Subgroups — #72320910

Order 1024.

769 conjugacy classes of subgroups.

The subgroup lattice has 489 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#483544	C₂	1	1	yes	maximal, characteristic
2	#483463	C₂	1	2	yes	maximal, complemented
3	#225782	C₂	1	1	yes	maximal, characteristic
4	#225720	C₂	1	1	yes	maximal, characteristic
5	#140497	C₂	1	1	yes	maximal, characteristic, complemented
6	#140494	C₂	1	1	yes	maximal, characteristic, complemented
7	#136464	C₂	1	2	yes	maximal, complemented
8	#136462	C₂	1	2	yes	maximal, complemented
9	#135794	C₂	1	1	yes	maximal, characteristic, complemented
10	#135073	C₂	1	2	yes	maximal, complemented
11	C₈×#365	C₂	1	1	yes	maximal, characteristic, complemented
12	#33484	C₂²	1	2	yes	—
13	#22688	—	2	1	no	—
14	#18055	—	2	1	no	—
15	C₈×#135	C₂²	1	1	yes	characteristic
16	#17834	C₂²	1	2	yes	—
17	#17826	C₂²	1	2	yes	—
18	C₄×#365	C₂²	1	1	yes	characteristic
19	#12054	C₄	1	1	yes	characteristic, complemented
20	#12054	C₄	1	1	yes	characteristic, complemented
21	#12049	C₄	1	2	yes	complemented
22	#12049	C₄	1	2	yes	complemented
23	C₁₆×D₈	C₄	1	1	yes	characteristic, complemented
24	C₁₆×D₈	C₄	1	1	yes	characteristic, complemented
25	#12030	—	2	2	no	—
26	#12030	C₂²	1	2	yes	—
27	#12029	C₂²	1	2	yes	—
28	#12028	—	2	2	no	—
29	#12020	C₂²	1	2	yes	—
30	#12020	C₂²	1	2	yes	—
31	#12019	—	2	2	no	—
32	#12013	C₂²	1	1	yes	characteristic
33	#12000	C₂²	1	1	yes	characteristic
34	C₂×#1368	—	2	2	no	—
35	#11615	C₂²	1	2	yes	—
36	C₈×M₃₂	C₂²	1	1	yes	characteristic
37	#9634	—	2	1	no	—
38	#9628	—	2	1	no	—
39	#8904	—	2	2	no	—
40	#8900	—	2	2	no	—
41	#8824	C₂²	1	1	yes	characteristic
42	#8822	C₂²	1	1	yes	characteristic
43	#8670	C₂²	1	2	yes	—
44	#8666	C₂²	1	2	yes	—
45	C₈×#108	C₂²	1	1	yes	characteristic
46	C₈×#106	C₂²	1	1	yes	characteristic
47	#7302	C₂²	1	2	yes	—
48	#7300	C₂²	1	2	yes	—
49	#7174	C₂²	1	1	yes	characteristic
50	#7173	C₂²	1	1	yes	characteristic
51	#2990	—	2	2	no	—
52	C₈×#41	C₂³	1	2	yes	—
53	C₂×#443	—	4	1	no	—
54	C₄×#135	D₄	1	1	yes	characteristic
55	#2906	—	2	2	no	—
