Subgroups — #61487

Order 256.

900 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3521	C₂	1	2	yes	maximal, complemented
2	#3393	C₂	1	1	yes	maximal, characteristic, complemented
3	#3380	C₂	1	1	yes	maximal, characteristic, complemented
4	#3376	C₂	1	2	yes	maximal, complemented
5	#3342	C₂	1	1	yes	maximal, characteristic, complemented
6	#3339	C₂	1	1	yes	maximal, characteristic, complemented
7	#3336	C₂	1	1	yes	maximal, characteristic, complemented
8	#3323	C₂	1	2	yes	maximal, complemented
9	#3311	C₂	1	2	yes	maximal, complemented
10	#3307	C₂	1	2	yes	maximal, complemented
11	#3283	C₂	1	1	yes	maximal, characteristic, complemented
12	#3280	C₂	1	1	yes	maximal, characteristic, complemented
13	#3280	C₂	1	1	yes	maximal, characteristic, complemented
14	#3177	C₂	1	1	yes	maximal, characteristic, complemented
15	#3175	C₂	1	1	yes	maximal, characteristic, complemented
16	#3168	C₂	1	1	yes	maximal, characteristic, complemented
17	#3125	C₂	1	2	yes	maximal, complemented
18	#3123	C₂	1	2	yes	maximal, complemented
19	#3111	C₂	1	2	yes	maximal, complemented
20	#2966	C₂	1	1	yes	maximal, characteristic, complemented
21	#2951	C₂	1	1	yes	maximal, characteristic, complemented
22	#2948	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄×#135	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#135	C₂²	1	1	yes	characteristic
25	C₂×#135	C₂²	1	1	yes	characteristic
26	C₂²×D₈	C₂²	1	1	yes	characteristic
27	#556	C₂²	1	2	yes	—
28	#556	C₂²	1	2	yes	complemented
29	#554	C₂²	1	2	yes	complemented
30	#553	—	2	2	no	—
31	#553	C₂²	1	2	yes	complemented
32	#552	—	2	2	no	—
33	#552	C₂²	1	2	yes	—
34	#551	—	2	2	no	—
35	#551	—	2	2	no	—
36	#547	C₂²	1	2	yes	complemented
37	#546	C₂²	1	2	yes	—
38	#546	C₂²	1	2	yes	—
39	#542	C₂²	1	2	yes	complemented
40	#541	C₂²	1	2	yes	—
41	#539	—	2	2	no	—
42	#538	—	2	2	no	—
43	#529	—	2	2	no	—
44	#529	C₂²	1	1	yes	characteristic
45	#529	C₂²	1	2	yes	complemented
46	C₂×#126	—	2	2	no	—
47	#520	C₂²	1	2	yes	complemented
48	#518	C₂²	1	2	yes	—
49	C₄×#41	C₂²	1	2	yes	complemented
50	#500	C₂²	1	1	yes	characteristic, complemented
51	#499	C₂²	1	1	yes	characteristic, complemented
52	#499	C₂²	1	1	yes	characteristic, complemented
53	#495	C₂²	1	1	yes	characteristic
54	#495	C₂²	1	1	yes	characteristic
55	#494	C₂²	1	1	yes	characteristic, complemented
56	#491	C₂²	1	2	yes	complemented
57	#489	C₂²	1	2	yes	complemented
58	#488	C₂²	1	2	yes	complemented
59	#485	C₂²	1	2	yes	—
60	#485	C₂²	1	2	yes	—
61	#485	C₂²	1	2	yes	complemented
62	#483	C₂²	1	2	yes	complemented
