Subgroups — #61275

Order 256.

882 conjugacy classes of subgroups.

The subgroup lattice has 562 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, complemented
2	#3493	C₂	1	1	yes	maximal, characteristic
3	#3356	C₂	1	2	yes	maximal, complemented
4	#3351	C₂	1	2	yes	maximal, complemented
5	#3349	C₂	1	2	yes	maximal, complemented
6	#3349	C₂	1	2	yes	maximal, complemented
7	#3348	C₂	1	2	yes	maximal, complemented
8	#3346	C₂	1	2	yes	maximal, complemented
9	#3340	C₂	1	2	yes	maximal, complemented
10	#3336	C₂	1	2	yes	maximal, complemented
11	#3163	C₂	1	1	yes	maximal, characteristic, complemented
12	#3099	C₂	1	1	yes	maximal, characteristic, complemented
13	#3097	C₂	1	1	yes	maximal, characteristic, complemented
14	#3091	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#485	C₂	1	1	yes	maximal, characteristic, complemented
16	#3083	C₂	1	1	yes	maximal, characteristic, complemented
17	#3082	C₂	1	1	yes	maximal, characteristic, complemented
18	#3063	C₂	1	1	yes	maximal, characteristic, complemented
19	#3056	C₂	1	1	yes	maximal, characteristic, complemented
20	#2947	C₂	1	1	yes	maximal, characteristic, complemented
21	#2933	C₂	1	1	yes	maximal, characteristic, complemented
22	#2913	C₂	1	1	yes	maximal, characteristic, complemented
23	#2911	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#137	C₂²	1	1	yes	characteristic
25	C₂×#131	C₂²	1	1	yes	characteristic
26	C₂²×M₁₆	C₂²	1	1	yes	characteristic
27	#556	—	2	1	no	—
28	#556	C₂²	1	2	yes	—
29	#556	C₂²	1	2	yes	—
30	#555	—	2	1	no	—
31	#555	C₂²	1	2	yes	—
32	#554	C₂²	1	2	yes	—
33	#553	—	2	1	no	—
34	#553	C₂²	1	2	yes	—
35	#552	—	2	2	no	—
36	#552	—	2	1	no	—
37	#552	C₂²	1	2	yes	—
38	#552	C₂²	1	2	yes	—
39	#552	C₂²	1	2	yes	—
40	#551	—	2	2	no	—
41	#544	C₂²	1	1	yes	characteristic
42	#544	C₂²	1	1	yes	characteristic
43	#542	—	2	1	no	—
44	#541	—	2	1	no	—
45	#538	—	2	2	no	—
46	#537	C₂²	1	1	yes	characteristic
47	#536	C₂²	1	1	yes	characteristic
48	#533	—	2	1	no	—
49	#529	—	2	2	no	—
50	#529	—	2	1	no	—
51	#525	C₂²	1	1	yes	characteristic
52	#525	C₂²	1	1	yes	characteristic
53	C₂×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
54	#520	C₂²	1	1	yes	characteristic
55	#520	C₂²	1	1	yes	characteristic
56	#520	C₂²	1	1	yes	characteristic
57	#519	C₂²	1	1	yes	characteristic
58	C₂×#117	C₂²	1	1	yes	characteristic
59	C₂×#117	C₂²	1	1	yes	characteristic
60	#501	C₂²	1	2	yes	complemented
61	#501	C₂²	1	2	yes	complemented