56	#2183	C₂×C₄	1	2	yes	—
57	#2183	C₂×C₄	1	2	yes	—
58	#2168	—	2	2	no	—
59	#2168	—	2	2	no	—
60	D₄×C₁₆	C₂×C₄	1	2	yes	—
61	D₄×C₁₆	C₂×C₄	1	2	yes	—
62	#2163	—	2	2	no	—
63	#2163	C₂³	1	2	yes	—
64	C₂×#365	—	2	1	no	—
65	C₄×M₃₂	C₂³	1	1	yes	characteristic
66	C₄×M₃₂	C₂³	1	1	yes	characteristic
67	C₂×#346	—	2	2	no	—
68	#1945	—	4	1	no	—
69	#1866	—	4	2	no	—
70	#1848	—	2	1	no	—
71	#1837	—	2	1	no	—
72	#1806	—	2	2	no	—
73	C₄×#108	C₂³	1	1	yes	characteristic
74	C₄×#106	C₂³	1	1	yes	characteristic
75	C₈×C₄⋊C₄	—	2	1	no	—
76	#1591	—	4	1	no	—
77	#1585	—	4	2	no	—
78	C₈×Q₁₆	C₂×C₄	1	1	yes	characteristic
79	C₈×Q₁₆	Q₈	1	1	yes	characteristic
80	C₈×SD₁₆	C₂×C₄	1	2	yes	—
81	C₈×SD₁₆	Q₈	1	2	yes	—
82	C₈×D₈	—	4	1	no	—
83	C₈×D₈	C₂×C₄	1	1	yes	characteristic
84	C₈×D₈	Q₈	1	1	yes	characteristic
85	#1574	—	2	2	no	—
86	#1573	—	4	2	no	—
87	#1570	—	2	2	no	—
88	#1570	—	4	2	no	—
89	#1568	—	2	2	no	—
90	#1567	—	2	1	no	—
91	#1566	—	2	2	no	—
92	#1566	—	2	1	no	—
93	#1566	C₂³	1	2	yes	—
94	#1566	C₂³	1	2	yes	—
95	#1564	D₄	1	1	yes	characteristic
96	#1564	C₂³	1	1	yes	characteristic
97	C₂×#334	—	2	2	no	—
98	C₂×#334	—	2	2	no	—
99	C₂×#334	C₂³	1	1	yes	characteristic
100	#1489	—	2	2	no	—
101	#1476	D₄	1	2	yes	—
102	C₈×M₁₆	—	2	1	no	—
103	C₂×C₈²	C₂³	1	1	yes	characteristic
104	#1383	—	2	1	no	—
105	#1370	C₂×C₄	1	1	yes	characteristic
106	#1370	C₂×C₄	1	1	yes	characteristic
107	#1368	—	2	2	no	—
108	#1368	—	2	2	no	—
109	#1368	—	2	2	no	—
110	#1368	—	2	2	no	—
111	#1368	—	2	2	no	—
112	#1368	—	2	2	no	—
113	#1368	—	4	2	no	—
114	#1368	D₄	1	1	yes	characteristic
115	#1368	D₄	1	1	yes	characteristic
116	#1368	D₄	1	1	yes	characteristic
117	#1368	D₄	1	1	yes	characteristic
118	#1367	C₂×C₄	1	2	yes	—
119	Q₈⋊C₁₆	C₂×C₄	1	2	yes	—
120	Q₈⋊C₁₆	C₂×C₄	1	2	yes	—
121	D₄⋊C₁₆	C₂×C₄	1	2	yes	—
122	D₄⋊C₁₆	C₂×C₄	1	2	yes	—
123	#1311	C₂×C₄	1	1	yes	characteristic
124	#1311	C₂×C₄	1	1	yes	characteristic
125	C₈×C₁₆	C₂×C₄	1	1	yes	characteristic
126	C₈×C₁₆	C₂×C₄	1	1	yes	characteristic
127	#1303	—	2	2	no	—
128	#1299	—	2	2	no	—
129	#1279	—	2	1	no	—
130	#1278	—	2	1	no	—