63	#482	C₂²	1	2	yes	complemented
64	#481	C₂²	1	2	yes	complemented
65	#479	C₂²	1	2	yes	complemented
66	#478	C₂²	1	2	yes	complemented
67	#478	C₂²	1	2	yes	complemented
68	#478	C₂²	1	2	yes	complemented
69	#476	C₂²	1	2	yes	complemented
70	#475	C₂²	1	2	yes	complemented
71	#470	C₂²	1	2	yes	—
72	#468	C₂²	1	2	yes	complemented
73	#467	C₂²	1	1	yes	characteristic
74	#467	C₂²	1	1	yes	characteristic
75	#467	C₂²	1	1	yes	characteristic, complemented
76	#467	C₂²	1	1	yes	characteristic, complemented
77	#466	C₂²	1	1	yes	characteristic
78	#466	C₂²	1	1	yes	characteristic
79	#465	C₂²	1	2	yes	complemented
80	#464	C₂²	1	2	yes	complemented
81	#464	C₂²	1	2	yes	complemented
82	#463	C₂²	1	2	yes	—
83	#463	C₂²	1	2	yes	—
84	#461	C₂²	1	2	yes	complemented
85	#461	C₂²	1	2	yes	complemented
86	#452	C₂²	1	2	yes	complemented
87	#452	C₂²	1	2	yes	complemented
88	#450	C₂²	1	2	yes	—
89	#450	C₂²	1	2	yes	—
90	#449	C₂²	1	2	yes	—
91	#449	C₂²	1	2	yes	—
92	#446	C₂²	1	1	yes	characteristic, complemented
93	C₈×Q₈	C₂²	1	1	yes	characteristic, complemented
94	#442	C₂²	1	2	yes	—
95	#442	C₂²	1	2	yes	—
96	#441	C₂²	1	2	yes	complemented
97	#440	C₂²	1	2	yes	complemented
98	#440	C₂²	1	2	yes	complemented
99	#440	C₂²	1	2	yes	complemented
100	C₄×Q₁₆	C₂²	1	1	yes	characteristic, complemented
101	C₄×Q₁₆	C₂²	1	1	yes	characteristic, complemented
102	C₄×Q₁₆	C₂²	1	1	yes	characteristic, complemented
103	C₄×Q₁₆	C₂²	1	1	yes	characteristic, complemented
104	C₄×SD₁₆	C₂²	1	2	yes	complemented
105	C₄×SD₁₆	C₂²	1	2	yes	complemented
106	C₄×SD₁₆	C₂²	1	2	yes	complemented
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	C₄×D₈	C₂²	1	1	yes	characteristic
111	C₄×D₈	C₂²	1	1	yes	characteristic
112	C₄×D₈	C₂²	1	1	yes	characteristic
113	#436	C₂²	1	1	yes	characteristic
114	#435	C₂²	1	1	yes	characteristic
115	#435	C₂²	1	1	yes	characteristic, complemented
116	C₈×D₄	C₂²	1	1	yes	characteristic
117	C₈×D₄	C₂²	1	1	yes	characteristic
118	C₈×D₄	C₂²	1	1	yes	characteristic, complemented
119	#433	C₂²	1	1	yes	characteristic
120	#433	C₂²	1	1	yes	characteristic, complemented
121	#432	C₂²	1	1	yes	characteristic, complemented
122	#427	C₂²	1	1	yes	characteristic
123	#427	C₂²	1	1	yes	characteristic, complemented
124	C₂×#107	C₂²	1	1	yes	characteristic, complemented
125	#418	C₂²	1	2	yes	—
126	#417	C₂²	1	2	yes	complemented
127	#416	C₂²	1	2	yes	complemented
128	#405	C₂²	1	1	yes	characteristic
129	#405	C₂²	1	1	yes	characteristic, complemented
130	C₂×C₄×C₈	C₂²	1	1	yes	characteristic, complemented
131	C₂×#41	C₂³	1	2	yes	—
132	C₂×#41	C₂³	1	2	yes	—