62	#499	C₂²	1	2	yes	complemented
63	#498	C₂²	1	2	yes	complemented
64	#485	C₂²	1	1	yes	characteristic
65	#485	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	1	yes	characteristic
70	#485	C₂²	1	2	yes	complemented
71	#485	C₂²	1	2	yes	complemented
72	#485	C₂²	1	2	yes	complemented
73	#484	C₂²	1	1	yes	characteristic
74	#484	C₂²	1	2	yes	complemented
75	#483	C₂²	1	1	yes	characteristic
76	#483	C₂²	1	2	yes	complemented
77	#483	C₂²	1	2	yes	complemented
78	#482	C₂²	1	1	yes	characteristic
79	#482	C₂²	1	1	yes	characteristic
80	#482	C₂²	1	2	yes	complemented
81	#481	C₂²	1	1	yes	characteristic
82	#481	C₂²	1	2	yes	complemented
83	#480	C₂²	1	1	yes	characteristic
84	#479	C₂²	1	2	yes	complemented
85	#479	C₂²	1	2	yes	complemented
86	#479	C₂²	1	2	yes	complemented
87	#478	C₂²	1	2	yes	complemented
88	#477	C₂²	1	2	yes	complemented
89	#477	C₂²	1	2	yes	complemented
90	#475	C₂²	1	2	yes	complemented
91	#474	C₂²	1	2	yes	complemented
92	#470	C₂²	1	2	yes	—
93	#470	C₂²	1	2	yes	complemented
94	#468	C₂²	1	2	yes	—
95	#468	C₂²	1	2	yes	complemented
96	#467	C₂²	1	2	yes	—
97	#467	C₂²	1	2	yes	complemented
98	#465	C₂²	1	2	yes	—
99	#465	C₂²	1	2	yes	complemented
100	#441	C₂²	1	2	yes	complemented
101	#440	C₂²	1	2	yes	complemented
102	C₄×Q₁₆	C₂²	1	2	yes	complemented
103	C₄×SD₁₆	C₂²	1	2	yes	complemented
104	#436	C₂²	1	2	yes	—
105	#435	C₂²	1	2	yes	—
106	#435	C₂²	1	2	yes	—
107	C₈×D₄	C₂²	1	2	yes	—
108	#428	C₂²	1	1	yes	characteristic
109	#428	C₂²	1	1	yes	characteristic
110	#428	C₂²	1	2	yes	—
111	#428	C₂²	1	2	yes	—
112	#428	C₂²	1	1	yes	characteristic
113	#428	C₂²	1	1	yes	characteristic
114	#428	C₂²	1	1	yes	characteristic
115	#428	C₂²	1	2	yes	complemented
116	#428	C₂²	1	2	yes	complemented
117	#427	C₂²	1	2	yes	—
118	#427	C₂²	1	1	yes	characteristic
119	#427	C₂²	1	2	yes	—
120	#427	C₂²	1	1	yes	characteristic
121	#427	C₂²	1	2	yes	complemented
122	C₂×#107	C₂²	1	1	yes	characteristic
123	C₂×#107	C₂²	1	2	yes	complemented
124	C₂×#106	C₂²	1	1	yes	characteristic
125	#424	C₂²	1	1	yes	characteristic
126	#419	C₂²	1	1	yes	characteristic
127	#417	C₂²	1	1	yes	characteristic
128	#416	C₂²	1	1	yes	characteristic
129	#416	C₂²	1	1	yes	characteristic
130	C₂×#103	C₂²	1	1	yes	characteristic
131	C₂×#103	C₂²	1	1	yes	characteristic
132	#408	C₂²	1	1	yes	characteristic
133	C₂×C₂²⋊C₈	C₂²	1	1	yes	characteristic
134	#405	C₂²	1	1	yes	characteristic
135	C₂×#41	C₂³	1	1	yes	characteristic
136	C₂×#41	C₂³	1	1	yes	characteristic
