Subgroups — #61386

Order 256.

845 conjugacy classes of subgroups.

The subgroup lattice has 529 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3504	C₂	1	1	yes	maximal, characteristic
2	#3502	C₂	1	1	yes	maximal, characteristic, complemented
3	#3390	C₂	1	2	yes	maximal, complemented
4	#3390	C₂	1	2	yes	maximal, complemented
5	#3388	C₂	1	2	yes	maximal, complemented
6	#3388	C₂	1	2	yes	maximal, complemented
7	#3387	C₂	1	2	yes	maximal, complemented
8	#3385	C₂	1	2	yes	maximal, complemented
9	#3383	C₂	1	2	yes	maximal, complemented
10	#3381	C₂	1	2	yes	maximal, complemented
11	#3166	C₂	1	1	yes	maximal, characteristic, complemented
12	#3164	C₂	1	1	yes	maximal, characteristic, complemented
13	#3163	C₂	1	1	yes	maximal, characteristic, complemented
14	#3084	C₂	1	1	yes	maximal, characteristic
15	#3083	C₂	1	1	yes	maximal, characteristic
16	#3082	C₂	1	1	yes	maximal, characteristic, complemented
17	#3082	C₂	1	1	yes	maximal, characteristic, complemented
18	#3076	C₂	1	1	yes	maximal, characteristic
19	C₂×#479	C₂	1	1	yes	maximal, characteristic, complemented
20	#2962	C₂	1	1	yes	maximal, characteristic, complemented
21	#2947	C₂	1	1	yes	maximal, characteristic
22	#2947	C₂	1	1	yes	maximal, characteristic
23	C₄×#137	C₂	1	1	yes	maximal, characteristic
24	C₂×#137	C₂²	1	1	yes	characteristic
25	Q₈²	—	2	1	no	—
26	Q₈²	C₂²	1	2	yes	—
27	#557	—	2	1	no	—
28	#557	—	2	1	no	—
29	#557	—	2	1	no	—
30	#557	C₂²	1	2	yes	—
31	#557	C₂²	1	2	yes	—
32	#557	C₂²	1	2	yes	—
33	#557	C₂²	1	2	yes	—
34	#557	C₂²	1	2	yes	—
35	#554	—	2	2	no	—
36	#554	—	2	2	no	—
37	#554	C₂²	1	2	yes	—
38	#554	C₂²	1	2	yes	—
39	#544	—	2	1	no	—
40	#544	—	2	1	no	—
41	#544	—	2	2	no	—
42	#544	C₂²	1	1	yes	characteristic
43	#544	C₂²	1	1	yes	characteristic
44	#544	C₂²	1	1	yes	characteristic
45	#544	C₂²	1	1	yes	characteristic
46	#533	—	2	1	no	—
47	#533	—	2	2	no	—
48	#533	C₂²	1	1	yes	characteristic
49	#533	C₂²	1	1	yes	characteristic
50	C₂×#125	—	2	1	no	—
51	C₂×#125	C₂²	1	1	yes	characteristic
52	#520	C₂²	1	1	yes	characteristic
53	#520	C₂²	1	1	yes	characteristic
54	#519	C₂²	1	1	yes	characteristic
55	#519	C₂²	1	1	yes	characteristic
56	C₄×#41	C₂²	1	1	yes	characteristic
57	C₂×C₄×Q₈	C₂²	1	1	yes	characteristic
58	#501	C₂²	1	2	yes	—
59	#501	C₂²	1	2	yes	—