131	C₂×#135	SD₁₆	1	1	yes	characteristic
132	C₂×#131	—	4	2	no	—
133	C₄×#41	C₂×D₄	1	2	yes	—
134	C₂×M₃₂	—	2	1	no	—
135	C₂×M₃₂	#41	1	1	yes	characteristic
136	C₂×M₃₂	#41	1	1	yes	characteristic
137	C₂²×C₁₆	—	2	2	no	—
138	C₂²×C₁₆	—	2	2	no	—
139	#446	—	4	2	no	—
140	C₈×Q₈	C₂²×C₄	1	2	yes	—
141	C₈×Q₈	C₂×Q₈	1	2	yes	—
142	#443	—	8	4	no	—
143	C₄×Q₁₆	C₄⋊C₄	1	1	yes	characteristic
144	C₄×Q₁₆	SD₁₆	1	1	yes	characteristic
145	C₄×SD₁₆	C₄⋊C₄	1	2	yes	—
146	C₄×SD₁₆	SD₁₆	1	2	yes	—
147	C₄×D₈	C₄⋊C₄	1	1	yes	characteristic
148	C₄×D₈	SD₁₆	1	1	yes	characteristic
149	#435	—	8	2	no	—
150	C₈×D₄	—	2	2	no	—
151	C₈×D₄	—	2	2	no	—
152	C₈×D₄	—	4	2	no	—
153	C₈×D₄	C₂²×C₄	1	2	yes	—
154	C₈×D₄	C₂×Q₈	1	2	yes	—
155	#432	—	4	2	no	—
156	#431	—	2	2	no	—
157	#431	—	2	1	no	—
158	#431	C₂×D₄	1	2	yes	—
159	C₂×#108	—	2	1	no	—
160	C₂×#108	—	4	1	no	—
161	C₂×#108	—	4	1	no	—
162	#427	SD₁₆	1	1	yes	characteristic
163	C₂×#106	—	2	1	no	—
164	#424	—	4	2	no	—
165	#424	—	8	2	no	—
166	#423	—	2	2	no	—
167	#423	—	2	2	no	—
168	#423	—	4	2	no	—
169	C₂×C₄⋊C₈	—	2	1	no	—
170	C₂×C₄⋊C₈	—	4	2	no	—
171	C₂×C₄⋊C₈	—	4	2	no	—
172	C₂×#104	—	4	2	no	—
173	#416	SD₁₆	1	2	yes	—
174	C₄×M₁₆	—	2	1	no	—
175	C₂×C₄×C₈	—	2	2	no	—
176	C₂×C₄×C₈	—	4	1	no	—
177	C₂×C₄×C₈	C₂×D₄	1	1	yes	characteristic
178	C₂×C₄×C₈	C₂×D₄	1	1	yes	characteristic
179	C₂×C₄×C₈	C₂⁴	1	1	yes	characteristic
180	C₄×C₄⋊C₄	—	2	1	no	—
181	#365	—	2	4	no	—
182	C₄⋊C₁₆	—	2	2	no	—
183	C₄⋊C₁₆	—	2	2	no	—
184	C₄⋊C₁₆	C₂²×C₄	1	2	yes	—
185	C₄⋊C₁₆	C₂²×C₄	1	2	yes	—
186	C₂²⋊C₁₆	—	2	2	no	—
187	C₂²⋊C₁₆	—	2	2	no	—
188	C₂²⋊C₁₆	—	2	2	no	—
189	#346	—	2	2	no	—
190	#346	—	2	2	no	—
191	#346	—	2	2	no	—
192	#346	—	2	1	no	—
193	#346	C₂×D₄	1	1	yes	characteristic
194	#346	C₂×D₄	1	1	yes	characteristic
195	C₄×C₁₆	C₂²×C₄	1	1	yes	characteristic
196	C₄×C₁₆	C₂²×C₄	1	1	yes	characteristic
197	C₄×C₁₆	C₂²×C₄	1	1	yes	characteristic
198	C₄×C₁₆	C₂²×C₄	1	1	yes	characteristic
199	#341	—	2	1	no	—
200	#341	—	8	1	no	—
201	#340	—	2	1	no	—
202	#339	—	4	2	no	—
203	#336	—	4	1	no	—
204	#335	—	2	1	no	—
205	#335	—	4	2	no	—
206	#335	—	4	1	no	—
207	#335	—	4	1	no	—