137	C₂²×Q₈	C₂³	1	1	yes	characteristic
138	C₂³×C₄	C₂³	1	1	yes	characteristic
139	#137	—	2	4	no	—
140	C₂×Q₁₆	C₂³	1	2	yes	—
141	C₂×SD₁₆	C₂³	1	2	yes	—
142	#131	—	2	4	no	—
143	C₂×M₁₆	—	2	4	no	—
144	C₂×M₁₆	C₂³	1	1	yes	characteristic
145	C₂×M₁₆	C₂³	1	2	yes	—
146	C₂×M₁₆	C₂³	1	2	yes	—
147	C₂×M₁₆	C₂³	1	1	yes	characteristic
148	C₂²×C₈	C₂³	1	2	yes	—
149	C₂²×C₈	C₂³	1	1	yes	characteristic
150	C₂²×C₈	C₂³	1	2	yes	—
151	C₂²×C₈	C₂³	1	1	yes	characteristic
152	C₄⋊Q₈	—	2	1	no	—
153	C₄⋊Q₈	—	2	1	no	—
154	C₄⋊Q₈	—	2	1	no	—
155	C₄⋊Q₈	C₂³	1	2	yes	—
156	C₄⋊Q₈	C₂³	1	2	yes	—
157	#126	—	2	2	no	—
158	#126	—	2	2	no	—
159	#126	—	2	2	no	—
160	#126	—	2	2	no	—
161	#126	—	2	2	no	—
162	#126	—	2	2	no	—
163	#126	—	2	2	no	—
164	#126	—	2	2	no	—
165	#125	—	2	1	no	—
166	#125	—	2	2	no	—
167	#125	—	2	2	no	—
168	#125	—	2	2	no	—
169	#125	—	2	2	no	—
170	#125	—	2	1	no	—
171	#125	C₂³	1	2	yes	—
172	#125	C₂³	1	2	yes	—
173	#124	—	2	1	no	—
174	#124	—	2	2	no	—
175	#124	—	2	2	no	—
176	#124	—	2	2	no	—
177	#124	—	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	1	no	—
183	#123	—	2	2	no	—
184	#123	D₄	1	2	yes	—
185	C₂²⋊Q₈	—	2	1	no	—
186	C₂²⋊Q₈	—	2	1	no	—
187	C₂²⋊Q₈	—	2	1	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	D₄	1	1	yes	characteristic
193	C₂²⋊Q₈	D₄	1	1	yes	characteristic
194	C₂²⋊Q₈	C₂³	1	2	yes	—
195	C₂²⋊Q₈	C₂³	1	2	yes	—
196	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
197	C₂²⋊Q₈	C₂³	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	1	no	—
203	#121	—	2	2	no	—
204	#121	—	2	2	no	—
205	#121	D₄	1	1	yes	characteristic
206	#121	D₄	1	1	yes	characteristic
207	#121	C₂³	1	1	yes	characteristic
208	#121	C₂³	1	1	yes	characteristic
209	#121	C₂³	1	2	yes	—
210	#120	—	2	1	no	—
211	#120	D₄	1	2	yes	—
212	C₄×Q₈	—	2	1	no	—
213	C₄×Q₈	—	2	1	no	—
214	C₄×Q₈	—	2	1	no	—
215	C₄×Q₈	—	2	1	no	—
216	C₄×Q₈	—	2	2	no	—
217	C₄×Q₈	—	2	2	no	—
218	C₄×Q₈	C₂³	1	2	yes	—
219	C₄×Q₈	C₂³	1	2	yes	—
220	C₄×Q₈	C₂³	1	2	yes	—
221	C₄×D₄	—	2	2	no	—
222	C₄×D₄	—	2	1	no	—
223	C₄×D₄	—	2	2	no	—
224	C₄×D₄	—	2	1	no	—
225	C₄×D₄	—	2	2	no	—
226	C₄×D₄	—	2	1	no	—
227	C₄×D₄	—	2	1	no	—
228	C₄×D₄	—	2	2	no	—
229	C₄×D₄	—	2	2	no	—
230	C₄×D₄	C₂³	1	2	yes	—
231	C₄×D₄	C₂³	1	2	yes	—
232	C₄×D₄	C₂³	1	2	yes	—
233	#117	—	2	1	no	—
234	#117	—	2	1	no	—
235	#117	—	2	1	no	—
236	#117	—	2	1	no	—
237	#117	—	2	1	no	—
238	#117	—	2	2	no	—
239	#117	—	2	2	no	—
240	#117	—	2	2	no	—
241	#117	—	2	2	no	—
242	#117	—	2	2	no	—
243	#117	C₂³	1	1	yes	characteristic