60	#501	C₂²	1	2	yes	—
61	#501	C₂²	1	2	yes	—
62	#501	C₂²	1	2	yes	—
63	#501	C₂²	1	2	yes	—
64	#500	C₂²	1	2	yes	—
65	#499	C₂²	1	2	yes	—
66	#499	C₂²	1	2	yes	—
67	#499	C₂²	1	2	yes	—
68	#499	C₂²	1	2	yes	—
69	#498	C₂²	1	2	yes	—
70	#479	C₂²	1	2	yes	—
71	#479	C₂²	1	2	yes	—
72	#479	C₂²	1	2	yes	—
73	#479	C₂²	1	2	yes	—
74	#479	C₂²	1	1	yes	characteristic
75	#479	C₂²	1	1	yes	characteristic
76	#479	C₂²	1	2	yes	—
77	#479	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	1	yes	characteristic
83	#478	C₂²	1	1	yes	characteristic
84	#478	C₂²	1	2	yes	—
85	#478	C₂²	1	2	yes	—
86	#477	C₂²	1	1	yes	characteristic
87	#477	C₂²	1	2	yes	—
88	#477	C₂²	1	2	yes	—
89	#477	C₂²	1	2	yes	—
90	#476	C₂²	1	1	yes	characteristic
91	#476	C₂²	1	2	yes	—
92	#475	C₂²	1	1	yes	characteristic
93	#475	C₂²	1	2	yes	—
94	#475	C₂²	1	2	yes	—
95	#475	C₂²	1	2	yes	—
96	#474	C₂²	1	1	yes	characteristic
97	#474	C₂²	1	2	yes	—
98	#446	C₂²	1	2	yes	—
99	#446	C₂²	1	2	yes	—
100	#446	C₂²	1	2	yes	—
101	C₈×Q₈	C₂²	1	2	yes	—
102	#441	C₂²	1	2	yes	—
103	#441	C₂²	1	2	yes	—
104	#441	C₂²	1	2	yes	—
105	#440	C₂²	1	2	yes	—
106	#440	C₂²	1	2	yes	—
107	#440	C₂²	1	2	yes	—
108	C₄×Q₁₆	C₂²	1	2	yes	—
109	C₄×Q₁₆	C₂²	1	2	yes	—
110	C₄×Q₁₆	C₂²	1	2	yes	—
111	C₄×SD₁₆	C₂²	1	2	yes	—
112	C₄×SD₁₆	C₂²	1	2	yes	—
113	C₄×SD₁₆	C₂²	1	2	yes	—
114	#428	C₂²	1	1	yes	characteristic
115	#428	C₂²	1	1	yes	characteristic
116	#428	C₂²	1	1	yes	characteristic
117	#428	C₂²	1	1	yes	characteristic
118	#428	C₂²	1	1	yes	characteristic
119	#427	C₂²	1	1	yes	characteristic
120	#427	C₂²	1	1	yes	characteristic
121	C₂×#107	C₂²	1	1	yes	characteristic
122	C₂×#106	C₂²	1	1	yes	characteristic
123	#424	C₂²	1	1	yes	characteristic
124	#424	C₂²	1	1	yes	characteristic
125	C₂×C₄⋊C₈	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	#405	C₂²	1	1	yes	characteristic
133	#405	C₂²	1	1	yes	characteristic
134	C₄×M₁₆	C₂²	1	1	yes	characteristic
135	C₂×#41	C₂³	1	1	yes	characteristic
136	C₂²×Q₈	C₂³	1	1	yes	characteristic
137	#137	Q₈	1	8	yes	complemented
138	C₂×Q₁₆	C₂³	1	2	yes	—
139	C₂×SD₁₆	C₂³	1	2	yes	—
140	C₂×M₁₆	C₂³	1	1	yes	characteristic
141	C₂×M₁₆	C₂³	1	1	yes	characteristic
142	C₂²×C₈	C₂³	1	1	yes	characteristic
143	C₂²×C₈	C₂³	1	1	yes	characteristic
144	C₄⋊Q₈	—	2	2	no	—
145	C₄⋊Q₈	—	2	2	no	—