208	#335	C₄⋊C₄	1	1	yes	characteristic
209	#335	C₄⋊C₄	1	1	yes	characteristic
210	#334	—	2	2	no	—
211	#334	—	2	2	no	—
212	#334	—	2	1	no	—
213	#334	—	2	2	no	—
214	#334	—	2	2	no	—
215	#334	—	4	2	no	—
216	#334	—	4	2	no	—
217	#334	—	4	2	no	—
218	#334	—	8	1	no	—
219	#334	C₄⋊C₄	1	2	yes	—
220	#334	C₂×D₄	1	1	yes	characteristic
221	#334	C₂×D₄	1	1	yes	characteristic
222	#334	C₂×D₄	1	1	yes	characteristic
223	#334	C₂×D₄	1	1	yes	characteristic
224	Q₈⋊C₈	—	4	2	no	—
225	Q₈⋊C₈	C₄⋊C₄	1	2	yes	—
226	Q₈⋊C₈	C₄⋊C₄	1	2	yes	—
227	D₄⋊C₈	—	4	2	no	—
228	D₄⋊C₈	C₄⋊C₄	1	2	yes	—
229	D₄⋊C₈	C₄⋊C₄	1	2	yes	—
230	#322	—	4	1	no	—
231	C₈²	—	4	1	no	—
232	C₈²	C₂²×C₄	1	1	yes	characteristic
233	C₈²	C₂²×C₄	1	1	yes	characteristic
234	C₈²	C₂×Q₈	1	1	yes	characteristic
235	C₈²	C₂×Q₈	1	1	yes	characteristic
236	C₂×#41	C₂×SD₁₆	1	2	yes	—
237	#135	—	2	4	no	—
238	C₂×Q₁₆	#106	1	1	yes	characteristic
239	C₂×SD₁₆	#106	1	2	yes	—
240	C₂×D₈	#106	1	1	yes	characteristic
241	#131	—	8	4	no	—
242	#131	—	16	2	no	—
243	C₂×M₁₆	—	4	1	no	—
244	C₂×M₁₆	—	4	2	no	—
245	C₂×M₁₆	—	4	2	no	—
246	C₂×M₁₆	—	8	2	no	—
247	C₂²×C₈	—	2	1	no	—
248	C₂²×C₈	—	2	2	no	—
249	C₂²×C₈	—	2	2	no	—
250	C₂²×C₈	—	4	1	no	—
251	C₂²×C₈	—	8	2	no	—
252	C₂²×C₈	—	8	2	no	—
253	C₂²×C₈	C₂×SD₁₆	1	1	yes	characteristic
254	C₂²×C₈	C₂×SD₁₆	1	1	yes	characteristic
255	C₂²×C₈	C₂×#41	1	1	yes	characteristic
256	C₂²×C₈	2₋¹⁺⁴	1	1	yes	characteristic
257	C₄×Q₈	C₂×C₄⋊C₄	1	2	yes	—
258	C₄×Q₈	C₂×SD₁₆	1	2	yes	—
259	C₄×D₄	—	2	2	no	—
260	C₄×D₄	—	2	2	no	—
261	C₄×D₄	C₂×C₄⋊C₄	1	2	yes	—
262	C₄×D₄	C₂×SD₁₆	1	2	yes	—
263	#117	—	2	2	no	—
264	#117	C₂×SD₁₆	1	2	yes	—
265	C₂×C₄⋊C₄	—	4	1	no	—
266	C₂×C₄²	—	2	2	no	—
267	C₂×C₄²	—	4	1	no	—
268	C₂×C₄²	C₂²×D₄	1	1	yes	characteristic
269	M₃₂	—	2	2	no	—
270	M₃₂	—	4	1	no	—
271	M₃₂	—	4	2	no	—
272	C₂×C₁₆	—	2	1	no	—
273	C₂×C₁₆	—	2	2	no	—
274	C₂×C₁₆	—	2	2	no	—
275	C₂×C₁₆	—	2	1	no	—
276	C₂×C₁₆	—	4	4	no	—
277	C₂×C₁₆	—	8	2	no	—
278	C₂×C₁₆	C₄×D₄	1	1	yes	characteristic
279	C₂×C₁₆	C₄×D₄	1	1	yes	characteristic
280	C₂×C₁₆	C₄×D₄	1	1	yes	characteristic
281	C₂×C₁₆	C₄×D₄	1	1	yes	characteristic