133	C₂²×D₄	C₂³	1	2	yes	—
134	#135	—	2	4	no	—
135	#135	—	2	4	no	—
136	C₂×Q₁₆	C₂³	1	1	yes	characteristic
137	C₂×Q₁₆	C₂³	1	1	yes	characteristic
138	C₂×Q₁₆	C₂³	1	2	yes	—
139	C₂×SD₁₆	C₂³	1	2	yes	—
140	C₂×SD₁₆	C₂³	1	2	yes	—
141	C₂×SD₁₆	C₂³	1	2	yes	—
142	C₂×SD₁₆	C₂³	1	2	yes	—
143	C₂×D₈	—	2	4	no	—
144	C₂×D₈	C₂³	1	1	yes	characteristic
145	C₂×D₈	C₂³	1	2	yes	—
146	C₂×D₈	C₂³	1	1	yes	characteristic
147	C₂×M₁₆	C₂³	1	1	yes	characteristic
148	C₂×M₁₆	C₂³	1	1	yes	characteristic
149	C₂²×C₈	C₂³	1	1	yes	characteristic
150	C₂²×C₈	C₂³	1	1	yes	characteristic
151	C₂²×C₈	C₂³	1	1	yes	characteristic
152	C₂²×C₈	C₂³	1	1	yes	characteristic
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	#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	#126	D₄	1	1	yes	characteristic
166	#126	D₄	1	1	yes	characteristic
167	#125	—	2	2	no	—
168	#125	—	2	2	no	—
169	#125	—	2	2	no	—
170	#125	D₄	1	1	yes	characteristic
171	#125	C₂³	1	2	yes	—
172	#125	C₂³	1	2	yes	—
173	#124	—	2	2	no	—
174	#124	—	2	2	no	—
175	#124	D₄	1	1	yes	characteristic
176	#124	C₂³	1	2	yes	—
177	#124	C₂³	1	2	yes	—
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	—	2	2	no	—
185	#123	—	2	2	no	—
186	#123	D₄	1	1	yes	characteristic
187	#123	D₄	1	1	yes	characteristic
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	D₄	1	1	yes	characteristic
194	C₂²⋊Q₈	C₂³	1	2	yes	—
195	C₂²⋊Q₈	C₂³	1	2	yes	—
196	C₂²⋊Q₈	C₂³	1	2	yes	—
197	C₂²⋊Q₈	C₂³	1	2	yes	—
198	#121	—	2	2	no	—
199	#121	—	2	2	no	—
200	#121	—	2	2	no	—
201	#121	—	2	2	no	—
202	#121	D₄	1	1	yes	characteristic
203	#121	C₂³	1	2	yes	—
204	#121	C₂³	1	2	yes	—
205	#120	—	2	2	no	—
206	#120	—	2	2	no	—
207	C₄×Q₈	—	2	2	no	—
208	C₄×Q₈	C₂³	1	2	yes	—
209	C₄×Q₈	C₂³	1	2	yes	—
210	C₄×Q₈	C₂³	1	2	yes	—
211	C₄×Q₈	C₂³	1	2	yes	—
212	C₄×Q₈	C₂³	1	1	yes	characteristic
213	C₄×D₄	—	2	2	no	—
214	C₄×D₄	—	2	2	no	—
215	C₄×D₄	—	2	2	no	—
216	C₄×D₄	—	2	2	no	—
217	C₄×D₄	—	2	2	no	—
218	C₄×D₄	—	2	2	no	—
219	C₄×D₄	—	2	2	no	—
220	C₄×D₄	—	2	2	no	—
221	C₄×D₄	C₂³	1	2	yes	—
222	C₄×D₄	C₂³	1	2	yes	—
223	C₄×D₄	C₂³	1	2	yes	—
224	C₄×D₄	C₂³	1	2	yes	—
225	C₄×D₄	C₂³	1	2	yes	—
226	C₄×D₄	C₂³	1	2	yes	—
227	C₄×D₄	C₂³	1	1	yes	characteristic
228	C₄×D₄	C₂³	1	1	yes	characteristic
229	C₄×D₄	C₂³	1	1	yes	characteristic
230	#117	—	2	2	no	—
231	#117	—	2	2	no	—
232	#117	—	2	2	no	—
233	#117	—	2	2	no	—
234	#117	—	2	2	no	—
235	#117	C₂³	1	2	yes	—
236	#117	C₂³	1	2	yes	—
237	#117	C₂³	1	1	yes	characteristic
238	#117	C₂³	1	1	yes	characteristic
239	C₂×C₄⋊C₄	—	2	2	no	—
240	C₂×C₄⋊C₄	—	2	2	no	—
241	C₂×C₄⋊C₄	—	2	2	no	—