146	C₄⋊Q₈	—	2	2	no	—
147	C₄⋊Q₈	—	2	2	no	—
148	C₄⋊Q₈	—	2	2	no	—
149	C₄⋊Q₈	—	2	1	no	—
150	C₄⋊Q₈	—	2	1	no	—
151	C₄⋊Q₈	—	2	2	no	—
152	C₄⋊Q₈	—	2	2	no	—
153	C₄⋊Q₈	—	2	2	no	—
154	C₄⋊Q₈	—	2	1	no	—
155	C₄⋊Q₈	—	2	1	no	—
156	C₄⋊Q₈	D₄	1	1	yes	characteristic
157	C₄⋊Q₈	D₄	1	1	yes	characteristic
158	C₄⋊Q₈	C₂³	1	1	yes	characteristic
159	C₄⋊Q₈	C₂³	1	1	yes	characteristic
160	C₄⋊Q₈	C₂³	1	2	yes	—
161	C₄⋊Q₈	C₂³	1	2	yes	—
162	C₄⋊Q₈	C₂³	1	2	yes	—
163	C₄⋊Q₈	C₂³	1	2	yes	—
164	#125	—	2	1	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	2	no	—
171	#125	—	2	2	no	—
172	#125	—	2	2	no	—
173	#125	—	2	2	no	—
174	#125	—	2	2	no	—
175	#125	—	2	2	no	—
176	#125	—	2	1	no	—
177	#125	—	2	1	no	—
178	#125	—	2	1	no	—
179	#125	—	2	1	no	—
180	#125	D₄	1	1	yes	characteristic
181	#125	D₄	1	1	yes	characteristic
182	#125	C₂³	1	2	yes	—
183	#125	C₂³	1	2	yes	—
184	#125	C₂³	1	1	yes	characteristic
185	#125	C₂³	1	1	yes	characteristic
186	#125	C₂³	1	2	yes	—
187	#125	C₂³	1	2	yes	—
188	#125	C₂³	1	2	yes	—
189	#125	C₂³	1	2	yes	—
190	C₂²⋊Q₈	—	2	2	no	—
191	C₂²⋊Q₈	—	2	2	no	—
192	C₂²⋊Q₈	—	2	1	no	—
193	C₂²⋊Q₈	—	2	1	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	—	2	2	no	—
200	C₂²⋊Q₈	—	2	2	no	—
201	C₂²⋊Q₈	—	2	2	no	—
202	C₂²⋊Q₈	D₄	1	2	yes	—
203	C₂²⋊Q₈	D₄	1	2	yes	—
204	C₄×Q₈	—	2	2	no	—
205	C₄×Q₈	—	2	1	no	—
206	C₄×Q₈	—	2	1	no	—
207	C₄×Q₈	—	2	1	no	—
208	C₄×Q₈	—	2	1	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	—	2	2	no	—
214	C₄×Q₈	—	2	1	no	—
215	C₄×Q₈	—	2	1	no	—
216	C₄×Q₈	—	2	1	no	—
217	C₄×Q₈	—	2	1	no	—
218	C₄×Q₈	C₂³	1	2	yes	—
219	C₄×Q₈	C₂³	1	2	yes	—
220	C₄×Q₈	C₂³	1	1	yes	characteristic
221	C₄×Q₈	C₂³	1	1	yes	characteristic
222	C₄×Q₈	C₂³	1	2	yes	—
223	C₄×Q₈	C₂³	1	2	yes	—
224	C₄×Q₈	C₂³	1	2	yes	—
225	C₄×Q₈	C₂³	1	2	yes	—
226	C₄×Q₈	C₂³	1	2	yes	—
227	C₄×Q₈	C₂³	1	2	yes	—
228	C₄×Q₈	C₂³	1	2	yes	—
229	C₄×Q₈	C₂³	1	2	yes	—
230	C₄×D₄	—	2	1	no	—
231	C₄×D₄	—	2	1	no	—
232	C₄×D₄	—	2	2	no	—
233	C₄×D₄	—	2	2	no	—
234	C₄×D₄	C₂³	1	1	yes	characteristic
235	C₄×D₄	C₂³	1	1	yes	characteristic
236	C₄×D₄	C₂³	1	2	yes	—
237	C₄×D₄	C₂³	1	2	yes	—
238	#117	—	2	1	no	—
239	#117	—	2	1	no	—
240	#117	—	2	2	no	—
241	#117	—	2	2	no	—
242	#117	—	2	1	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	1	yes	characteristic
247	#117	C₂³	1	1	yes	characteristic