244	#117	C₂³	1	1	yes	characteristic
245	#117	C₂³	1	1	yes	characteristic
246	#117	C₂³	1	2	yes	—
247	#117	C₂³	1	2	yes	—
248	#117	C₂³	1	1	yes	characteristic
249	#117	C₂³	1	1	yes	characteristic
250	#117	C₂³	1	2	yes	—
251	#117	C₂³	1	2	yes	—
252	#117	C₂³	1	1	yes	characteristic
253	C₂×C₄⋊C₄	—	2	1	no	—
254	C₂×C₄⋊C₄	—	2	1	no	—
255	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
256	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
257	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
258	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
259	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
260	C₂×C₄⋊C₄	C₂³	1	2	yes	—
261	C₂×C₄⋊C₄	C₂³	1	2	yes	—
262	C₂×C₂²⋊C₄	—	2	1	no	—
263	C₂×C₂²⋊C₄	—	2	1	no	—
264	C₂×C₂²⋊C₄	—	2	1	no	—
265	C₂×C₄²	—	2	1	no	—
266	C₂×C₄²	—	2	1	no	—
267	#107	C₂³	1	2	yes	—
268	#107	C₂³	1	2	yes	—
269	#107	C₂³	1	1	yes	characteristic
270	#107	C₂³	1	2	yes	—
271	#107	C₂³	1	2	yes	—
272	#107	C₂³	1	1	yes	characteristic
273	#107	C₂³	1	2	yes	—
274	#107	C₂³	1	2	yes	—
275	#107	C₂³	1	2	yes	—
276	#107	C₂³	1	1	yes	characteristic
277	#107	C₂³	1	1	yes	characteristic
278	#106	C₂³	1	2	yes	—
279	#106	C₂³	1	2	yes	—
280	#106	C₂³	1	2	yes	—
281	#106	C₂³	1	2	yes	—
282	#106	C₂³	1	2	yes	—
283	#106	C₂³	1	2	yes	—
284	#106	C₂³	1	1	yes	characteristic
285	#106	C₂³	1	1	yes	characteristic
286	#106	C₂³	1	1	yes	characteristic
287	#106	C₂³	1	1	yes	characteristic
288	#106	C₂³	1	2	yes	—
289	C₄⋊C₈	C₂³	1	2	yes	—
290	C₄⋊C₈	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	1	yes	characteristic
296	#103	C₂³	1	1	yes	characteristic
297	#103	C₂³	1	1	yes	characteristic
298	#103	C₂³	1	1	yes	characteristic
299	#103	C₂³	1	2	yes	—
300	#103	C₂³	1	2	yes	—
301	#103	C₂³	1	2	yes	—
302	#102	C₂³	1	1	yes	characteristic
303	#102	C₂³	1	1	yes	characteristic
304	#102	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
310	C₂²⋊C₈	C₂³	1	1	yes	characteristic
311	C₂²⋊C₈	C₂³	1	2	yes	—
312	C₂²⋊C₈	C₂³	1	2	yes	—
313	#97	C₂³	1	2	yes	—
314	C₄×C₈	C₂³	1	2	yes	—
315	C₂⁴	C₂×D₄	1	1	yes	characteristic
316	#41	—	2	2	no	—
317	#41	—	2	2	no	—
318	#41	—	2	2	no	—
319	#41	—	2	2	no	—
320	C₂×Q₈	—	2	1	no	—
321	C₂×Q₈	—	2	2	no	—
322	C₂×Q₈	—	2	2	no	—
323	C₂×Q₈	—	2	2	no	—
324	C₂×Q₈	—	2	2	no	—
325	C₂×Q₈	C₂×D₄	1	1	yes	characteristic
326	C₂×Q₈	C₂⁴	1	2	yes	—
327	C₂×Q₈	C₂⁴	1	1	yes	characteristic
328	C₂×D₄	—	2	1	no	—
329	C₂×D₄	—	2	1	no	—
330	C₂×D₄	—	2	1	no	—
331	C₂×D₄	—	2	2	no	—
332	C₂×D₄	C₂×D₄	1	2	yes	—