242	C₂×C₄⋊C₄	C₂³	1	2	yes	—
243	C₂×C₂²⋊C₄	—	2	2	no	—
244	C₂×C₂²⋊C₄	—	2	2	no	—
245	C₂×C₂²⋊C₄	—	2	2	no	—
246	C₂×C₂²⋊C₄	—	2	2	no	—
247	C₂×C₄²	—	2	2	no	—
248	C₂×C₄²	C₂³	1	1	yes	characteristic
249	#107	C₂³	1	1	yes	characteristic
250	#107	C₂³	1	1	yes	characteristic
251	#107	C₂³	1	2	yes	—
252	#107	C₂³	1	1	yes	characteristic
253	#107	C₂³	1	1	yes	characteristic
254	#107	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	C₄⋊C₈	C₂³	1	1	yes	characteristic
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	#103	C₂³	1	2	yes	—
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	#103	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	#102	C₂³	1	2	yes	—
279	#102	C₂³	1	2	yes	—
280	#102	C₂³	1	2	yes	—
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	C₂²⋊C₈	C₂³	1	1	yes	characteristic
285	C₂²⋊C₈	C₂³	1	1	yes	characteristic
286	C₂²⋊C₈	C₂³	1	1	yes	characteristic
287	#97	C₂³	1	1	yes	characteristic
288	#97	C₂³	1	1	yes	characteristic
289	#97	C₂³	1	1	yes	characteristic
290	#97	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	C₄×C₈	C₂³	1	1	yes	characteristic
295	C₄×C₈	C₂³	1	1	yes	characteristic
296	C₄×C₈	C₂³	1	1	yes	characteristic
297	C₂⁴	—	2	2	no	—
298	#41	—	2	4	no	—
299	#41	—	2	4	no	—
300	#41	—	4	2	no	—
301	#41	—	4	2	no	—
302	C₂×Q₈	—	2	2	no	—
303	C₂×Q₈	C₂×D₄	1	1	yes	characteristic
304	C₂×Q₈	C₂⁴	1	2	yes	—
305	C₂×Q₈	C₂⁴	1	2	yes	—
306	C₂×D₄	—	2	4	no	—
307	C₂×D₄	—	2	2	no	—
308	C₂×D₄	—	2	2	no	—
309	C₂×D₄	—	2	2	no	—
310	C₂×D₄	—	2	2	no	—
311	C₂×D₄	—	2	2	no	—
312	C₂×D₄	—	4	2	no	—
313	C₂×D₄	C₂×D₄	1	1	yes	characteristic
314	C₂×D₄	C₂×D₄	1	1	yes	characteristic
315	C₂×D₄	C₂×D₄	1	1	yes	characteristic
316	C₂×D₄	C₂⁴	1	2	yes	—
317	C₂×D₄	C₂⁴	1	2	yes	—
318	C₂²×C₄	—	2	2	no	—
319	C₂²×C₄	—	2	2	no	—
320	C₂²×C₄	—	2	2	no	—
321	C₂²×C₄	—	2	2	no	—
322	C₂²×C₄	—	2	2	no	—
323	C₂²×C₄	—	2	2	no	—
324	C₂²×C₄	—	2	2	no	—
325	C₂²×C₄	—	2	2	no	—
326	C₂²×C₄	—	2	2	no	—
327	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
328	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
329	C₂²×C₄	C₂⁴	1	1	yes	characteristic
330	C₂²×C₄	C₂⁴	1	1	yes	characteristic
331	C₂²×C₄	C₂⁴	1	1	yes	characteristic
332	Q₁₆	—	2	2	no	—
333	Q₁₆	—	2	2	no	—
334	Q₁₆	—	4	2	no	—
335	SD₁₆	—	2	4	no	—
336	SD₁₆	—	2	4	no	—
337	SD₁₆	—	4	2	no	—
338	SD₁₆	—	4	2	no	—
339	D₈	—	2	4	no	—
340	D₈	—	2	2	no	—
341	D₈	#41	1	4	yes	—
342	M₁₆	—	4	1	no	—
343	M₁₆	—	4	1	no	—
344	C₂×C₈	—	2	2	no	—
345	C₂×C₈	—	2	2	no	—
346	C₂×C₈	—	2	2	no	—
347	C₂×C₈	—	4	1	no	—
348	C₂×C₈	C₂⁴	1	1	yes	characteristic
349	C₂×C₈	C₂⁴	1	1	yes	characteristic