248	C₂×C₄⋊C₄	—	2	1	no	—
249	C₂×C₄⋊C₄	—	2	1	no	—
250	C₂×C₄⋊C₄	—	2	1	no	—
251	C₂×C₄⋊C₄	—	2	1	no	—
252	C₂×C₄⋊C₄	—	2	1	no	—
253	C₂×C₄⋊C₄	—	2	2	no	—
254	C₂×C₄⋊C₄	—	2	2	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×C₄²	—	2	1	no	—
259	C₂×C₄²	—	2	1	no	—
260	C₂×C₄²	C₂³	1	1	yes	characteristic
261	#107	C₂³	1	2	yes	—
262	#107	C₂³	1	2	yes	—
263	#107	C₂³	1	1	yes	characteristic
264	#107	C₂³	1	1	yes	characteristic
265	#107	C₂³	1	1	yes	characteristic
266	#107	C₂³	1	1	yes	characteristic
267	#107	C₂³	1	2	yes	—
268	#107	C₂³	1	2	yes	—
269	#107	C₂³	1	2	yes	—
270	#107	C₂³	1	2	yes	—
271	#107	C₂³	1	2	yes	—
272	#106	C₂³	1	2	yes	—
273	#106	C₂³	1	2	yes	—
274	#106	C₂³	1	1	yes	characteristic
275	#106	C₂³	1	1	yes	characteristic
276	#106	C₂³	1	1	yes	characteristic
277	#106	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	C₄⋊C₈	C₂³	1	1	yes	characteristic
284	C₄⋊C₈	C₂³	1	1	yes	characteristic
285	C₄⋊C₈	C₂³	1	1	yes	characteristic
286	C₄⋊C₈	C₂³	1	1	yes	characteristic
287	C₄⋊C₈	C₂³	1	2	yes	—
288	C₄⋊C₈	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	#97	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	C₄×C₈	C₂³	1	2	yes	—
313	#41	—	2	2	no	—
314	#41	C₂×Q₈	1	4	yes	—
315	C₂×Q₈	—	2	1	no	—
316	C₂×Q₈	—	2	1	no	—
317	C₂×Q₈	—	2	2	no	—
318	C₂×Q₈	—	2	2	no	—
319	C₂×Q₈	—	2	1	no	—
320	C₂×Q₈	—	2	2	no	—
321	C₂×Q₈	—	2	2	no	—
322	C₂×Q₈	—	2	2	no	—
323	C₂×Q₈	C₂×D₄	1	2	yes	—
324	C₂×Q₈	C₂×D₄	1	2	yes	—
325	C₂×Q₈	C₂×Q₈	1	4	yes	—
326	C₂×Q₈	C₂⁴	1	2	yes	—
327	C₂×Q₈	C₂⁴	1	1	yes	characteristic
328	C₂×D₄	—	2	1	no	—
329	C₂×D₄	C₂⁴	1	1	yes	characteristic
330	C₂²×C₄	—	2	1	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	2	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	C₂⁴	1	1	yes	characteristic
342	Q₁₆	C₂×Q₈	1	8	yes	—
343	SD₁₆	C₂×Q₈	1	8	yes	—
344	M₁₆	—	2	2	no	—
345	M₁₆	C₂×Q₈	1	4	yes	—
346	C₂×C₈	—	2	2	no	—
347	C₂×C₈	—	2	2	no	—
348	C₂×C₈	C₂⁴	1	1	yes	characteristic
349	C₂×C₈	C₂⁴	1	1	yes	characteristic
350	C₂×C₈	C₂⁴	1	2	yes	—
351	C₂×C₈	C₂⁴	1	1	yes	characteristic
352	C₂×C₈	C₂⁴	1	1	yes	characteristic
353	C₂×C₈	C₂⁴	1	2	yes	—
354	C₄⋊C₄	—	2	2	no	—
355	C₄⋊C₄	—	2	2	no	—
356	C₄⋊C₄	—	2	1	no	—
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	2	no	—
362	C₄⋊C₄	—	2	2	no	—
363	C₄⋊C₄	—	2	2	no	—