333	C₂×D₄	C₂×D₄	1	1	yes	characteristic
334	C₂×D₄	C₂×D₄	1	2	yes	—
335	C₂×D₄	C₂×D₄	1	2	yes	—
336	C₂×D₄	C₂⁴	1	1	yes	characteristic
337	C₂²×C₄	—	2	2	no	—
338	C₂²×C₄	—	2	2	no	—
339	C₂²×C₄	—	2	1	no	—
340	C₂²×C₄	—	2	1	no	—
341	C₂²×C₄	—	2	1	no	—
342	C₂²×C₄	—	2	1	no	—
343	C₂²×C₄	—	2	1	no	—
344	C₂²×C₄	—	2	1	no	—
345	C₂²×C₄	—	2	2	no	—
346	C₂²×C₄	—	2	2	no	—
347	C₂²×C₄	—	2	1	no	—
348	C₂²×C₄	—	2	2	no	—
349	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
350	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
351	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
352	C₂²×C₄	C₂⁴	1	2	yes	—
353	C₂²×C₄	C₂⁴	1	1	yes	characteristic
354	C₂²×C₄	C₂⁴	1	1	yes	characteristic
355	C₂²×C₄	C₂⁴	1	1	yes	characteristic
356	Q₁₆	—	2	4	no	—
357	SD₁₆	—	2	4	no	—
358	M₁₆	—	2	2	no	—
359	M₁₆	—	2	4	no	—
360	M₁₆	—	2	4	no	—
361	M₁₆	#41	1	4	yes	—
362	C₂×C₈	—	2	2	no	—
363	C₂×C₈	—	2	2	no	—
364	C₂×C₈	—	2	4	no	—
365	C₂×C₈	—	2	4	no	—
366	C₂×C₈	C₂⁴	1	1	yes	characteristic
367	C₂×C₈	C₂⁴	1	1	yes	characteristic
368	C₂×C₈	C₂⁴	1	1	yes	characteristic
369	C₂×C₈	C₂⁴	1	2	yes	—
370	C₂×C₈	C₂⁴	1	1	yes	characteristic
371	C₂×C₈	C₂⁴	1	2	yes	—
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	1	no	—
377	C₄⋊C₄	—	2	1	no	—
378	C₄⋊C₄	—	2	1	no	—
379	C₄⋊C₄	—	2	1	no	—
380	C₄⋊C₄	—	2	2	no	—
381	C₄⋊C₄	—	2	2	no	—
382	C₄⋊C₄	—	2	1	no	—
383	C₄⋊C₄	—	2	2	no	—
384	C₄⋊C₄	—	2	2	no	—
385	C₄⋊C₄	—	2	2	no	—
386	C₄⋊C₄	—	2	2	no	—
387	C₄⋊C₄	—	2	2	no	—
388	C₄⋊C₄	—	2	2	no	—
389	C₄⋊C₄	—	2	2	no	—
390	C₄⋊C₄	—	2	1	no	—
391	C₄⋊C₄	—	2	2	no	—
392	C₄⋊C₄	—	2	2	no	—
393	C₄⋊C₄	—	2	2	no	—
394	C₄⋊C₄	—	2	2	no	—
395	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
396	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
397	C₄⋊C₄	C₂×D₄	1	2	yes	—
398	C₄⋊C₄	C₂×D₄	1	2	yes	—
399	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
400	C₄⋊C₄	C₂⁴	1	2	yes	—
401	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
402	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
403	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
404	C₄⋊C₄	C₂⁴	1	2	yes	—
405	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
406	C₄⋊C₄	C₂⁴	1	2	yes	—
407	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
408	C₂²⋊C₄	—	2	1	no	—
409	C₂²⋊C₄	—	2	2	no	—
410	C₂²⋊C₄	—	2	2	no	—
411	C₂²⋊C₄	—	2	1	no	—
412	C₂²⋊C₄	—	2	1	no	—
413	C₂²⋊C₄	—	2	1	no	—
414	C₂²⋊C₄	—	2	2	no	—
415	C₂²⋊C₄	—	2	2	no	—
416	C₂²⋊C₄	—	2	2	no	—
417	C₂²⋊C₄	—	2	2	no	—
418	C₂²⋊C₄	—	2	1	no	—
