426	C₄²	—	2	1	no	—
427	C₄²	—	2	2	no	—
428	C₄²	—	2	2	no	—
429	C₄²	—	2	2	no	—
430	C₄²	—	2	1	no	—
431	C₄²	C₂×D₄	1	2	yes	—
432	C₄²	C₂×D₄	1	2	yes	—
433	C₄²	C₂⁴	1	2	yes	—
434	C₄²	C₂⁴	1	2	yes	—
435	C₂³	—	2	2	no	—
436	C₂³	—	2	1	no	—
437	C₂³	—	4	1	no	—
438	C₂³	—	4	1	no	—
439	C₂³	C₂²×D₄	1	1	yes	characteristic
440	C₂³	C₂²×D₄	1	1	yes	characteristic
441	C₂³	C₂²×D₄	1	1	yes	characteristic
442	Q₈	—	2	2	no	—
443	Q₈	—	2	2	no	—
444	Q₈	—	2	1	no	—
445	Q₈	—	2	1	no	—
446	Q₈	—	4	2	no	—
447	Q₈	—	8	2	no	—
448	Q₈	—	8	2	no	—
449	Q₈	—	8	2	no	—
450	Q₈	—	8	2	no	—
451	Q₈	—	8	2	no	—
452	D₄	—	2	1	no	—
453	D₄	—	2	1	no	—
454	D₄	—	4	2	no	—
455	D₄	—	4	2	no	—
456	D₄	—	8	1	no	—
457	C₂×C₄	—	2	2	no	—
458	C₂×C₄	—	2	2	no	—
459	C₂×C₄	—	2	2	no	—
460	C₂×C₄	—	2	1	no	—
461	C₂×C₄	—	2	1	no	—
462	C₂×C₄	—	2	1	no	—
463	C₂×C₄	—	2	1	no	—
464	C₂×C₄	—	2	1	no	—
465	C₂×C₄	—	2	1	no	—
466	C₂×C₄	—	2	2	no	—
467	C₂×C₄	—	2	1	no	—
468	C₂×C₄	—	2	2	no	—
469	C₂×C₄	—	2	1	no	—
470	C₂×C₄	—	2	1	no	—
471	C₂×C₄	—	2	2	no	—
472	C₂×C₄	—	2	1	no	—
473	C₂×C₄	—	2	1	no	—
474	C₂×C₄	—	2	2	no	—
475	C₂×C₄	—	4	2	no	—
476	C₂×C₄	—	4	2	no	—
477	C₂×C₄	—	4	2	no	—
478	C₂×C₄	—	4	2	no	—
479	C₂×C₄	—	8	2	no	—
480	C₂×C₄	—	8	1	no	—
481	C₂×C₄	—	8	1	no	—
482	C₂×C₄	—	8	1	no	—
483	C₂×C₄	—	8	1	no	—
484	C₂×C₄	—	8	1	no	—
485	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
486	C₂×C₄	C₂²×D₄	1	2	yes	—
487	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
488	C₂×C₄	C₂²×D₄	1	2	yes	—
489	C₂×C₄	C₂²×D₄	1	2	yes	—
490	C₂×C₄	C₂²×D₄	1	2	yes	—
491	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
492	C₂×C₄	2₋¹⁺⁴	1	2	yes	—
493	C₂×C₄	2₋¹⁺⁴	1	2	yes	—
494	C₂×C₄	C₂⁵	1	1	yes	characteristic
495	C₈	—	2	1	no	—
496	C₈	—	2	1	no	—
497	C₈	—	2	1	no	—
498	C₈	—	2	1	no	—
499	C₈	—	2	2	no	—
500	C₈	—	2	2	no	—
501	C₂²	—	2	1	no	—
502	C₂²	—	2	1	no	—
503	C₂²	—	2	1	no	—
504	C₂²	—	2	1	no	—
505	C₂²	—	2	1	no	—
506	C₂²	—	2	1	no	—
507	C₂²	—	2	1	no	—
508	C₂²	—	2	1	no	—
509	C₂²	—	4	1	no	—
510	C₂²	—	4	1	no	—
511	C₂²	—	4	1	no	—
512	C₂²	—	8	2	no	—
513	C₂²	#536	1	2	yes	—
514	C₂²	C₂³×D₄	1	1	yes	characteristic
515	C₄	—	2	2	no	—
516	C₄	—	2	2	no	—
517	C₄	—	2	2	no	—
518	C₄	—	2	2	no	—
519	C₄	—	2	1	no	—
520	C₄	—	2	1	no	—
521	C₄	—	4	2	no	—