350	C₂×C₈	C₂⁴	1	1	yes	characteristic
351	C₂×C₈	C₂⁴	1	1	yes	characteristic
352	C₂×C₈	C₂⁴	1	1	yes	characteristic
353	C₂×C₈	C₂⁴	1	1	yes	characteristic
354	C₂×C₈	C₂⁴	1	1	yes	characteristic
355	C₂×C₈	C₂⁴	1	1	yes	characteristic
356	C₄⋊C₄	—	2	2	no	—
357	C₄⋊C₄	—	2	2	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	2	no	—
369	C₄⋊C₄	—	2	2	no	—
370	C₄⋊C₄	—	2	2	no	—
371	C₄⋊C₄	—	2	2	no	—
372	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
373	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
374	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
375	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
376	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
377	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
378	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
379	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
380	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
381	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
382	C₄⋊C₄	C₂⁴	1	2	yes	—
383	C₄⋊C₄	C₂⁴	1	2	yes	—
384	C₄⋊C₄	C₂⁴	1	2	yes	—
385	C₄⋊C₄	C₂⁴	1	2	yes	—
386	C₂²⋊C₄	—	2	2	no	—
387	C₂²⋊C₄	—	2	2	no	—
388	C₂²⋊C₄	—	2	2	no	—
389	C₂²⋊C₄	—	2	2	no	—
390	C₂²⋊C₄	—	2	2	no	—
391	C₂²⋊C₄	—	2	2	no	—
392	C₂²⋊C₄	—	2	2	no	—
393	C₂²⋊C₄	—	2	2	no	—
394	C₂²⋊C₄	—	2	2	no	—
395	C₂²⋊C₄	—	2	2	no	—
396	C₂²⋊C₄	—	2	2	no	—
397	C₂²⋊C₄	—	2	2	no	—
398	C₂²⋊C₄	—	2	2	no	—
399	C₂²⋊C₄	—	2	2	no	—
400	C₂²⋊C₄	—	2	2	no	—
401	C₂²⋊C₄	—	2	2	no	—
402	C₂²⋊C₄	—	2	2	no	—
403	C₂²⋊C₄	—	2	2	no	—
404	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
405	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
406	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
407	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
408	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
409	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
410	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
411	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
412	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
413	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
414	C₄²	—	2	2	no	—
415	C₄²	—	2	2	no	—
416	C₄²	—	2	2	no	—
417	C₄²	—	2	2	no	—
418	C₄²	—	2	2	no	—
419	C₄²	—	2	2	no	—
420	C₄²	C₂×D₄	1	1	yes	characteristic
421	C₄²	C₂×D₄	1	1	yes	characteristic
422	C₄²	C₂⁴	1	1	yes	characteristic
423	C₄²	C₂⁴	1	1	yes	characteristic
424	C₄²	C₂⁴	1	1	yes	characteristic
425	C₄²	C₂⁴	1	1	yes	characteristic
426	C₂³	—	2	2	no	—
427	C₂³	—	2	2	no	—
428	C₂³	—	4	4	no	—
429	C₂³	—	8	2	no	—
430	C₂³	—	8	2	no	—