419	C₂²⋊C₄	—	2	2	no	—
420	C₂²⋊C₄	—	2	2	no	—
421	C₂²⋊C₄	—	2	1	no	—
422	C₂²⋊C₄	—	2	1	no	—
423	C₂²⋊C₄	—	2	2	no	—
424	C₂²⋊C₄	—	2	1	no	—
425	C₂²⋊C₄	—	2	2	no	—
426	C₂²⋊C₄	—	2	2	no	—
427	C₂²⋊C₄	—	2	1	no	—
428	C₂²⋊C₄	C₂×D₄	1	2	yes	—
429	C₂²⋊C₄	C₂×D₄	1	2	yes	—
430	C₂²⋊C₄	C₂×D₄	1	2	yes	—
431	C₂²⋊C₄	C₂×D₄	1	2	yes	—
432	C₂²⋊C₄	C₂×D₄	1	2	yes	—
433	C₄²	—	2	2	no	—
434	C₄²	—	2	1	no	—
435	C₄²	—	2	1	no	—
436	C₄²	—	2	2	no	—
437	C₄²	—	2	1	no	—
438	C₄²	—	2	1	no	—
439	C₄²	—	2	2	no	—
440	C₄²	—	2	2	no	—
441	C₄²	—	2	2	no	—
442	C₄²	—	2	2	no	—
443	C₄²	—	2	2	no	—
444	C₄²	—	2	1	no	—
445	C₄²	C₂⁴	1	2	yes	—
446	C₂³	—	2	2	no	—
447	C₂³	—	2	1	no	—
448	C₂³	—	4	1	no	—
449	C₂³	—	4	1	no	—
450	C₂³	C₂²×D₄	1	1	yes	characteristic
451	C₂³	C₂²×D₄	1	1	yes	characteristic
452	C₂³	C₂²×D₄	1	2	yes	—
453	C₂³	C₂²×D₄	1	1	yes	characteristic
454	Q₈	—	2	2	no	—
455	Q₈	—	2	2	no	—
456	Q₈	—	2	1	no	—
457	Q₈	—	2	2	no	—
458	Q₈	—	2	1	no	—
459	Q₈	—	4	2	no	—
460	Q₈	—	8	2	no	—
461	Q₈	—	8	2	no	—
462	D₄	—	2	4	no	—
463	D₄	—	2	2	no	—
464	D₄	—	2	1	no	—
465	D₄	—	2	1	no	—
466	D₄	—	4	2	no	—
467	D₄	—	4	2	no	—
468	D₄	—	4	2	no	—
469	D₄	—	8	1	no	—
470	D₄	—	8	2	no	—
471	D₄	—	8	1	no	—
472	C₂×C₄	—	2	2	no	—
473	C₂×C₄	—	2	2	no	—
474	C₂×C₄	—	2	2	no	—
475	C₂×C₄	—	2	1	no	—
476	C₂×C₄	—	2	2	no	—
477	C₂×C₄	—	2	1	no	—
478	C₂×C₄	—	2	1	no	—
479	C₂×C₄	—	2	1	no	—
480	C₂×C₄	—	2	2	no	—
481	C₂×C₄	—	2	1	no	—
482	C₂×C₄	—	2	2	no	—
483	C₂×C₄	—	2	1	no	—
484	C₂×C₄	—	2	1	no	—
485	C₂×C₄	—	2	1	no	—
486	C₂×C₄	—	2	1	no	—
487	C₂×C₄	—	2	2	no	—
488	C₂×C₄	—	2	2	no	—
489	C₂×C₄	—	2	1	no	—
490	C₂×C₄	—	2	1	no	—
491	C₂×C₄	—	2	2	no	—
492	C₂×C₄	—	4	2	no	—
493	C₂×C₄	—	4	2	no	—
494	C₂×C₄	—	4	2	no	—
495	C₂×C₄	—	8	2	no	—
496	C₂×C₄	—	8	1	no	—
497	C₂×C₄	—	8	2	no	—
498	C₂×C₄	—	8	2	no	—
499	C₂×C₄	—	8	1	no	—
500	C₂×C₄	—	8	1	no	—
501	C₂×C₄	—	8	1	no	—
502	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
503	C₂×C₄	C₂²×D₄	1	2	yes	—
504	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
505	C₂×C₄	C₂²×D₄	1	2	yes	—
506	C₂×C₄	C₂²×D₄	1	2	yes	—
507	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
508	C₂×C₄	C₂×#41	1	2	yes	—
509	C₂×C₄	2₋¹⁺⁴	1	2	yes	—
510	C₂×C₄	C₂⁵	1	1	yes	characteristic
511	C₈	—	2	1	no	—
512	C₈	—	2	1	no	—
513	C₈	—	2	2	no	—
514	C₈	—	2	1	no	—
515	C₈	—	2	1	no	—
516	C₈	C₂×#41	1	4	yes	—
517	C₂²	—	2	1	no	—
518	C₂²	—	2	1	no	—
519	C₂²	—	2	2	no	—
520	C₂²	—	2	1	no	—
521	C₂²	—	2	1	no	—
522	C₂²	—	2	1	no	—
523	C₂²	—	2	2	no	—
524	C₂²	—	2	1	no	—
525	C₂²	—	2	1	no	—