522	C₄	—	4	2	no	—
523	C₄	—	4	1	no	—
524	C₄	—	4	1	no	—
525	C₄	—	4	1	no	—
526	C₄	—	4	2	no	—
527	C₄	—	4	1	no	—
528	C₄	—	4	1	no	—
529	C₄	—	4	1	no	—
530	C₄	—	4	1	no	—
531	C₄	—	4	2	no	—
532	C₄	#536	1	2	yes	—
533	C₄	C₂×2₋¹⁺⁴	1	1	yes	characteristic
534	C₄	C₂×2₋¹⁺⁴	1	1	yes	characteristic
535	C₂	—	2	2	no	—
536	C₂	—	4	1	no	—
537	C₂	—	4	1	no	—
538	C₂	—	8	1	no	—
539	C₂	C₂×#536	1	1	yes	characteristic
540	C₂	#3584	1	1	yes	characteristic
541	C₂	#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵
prime radical	#525	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂×#117 ◁ G
LECS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
2. #3458	C₂	semidirect
3. #3244	C₂	semidirect
4. #3243	C₂	semidirect
5. #3242	C₂	semidirect
6. #3242	C₂	semidirect
7. #3240	C₂	semidirect
8. #3237	C₂	semidirect
9. #3233	C₂	semidirect
10. #3231	C₂	semidirect
11. #3164	C₂	semidirect
12. #3163	C₂	semidirect
13. #3137	C₂	semidirect
14. #3137	C₂	semidirect
15. #3095	C₂	semidirect
18. C₂×#485	C₂	semidirect
19. #3084	C₂	semidirect
20. #3083	C₂	semidirect
21. #3082	C₂	semidirect
22. #3082	C₂	semidirect
23. #2924	C₂	semidirect
57. #501	C₂²	semidirect
58. #501	C₂²	semidirect
59. #501	C₂²	semidirect
60. #501	C₂²	semidirect
61. #500	C₂²	semidirect
62. #499	C₂²	semidirect
63. #499	C₂²	semidirect
64. #498	C₂²	semidirect
65. #491	C₂²	semidirect
66. #491	C₂²	semidirect
67. #489	C₂²	semidirect
68. #489	C₂²	semidirect
69. #488	C₂²	semidirect
70. #488	C₂²	semidirect
71. #487	C₂²	semidirect
72. #487	C₂²	semidirect
93. #479	C₂²	semidirect
94. #479	C₂²	semidirect
95. #479	C₂²	semidirect
96. #479	C₂²	semidirect
97. #479	C₂²	semidirect
98. #479	C₂²	semidirect
99. #478	C₂²	semidirect
100. #478	C₂²	semidirect
101. #477	C₂²	semidirect
102. #477	C₂²	semidirect
103. #477	C₂²	semidirect
104. #476	C₂²	semidirect
105. #475	C₂²	semidirect
106. #475	C₂²	semidirect
107. #475	C₂²	semidirect
108. #474	C₂²	semidirect

Maximal subgroups

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

subgroup	index
#3495	2
#3458	2
#3244	2
#3243	2
#3242	2
#3240	2
#3237	2
#3233	2
#3231	2
#3164	2
#3163	2
#3137	2
#3095	2
#3093	2
#3091	2
C₂×#485	2
#3084	2
#3083	2
#3082	2
#2924	2