431	C₂³	C₂²×D₄	1	1	yes	characteristic
432	C₂³	C₂²×D₄	1	1	yes	characteristic
433	C₂³	C₂²×D₄	1	1	yes	characteristic
434	Q₈	—	2	2	no	—
435	Q₈	—	2	2	no	—
436	Q₈	—	2	2	no	—
437	Q₈	—	2	2	no	—
438	Q₈	—	4	1	no	—
439	Q₈	—	8	2	no	—
440	D₄	—	2	2	no	—
441	D₄	—	2	2	no	—
442	D₄	—	2	2	no	—
443	D₄	—	4	1	no	—
444	D₄	—	4	1	no	—
445	D₄	—	4	1	no	—
446	D₄	—	4	4	no	—
447	D₄	—	4	4	no	—
448	D₄	—	4	4	no	—
449	D₄	—	8	2	no	—
450	D₄	—	8	2	no	—
451	D₄	C₂×#41	1	4	yes	—
452	C₂×C₄	—	2	1	no	—
453	C₂×C₄	—	2	1	no	—
454	C₂×C₄	—	2	1	no	—
455	C₂×C₄	—	2	1	no	—
456	C₂×C₄	—	2	1	no	—
457	C₂×C₄	—	2	1	no	—
458	C₂×C₄	—	2	2	no	—
459	C₂×C₄	—	2	2	no	—
460	C₂×C₄	—	2	2	no	—
461	C₂×C₄	—	2	2	no	—
462	C₂×C₄	—	2	2	no	—
463	C₂×C₄	—	2	2	no	—
464	C₂×C₄	—	4	1	no	—
465	C₂×C₄	—	4	1	no	—
466	C₂×C₄	—	4	4	no	—
467	C₂×C₄	—	4	4	no	—
468	C₂×C₄	—	8	2	no	—
469	C₂×C₄	—	8	2	no	—
470	C₂×C₄	—	8	2	no	—
471	C₂×C₄	—	8	2	no	—
472	C₂×C₄	—	8	2	no	—
473	C₂×C₄	—	8	2	no	—
474	C₂×C₄	—	8	2	no	—
475	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
476	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
477	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
478	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
479	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
480	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
481	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
482	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
483	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
484	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
485	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
486	C₂×C₄	C₂⁵	1	1	yes	characteristic
487	C₈	—	2	1	no	—
488	C₈	—	2	1	no	—
489	C₈	—	2	1	no	—
490	C₈	—	2	1	no	—
491	C₈	—	2	1	no	—
492	C₈	—	2	1	no	—
493	C₈	—	2	1	no	—
494	C₈	C₂×#41	1	2	yes	—
495	C₂²	—	2	1	no	—
496	C₂²	—	2	1	no	—
497	C₂²	—	2	1	no	—
498	C₂²	—	2	1	no	—
499	C₂²	—	2	1	no	—
500	C₂²	—	2	1	no	—
501	C₂²	—	2	1	no	—
502	C₂²	—	2	1	no	—
503	C₂²	—	2	1	no	—
504	C₂²	—	2	4	no	—
505	C₂²	—	4	2	no	—
506	C₂²	—	4	2	no	—
507	C₂²	—	4	2	no	—
508	C₂²	—	4	2	no	—
509	C₂²	—	4	2	no	—
510	C₂²	—	16	4	no	—
511	C₂²	C₂³×D₄	1	1	yes	characteristic
512	C₄	—	2	1	no	—
513	C₄	—	2	1	no	—
514	C₄	—	2	1	no	—
515	C₄	—	2	1	no	—
516	C₄	—	2	1	no	—
517	C₄	—	2	1	no	—
518	C₄	—	2	1	no	—
519	C₄	—	2	1	no	—
520	C₄	—	2	1	no	—
521	C₄	—	2	1	no	—
522	C₄	—	2	1	no	—
523	C₄	—	4	2	no	—
524	C₄	—	4	2	no	—
525	C₄	—	4	2	no	—
526	C₄	—	4	2	no	—
527	C₄	—	4	2	no	—
528	C₄	—	4	2	no	—
529	C₄	C₂²×#41	1	1	yes	characteristic
530	C₄	#585	1	1	yes	characteristic