526	C₂²	—	2	1	no	—
527	C₂²	—	2	2	no	—
528	C₂²	—	4	1	no	—
529	C₂²	—	4	1	no	—
530	C₂²	—	4	1	no	—
531	C₂²	—	8	2	no	—
532	C₂²	#547	1	2	yes	—
533	C₂²	C₂³×D₄	1	1	yes	characteristic
534	C₄	—	2	2	no	—
535	C₄	—	2	2	no	—
536	C₄	—	2	1	no	—
537	C₄	—	2	1	no	—
538	C₄	—	2	2	no	—
539	C₄	—	4	2	no	—
540	C₄	—	4	1	no	—
541	C₄	—	4	1	no	—
542	C₄	—	4	2	no	—
543	C₄	—	4	1	no	—
544	C₄	—	4	1	no	—
545	C₄	—	4	1	no	—
546	C₄	—	4	2	no	—
547	C₄	—	4	1	no	—
548	C₄	—	4	1	no	—
549	C₄	—	4	2	no	—
550	C₄	#547	1	2	yes	—
551	C₄	C₂²×#41	1	1	yes	characteristic
552	C₄	C₂×2₋¹⁺⁴	1	1	yes	characteristic
553	C₂	—	2	2	no	—
554	C₂	—	4	2	no	—
555	C₂	—	4	1	no	—
556	C₂	—	4	1	no	—
557	C₂	—	8	1	no	—
558	C₂	C₂×#547	1	1	yes	characteristic
559	C₂	#3584	1	1	yes	characteristic
560	C₂	#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵
prime radical	#3493	C₂
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. #3495	C₂	semidirect
3. #3356	C₂	semidirect
4. #3351	C₂	semidirect
5. #3349	C₂	semidirect
6. #3349	C₂	semidirect
7. #3348	C₂	semidirect
8. #3346	C₂	semidirect
9. #3340	C₂	semidirect
10. #3336	C₂	semidirect
11. #3163	C₂	semidirect
12. #3099	C₂	semidirect
13. #3097	C₂	semidirect
14. #3091	C₂	semidirect
15. C₂×#485	C₂	semidirect
16. #3083	C₂	semidirect
17. #3082	C₂	semidirect
18. #3063	C₂	semidirect
19. #3056	C₂	semidirect
20. #2947	C₂	semidirect
21. #2933	C₂	semidirect
22. #2913	C₂	semidirect
23. #2911	C₂	semidirect
60. #501	C₂²	semidirect
61. #501	C₂²	semidirect
62. #499	C₂²	semidirect
63. #498	C₂²	semidirect
70. #485	C₂²	semidirect
71. #485	C₂²	semidirect
72. #485	C₂²	semidirect
74. #484	C₂²	semidirect
76. #483	C₂²	semidirect
77. #483	C₂²	semidirect
80. #482	C₂²	semidirect
82. #481	C₂²	semidirect
84. #479	C₂²	semidirect
85. #479	C₂²	semidirect
86. #479	C₂²	semidirect
87. #478	C₂²	semidirect
88. #477	C₂²	semidirect
89. #477	C₂²	semidirect
90. #475	C₂²	semidirect
91. #474	C₂²	semidirect
93. #470	C₂²	semidirect
95. #468	C₂²	semidirect
97. #467	C₂²	semidirect
99. #465	C₂²	semidirect
100. #441	C₂²	semidirect
101. #440	C₂²	semidirect
102. C₄×Q₁₆	C₂²	semidirect
103. C₄×SD₁₆	C₂²	semidirect
115. #428	C₂²	semidirect
116. #428	C₂²	semidirect
121. #427	C₂²	semidirect
123. C₂×#107	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
#3493	2
#3356	2
#3351	2
#3349	2
#3348	2
#3346	2
#3340	2
#3336	2
#3163	2
#3099	2
#3097	2
#3091	2
C₂×#485	2
#3083	2
#3082	2
#3063	2
#3056	2
#2947	2
#2933	2
#2913	2
#2911	2