282	#108	—	2	2	no	—
283	#108	—	4	1	no	—
284	#108	—	8	2	no	—
285	#108	—	16	1	no	—
286	#107	#106	1	1	yes	characteristic
287	#107	#106	1	1	yes	characteristic
288	#106	—	2	2	no	—
289	#106	—	4	1	no	—
290	#106	#106	1	2	yes	—
291	C₄⋊C₈	—	2	2	no	—
292	C₄⋊C₈	—	2	2	no	—
293	C₄⋊C₈	—	2	1	no	—
294	C₄⋊C₈	—	2	1	no	—
295	C₄⋊C₈	—	2	1	no	—
296	C₄⋊C₈	—	2	1	no	—
297	C₄⋊C₈	—	4	2	no	—
298	C₄⋊C₈	—	4	2	no	—
299	C₄⋊C₈	—	4	2	no	—
300	C₄⋊C₈	—	4	1	no	—
301	C₄⋊C₈	—	4	2	no	—
302	C₄⋊C₈	—	8	2	no	—
303	C₄⋊C₈	—	8	2	no	—
304	C₄⋊C₈	—	8	2	no	—
305	C₄⋊C₈	C₂×C₄⋊C₄	1	2	yes	—
306	C₄⋊C₈	C₂×C₄⋊C₄	1	2	yes	—
307	#104	—	8	4	no	—
308	#103	#106	1	2	yes	—
309	#103	#106	1	2	yes	—
310	#102	#106	1	2	yes	—
311	#102	#106	1	2	yes	—
312	C₂²⋊C₈	—	2	2	no	—
313	C₂²⋊C₈	—	2	2	no	—
314	C₂²⋊C₈	—	2	2	no	—
315	C₂²⋊C₈	—	4	1	no	—
316	C₂²⋊C₈	—	8	2	no	—
317	#97	—	4	1	no	—
318	#97	—	8	2	no	—
319	C₄×C₈	—	2	2	no	—
320	C₄×C₈	—	2	2	no	—
321	C₄×C₈	—	2	2	no	—
322	C₄×C₈	—	2	1	no	—
323	C₄×C₈	—	4	1	no	—
324	C₄×C₈	—	4	1	no	—
325	C₄×C₈	—	8	2	no	—
326	C₄×C₈	C₂×C₄⋊C₄	1	1	yes	characteristic
327	C₄×C₈	C₂×C₄⋊C₄	1	1	yes	characteristic
328	C₄×C₈	C₂×C₄⋊C₄	1	1	yes	characteristic
329	C₄×C₈	C₂×C₄⋊C₄	1	1	yes	characteristic
330	C₄×C₈	C₂×SD₁₆	1	1	yes	characteristic
331	C₄×C₈	C₂×SD₁₆	1	1	yes	characteristic
332	C₄×C₈	C₂³×C₄	1	1	yes	characteristic
333	C₄×C₈	C₂²×D₄	1	1	yes	characteristic
334	C₄×C₈	C₂²×Q₈	1	1	yes	characteristic
335	C₄×C₈	H(5,𝔽₂)	1	1	yes	characteristic
336	#95	—	4	1	no	—
337	#41	—	2	4	no	—
338	#41	—	4	2	no	—
339	C₂×Q₈	C₂×#106	1	2	yes	—
340	C₂×D₄	—	2	2	no	—
341	C₂×D₄	C₂×#106	1	2	yes	—
342	C₂²×C₄	—	2	2	no	—
343	C₂²×C₄	—	2	2	no	—
344	C₂²×C₄	—	2	2	no	—
345	C₂²×C₄	—	8	1	no	—
346	C₂²×C₄	#547	1	1	yes	characteristic
347	C₂²×C₄	C₂²×SD₁₆	1	1	yes	characteristic
348	C₂²×C₄	#577	1	1	yes	characteristic
349	Q₁₆	—	2	2	no	—
350	SD₁₆	—	2	4	no	—
351	D₈	#365	1	4	yes	complemented
352	M₁₆	—	4	2	no	—
353	M₁₆	—	8	1	no	—
354	M₁₆	—	8	2	no	—
355	M₁₆	—	8	2	no	—
356	M₁₆	—	16	4	no	—
357	M₁₆	—	16	2	no	—
358	C₂×C₈	—	2	2	no	—
359	C₂×C₈	—	2	1	no	—
360	C₂×C₈	—	2	1	no	—