531	C₂	—	4	1	no	—
532	C₂	—	4	1	no	—
533	C₂	—	4	1	no	—
534	C₂	—	4	4	no	—
535	C₂	—	8	2	no	—
536	C₂	D₄×#41	1	1	yes	characteristic
537	C₂	#3584	1	1	yes	characteristic
538	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. #3521	C₂	semidirect
2. #3393	C₂	semidirect
3. #3380	C₂	semidirect
4. #3376	C₂	semidirect
5. #3342	C₂	semidirect
6. #3339	C₂	semidirect
7. #3336	C₂	semidirect
8. #3323	C₂	semidirect
9. #3311	C₂	semidirect
10. #3307	C₂	semidirect
11. #3283	C₂	semidirect
12. #3280	C₂	semidirect
13. #3280	C₂	semidirect
14. #3177	C₂	semidirect
15. #3175	C₂	semidirect
16. #3168	C₂	semidirect
17. #3125	C₂	semidirect
18. #3123	C₂	semidirect
19. #3111	C₂	semidirect
20. #2966	C₂	semidirect
21. #2951	C₂	semidirect
22. #2948	C₂	semidirect
23. C₄×#135	C₂	semidirect
28. #556	C₂²	semidirect
29. #554	C₂²	semidirect
31. #553	C₂²	semidirect
36. #547	C₂²	semidirect
39. #542	C₂²	semidirect
45. #529	C₂²	semidirect
47. #520	C₂²	semidirect
49. C₄×#41	C₂²	semidirect
50. #500	C₂²	semidirect
51. #499	C₂²	semidirect
52. #499	C₂²	semidirect
55. #494	C₂²	semidirect
56. #491	C₂²	semidirect
57. #489	C₂²	semidirect
58. #488	C₂²	semidirect
61. #485	C₂²	semidirect
62. #483	C₂²	semidirect
63. #482	C₂²	semidirect
64. #481	C₂²	semidirect
65. #479	C₂²	semidirect
66. #478	C₂²	semidirect
67. #478	C₂²	semidirect
68. #478	C₂²	semidirect
69. #476	C₂²	semidirect
70. #475	C₂²	semidirect
72. #468	C₂²	semidirect
75. #467	C₂²	semidirect
76. #467	C₂²	semidirect
79. #465	C₂²	semidirect
80. #464	C₂²	semidirect
81. #464	C₂²	semidirect
84. #461	C₂²	semidirect
85. #461	C₂²	semidirect
86. #452	C₂²	semidirect
87. #452	C₂²	semidirect
92. #446	C₂²	semidirect
93. C₈×Q₈	C₂²	semidirect
96. #441	C₂²	semidirect
97. #440	C₂²	semidirect
98. #440	C₂²	semidirect
99. #440	C₂²	semidirect
100. C₄×Q₁₆	C₂²	semidirect
101. C₄×Q₁₆	C₂²	semidirect
102. C₄×Q₁₆	C₂²	semidirect
103. C₄×Q₁₆	C₂²	semidirect
104. C₄×SD₁₆	C₂²	semidirect
105. C₄×SD₁₆	C₂²	semidirect
106. C₄×SD₁₆	C₂²	semidirect
115. #435	C₂²	semidirect
118. C₈×D₄	C₂²	semidirect
120. #433	C₂²	semidirect
121. #432	C₂²	semidirect
123. #427	C₂²	semidirect
124. C₂×#107	C₂²	semidirect
126. #417	C₂²	semidirect
127. #416	C₂²	semidirect
129. #405	C₂²	semidirect
130. C₂×C₄×C₈	C₂²	semidirect

Maximal subgroups

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

subgroup	index
#3521	2
#3393	2
#3380	2
#3376	2
#3342	2
#3339	2
#3336	2
#3323	2
#3311	2
#3307	2
#3283	2
#3280	2
#3177	2
#3175	2
#3168	2
#3125	2
#3123	2
#3111	2
#2966	2
#2951	2
#2948	2
C₄×#135	2