364	C₄⋊C₄	—	2	2	no	—
365	C₄⋊C₄	—	2	2	no	—
366	C₄⋊C₄	—	2	2	no	—
367	C₄⋊C₄	—	2	2	no	—
368	C₄⋊C₄	—	2	1	no	—
369	C₄⋊C₄	—	2	1	no	—
370	C₄⋊C₄	—	2	1	no	—
371	C₄⋊C₄	—	2	2	no	—
372	C₄⋊C₄	—	2	2	no	—
373	C₄⋊C₄	—	2	2	no	—
374	C₄⋊C₄	—	2	2	no	—
375	C₄⋊C₄	—	2	1	no	—
376	C₄⋊C₄	—	2	1	no	—
377	C₄⋊C₄	—	2	1	no	—
378	C₄⋊C₄	—	2	2	no	—
379	C₄⋊C₄	—	2	2	no	—
380	C₄⋊C₄	—	2	1	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	1	no	—
386	C₄⋊C₄	—	2	1	no	—
387	C₄⋊C₄	—	2	2	no	—
388	C₄⋊C₄	—	2	2	no	—
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	C₂×D₄	1	2	yes	—
393	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
394	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
395	C₄⋊C₄	C₂×D₄	1	2	yes	—
396	C₄⋊C₄	C₂×D₄	1	2	yes	—
397	C₄⋊C₄	C₂×D₄	1	2	yes	—
398	C₄⋊C₄	C₂×D₄	1	2	yes	—
399	C₄⋊C₄	C₂⁴	1	2	yes	—
400	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
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	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	C₂×D₄	1	2	yes	—
416	C₂²⋊C₄	C₂×D₄	1	2	yes	—
417	C₄²	—	2	1	no	—
418	C₄²	—	2	1	no	—
419	C₄²	—	2	1	no	—
420	C₄²	—	2	2	no	—
421	C₄²	—	2	2	no	—
422	C₄²	—	2	2	no	—
423	C₄²	—	2	2	no	—
424	C₄²	—	2	2	no	—
425	C₄²	—	2	2	no	—
426	C₄²	—	2	2	no	—
427	C₄²	—	2	2	no	—
428	C₄²	—	2	1	no	—
429	C₄²	—	2	1	no	—
430	C₄²	C₂×D₄	1	1	yes	characteristic
431	C₄²	C₂×D₄	1	1	yes	characteristic
432	C₄²	C₂⁴	1	1	yes	characteristic
433	C₄²	C₂⁴	1	2	yes	—
434	C₄²	C₂⁴	1	2	yes	—
435	C₄²	C₂⁴	1	1	yes	characteristic
436	C₂³	—	2	1	no	—
437	C₂³	C₂²×D₄	1	1	yes	characteristic
438	Q₈	—	2	4	no	—
439	Q₈	—	2	2	no	—
440	Q₈	—	2	1	no	—
441	Q₈	—	4	2	no	—
442	Q₈	—	4	2	no	—
443	Q₈	—	4	2	no	—
444	Q₈	—	8	1	no	—
445	Q₈	—	8	2	no	—
446	Q₈	—	8	2	no	—
447	Q₈	—	8	2	no	—
448	Q₈	—	8	2	no	—
449	Q₈	C₂²×Q₈	1	4	yes	—
450	Q₈	C₂²×Q₈	1	2	yes	—
451	D₄	—	2	4	no	—
452	D₄	—	2	1	no	—
453	D₄	C₂²×Q₈	1	2	yes	—
454	C₂×C₄	—	2	4	no	—
455	C₂×C₄	—	2	1	no	—
456	C₂×C₄	—	2	2	no	—
457	C₂×C₄	—	2	4	no	—
458	C₂×C₄	—	2	1	no	—
459	C₂×C₄	—	2	1	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	2	no	—
465	C₂×C₄	—	2	2	no	—
466	C₂×C₄	—	2	2	no	—
467	C₂×C₄	—	4	1	no	—
468	C₂×C₄	—	4	1	no	—
469	C₂×C₄	—	8	1	no	—
470	C₂×C₄	—	8	2	no	—
471	C₂×C₄	—	8	1	no	—
472	C₂×C₄	—	8	2	no	—
473	C₂×C₄	—	8	1	no	—
474	C₂×C₄	—	8	1	no	—