361	C₂×C₈	—	2	2	no	—
362	C₂×C₈	—	2	2	no	—
363	C₂×C₈	—	2	1	no	—
364	C₂×C₈	—	2	1	no	—
365	C₂×C₈	—	4	1	no	—
366	C₂×C₈	—	4	1	no	—
367	C₂×C₈	—	4	2	no	—
368	C₂×C₈	—	4	2	no	—
369	C₂×C₈	—	4	1	no	—
370	C₂×C₈	—	4	1	no	—
371	C₂×C₈	—	4	1	no	—
372	C₂×C₈	—	4	1	no	—
373	C₂×C₈	—	8	2	no	—
374	C₂×C₈	—	8	1	no	—
375	C₂×C₈	—	8	1	no	—
376	C₂×C₈	—	8	1	no	—
377	C₂×C₈	—	8	1	no	—
378	C₂×C₈	—	8	2	no	—
379	C₂×C₈	—	8	2	no	—
380	C₂×C₈	—	16	4	no	—
381	C₂×C₈	—	32	2	no	—
382	C₂×C₈	C₂×#106	1	1	yes	characteristic
383	C₂×C₈	C₂×#106	1	1	yes	characteristic
384	C₂×C₈	C₂×#106	1	1	yes	characteristic
385	C₂×C₈	C₂×#106	1	1	yes	characteristic
386	C₂×C₈	C₂×C₄×D₄	1	1	yes	characteristic
387	C₂×C₈	#520	1	1	yes	characteristic
388	C₂×C₈	D₄×Q₈	1	1	yes	characteristic
389	C₂×C₈	#554	1	1	yes	characteristic
390	C₄⋊C₄	—	2	2	no	—
391	C₄⋊C₄	—	2	2	no	—
392	C₄⋊C₄	—	4	2	no	—
393	C₄⋊C₄	—	8	1	no	—
394	C₄⋊C₄	C₂×#106	1	2	yes	—
395	C₄⋊C₄	C₂×#106	1	2	yes	—
396	C₂²⋊C₄	—	2	2	no	—
397	C₂²⋊C₄	—	2	2	no	—
398	C₂²⋊C₄	—	2	2	no	—
399	C₄²	—	2	2	no	—
400	C₄²	—	2	2	no	—
401	C₄²	—	2	2	no	—
402	C₄²	—	8	1	no	—
403	C₄²	—	8	1	no	—
404	C₄²	C₂²×C₄⋊C₄	1	1	yes	characteristic
405	C₄²	D₄²	1	1	yes	characteristic
406	C₄²	C₂²×SD₁₆	1	1	yes	characteristic
407	C₄²	#577	1	1	yes	characteristic
408	C₁₆	—	2	2	no	—
409	C₁₆	—	2	1	no	—
410	C₁₆	—	2	1	no	—
411	C₁₆	—	2	1	no	—
412	C₁₆	—	4	1	no	—
413	C₁₆	—	4	2	no	—
414	C₁₆	—	4	2	no	—
415	C₁₆	#443	1	2	yes	complemented
416	C₂³	—	2	2	no	—
417	C₂³	#3335	1	1	yes	characteristic
418	Q₈	—	2	2	no	—
419	Q₈	—	2	2	no	—
420	D₄	—	2	2	no	—
421	D₄	—	4	4	no	—
422	D₄	C₂×#365	1	4	yes	—
423	C₂×C₄	—	2	1	no	—
424	C₂×C₄	—	2	1	no	—
425	C₂×C₄	—	2	1	no	—
426	C₂×C₄	—	2	1	no	—
427	C₂×C₄	—	2	2	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	2	2	no	—
430	C₂×C₄	—	4	1	no	—
431	C₂×C₄	—	4	4	no	—
432	C₂×C₄	—	4	2	no	—
433	C₂×C₄	—	4	2	no	—
434	C₂×C₄	—	8	2	no	—
435	C₂×C₄	—	8	2	no	—
436	C₂×C₄	—	16	1	no	—
437	C₂×C₄	—	16	1	no	—
438	C₂×C₄	D₄×C₄⋊C₄	1	1	yes	characteristic
439	C₂×C₄	C₂²×#106	1	1	yes	characteristic
440	C₂×C₄	#2912	1	1	yes	characteristic
441	C₂×C₄	D₄×SD₁₆	1	1	yes	characteristic
442	C₂×C₄	D₄×SD₁₆	1	1	yes	characteristic
443	C₂×C₄	#3335	1	1	yes	characteristic
444	C₈	—	2	1	no	—
445	C₈	—	2	1	no	—
446	C₈	—	2	1	no	—
447	C₈	—	2	1	no	—
448	C₈	—	2	1	no	—
449	C₈	—	2	1	no	—
450	C₈	—	4	1	no	—
451	C₈	—	4	1	no	—
452	C₈	—	4	2	no	—
453	C₈	—	4	2	no	—
454	C₈	—	8	1	no	—
455	C₈	—	8	1	no	—
456	C₈	—	8	1	no	—
457	C₈	—	8	1	no	—
458	C₈	—	8	2	no	—
459	C₈	—	16	2	no	—
460	C₈	—	16	2	no	—
461	C₈	C₂×#365	1	2	yes	—
462	C₈	C₂×#443	1	1	yes	characteristic
463	C₈	#2957	1	1	yes	characteristic
464	C₂²	—	2	1	no	—
465	C₂²	—	2	4	no	—
466	C₂²	—	2	1	no	—
467	C₂²	—	2	1	no	—
468	C₂²	—	4	2	no	—
469	C₂²	—	4	2	no	—
470	C₂²	D₄×#106	1	1	yes	characteristic
471	C₄	—	2	1	no	—
472	C₄	—	2	1	no	—
473	C₄	—	2	1	no	—
474	C₄	—	2	1	no	—
475	C₄	—	4	2	no	—
476	C₄	—	4	2	no	—
477	C₄	—	4	2	no	—
478	C₄	—	16	2	no	—
479	C₄	#22688	1	1	yes	characteristic
480	C₄	#22694	1	1	yes	characteristic
481	C₄	C₂²×#365	1	1	yes	characteristic
482	C₄	#33404	1	1	yes	characteristic
483	C₂	—	4	1	no	—
484	C₂	—	4	4	no	—
485	C₂	#225720	1	1	yes	characteristic
486	C₂	D₄×#365	1	1	yes	characteristic
487	C₂	#497839	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	D₄×#106
commutator	C₄×C₈	C₂³×C₄
Frattini, cosocle	C₂×C₄×C₈	C₂⁴
prime radical	C₂×#135	SD₁₆
LCS	G ▷ C₄×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₈×#135 ◁ G
LECS	G ▷ C₂×C₄×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
2. #483463	C₂	semidirect
5. #140497	C₂	semidirect
6. #140494	C₂	semidirect
7. #136464	C₂	semidirect
8. #136462	C₂	semidirect
9. #135794	C₂	semidirect
10. #135073	C₂	semidirect
11. C₈×#365	C₂	semidirect
19. #12054	C₄	semidirect
20. #12054	C₄	semidirect
21. #12049	C₄	semidirect
22. #12049	C₄	semidirect
23. C₁₆×D₈	C₄	semidirect
24. C₁₆×D₈	C₄	semidirect
351. D₈	#365	semidirect
415. C₁₆	#443	semidirect

Maximal subgroups

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

subgroup	index
#483544	2
#483463	2
#225782	2
#225720	2
#140497	2
#140494	2
#136464	2
#136462	2
#135794	2
#135073	2
C₈×#365	2