475	C₂×C₄	—	8	1	no	—
476	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
477	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
478	C₂×C₄	C₂²×D₄	1	2	yes	—
479	C₂×C₄	C₂²×D₄	1	2	yes	—
480	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
481	C₂×C₄	C₂²×D₄	1	2	yes	—
482	C₂×C₄	C₂²×D₄	1	2	yes	—
483	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
484	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
485	C₂×C₄	C₂²×Q₈	1	2	yes	—
486	C₂×C₄	2₋¹⁺⁴	1	2	yes	—
487	C₂×C₄	C₂⁵	1	1	yes	characteristic
488	C₈	—	2	1	no	—
489	C₈	—	2	1	no	—
490	C₈	—	2	1	no	—
491	C₈	—	2	1	no	—
492	C₈	—	2	2	no	—
493	C₈	C₂²×Q₈	1	4	yes	—
494	C₂²	—	2	1	no	—
495	C₂²	—	2	1	no	—
496	C₂²	—	2	2	no	—
497	C₂²	—	4	1	no	—
498	C₂²	—	4	1	no	—
499	C₂²	D₄×Q₈	1	2	yes	—
500	C₂²	C₂³×D₄	1	1	yes	characteristic
501	C₄	—	2	1	no	—
502	C₄	—	2	1	no	—
503	C₄	—	2	2	no	—
504	C₄	—	2	2	no	—
505	C₄	—	2	1	no	—
506	C₄	—	2	1	no	—
507	C₄	—	2	2	no	—
508	C₄	—	2	2	no	—
509	C₄	—	2	2	no	—
510	C₄	—	2	4	no	—
511	C₄	—	4	2	no	—
512	C₄	—	4	1	no	—
513	C₄	—	4	2	no	—
514	C₄	—	4	1	no	—
515	C₄	—	4	1	no	—
516	C₄	—	4	2	no	—
517	C₄	—	4	1	no	—
518	C₄	—	4	1	no	—
519	C₄	—	4	1	no	—
520	C₄	D₄×Q₈	1	2	yes	—
521	C₄	C₂³×Q₈	1	1	yes	characteristic
522	C₄	C₂×2₋¹⁺⁴	1	1	yes	characteristic
523	C₂	—	2	2	no	—
524	C₂	—	4	2	no	—
525	C₂	C₂×D₄×Q₈	1	1	yes	characteristic
526	C₂	#3584	1	1	yes	characteristic
527	C₂	#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵
prime radical	C₂×#41	C₂³
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂² ◁ #533 ◁ G
LECS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
2. #3502	C₂	semidirect
3. #3390	C₂	semidirect
4. #3390	C₂	semidirect
5. #3388	C₂	semidirect
6. #3388	C₂	semidirect
7. #3387	C₂	semidirect
8. #3385	C₂	semidirect
9. #3383	C₂	semidirect
10. #3381	C₂	semidirect
11. #3166	C₂	semidirect
12. #3164	C₂	semidirect
13. #3163	C₂	semidirect
16. #3082	C₂	semidirect
17. #3082	C₂	semidirect
19. C₂×#479	C₂	semidirect
20. #2962	C₂	semidirect
137. #137	Q₈	semidirect

Maximal subgroups

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

subgroup	index
#3504	2
#3502	2
#3390	2
#3388	2
#3387	2
#3385	2
#3383	2
#3381	2
#3166	2
#3164	2
#3163	2
#3084	2
#3083	2
#3082	2
#3076	2
C₂×#479	2
#2962	2
#2947	2
C₄×#137	2