Subgroups — #60890

Order 256.

850 conjugacy classes of subgroups.

The subgroup lattice has 550 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, complemented
2	#3460	C₂	1	1	yes	maximal, characteristic
3	#3244	C₂	1	2	yes	maximal, complemented
4	#3243	C₂	1	2	yes	maximal, complemented
5	#3241	C₂	1	2	yes	maximal, complemented
6	#3241	C₂	1	2	yes	maximal, complemented
7	#3240	C₂	1	2	yes	maximal, complemented
8	#3234	C₂	1	2	yes	maximal, complemented
9	#3232	C₂	1	2	yes	maximal, complemented
10	#3228	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	#3136	C₂	1	1	yes	maximal, characteristic, complemented
14	#3136	C₂	1	1	yes	maximal, characteristic, complemented
15	#3099	C₂	1	1	yes	maximal, characteristic, complemented
16	#3098	C₂	1	1	yes	maximal, characteristic, complemented
17	#3096	C₂	1	1	yes	maximal, characteristic, complemented
18	#3096	C₂	1	1	yes	maximal, characteristic, complemented
19	#3080	C₂	1	1	yes	maximal, characteristic, complemented
20	#3077	C₂	1	1	yes	maximal, characteristic, complemented
21	#3076	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×#478	C₂	1	1	yes	maximal, characteristic, complemented
23	#2925	C₂	1	1	yes	maximal, characteristic, complemented
24	#557	—	2	1	no	—
25	#557	—	2	1	no	—
26	#554	—	2	2	no	—
27	#554	—	2	2	no	—
28	#554	—	2	1	no	—
29	#554	—	2	1	no	—
30	#544	C₂²	1	1	yes	characteristic
31	#544	C₂²	1	1	yes	characteristic
32	#544	C₂²	1	1	yes	characteristic
33	#544	C₂²	1	2	yes	complemented
34	#544	C₂²	1	2	yes	complemented
35	#542	—	2	1	no	—
36	#542	C₂²	1	2	yes	—
37	#540	—	2	1	no	—
38	#540	C₂²	1	2	yes	—
39	#538	—	2	2	no	—
40	#537	C₂²	1	1	yes	characteristic
41	#535	C₂²	1	1	yes	characteristic
42	#535	C₂²	1	1	yes	characteristic
43	#533	C₂²	1	1	yes	characteristic
44	#533	C₂²	1	2	yes	complemented
45	#532	—	2	1	no	—
46	#532	C₂²	1	2	yes	—
47	#529	—	2	1	no	—
48	#529	C₂²	1	2	yes	—
49	C₂×#125	C₂²	1	1	yes	characteristic
50	C₂×#125	C₂²	1	2	yes	complemented
51	#525	—	2	2	no	—
52	#520	C₂²	1	1	yes	characteristic
53	#520	C₂²	1	1	yes	characteristic
54	C₄×#41	C₂²	1	1	yes	characteristic
55	C₄×#41	C₂²	1	1	yes	characteristic
56	C₂×C₄×D₄	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	#490	C₂²	1	2	yes	—
66	#490	C₂²	1	2	yes	—
67	#489	C₂²	1	2	yes	—
68	#489	C₂²	1	2	yes	—
69	#488	C₂²	1	2	yes	—
70	#488	C₂²	1	2	yes	—
71	#486	C₂²	1	2	yes	—
72	#486	C₂²	1	2	yes	—
73	#485	C₂²	1	2	yes	complemented
74	#485	C₂²	1	2	yes	complemented
75	#484	C₂²	1	2	yes	complemented
76	#483	C₂²	1	2	yes	complemented
77	#482	C₂²	1	2	yes	—
78	#482	C₂²	1	2	yes	—
79	#482	C₂²	1	2	yes	—
80	#482	C₂²	1	2	yes	—
81	#482	C₂²	1	2	yes	complemented
82	#482	C₂²	1	2	yes	complemented
83	#481	C₂²	1	2	yes	—
84	#481	C₂²	1	2	yes	—
85	#481	C₂²	1	2	yes	complemented
86	#480	C₂²	1	2	yes	—
87	#480	C₂²	1	2	yes	—
88	#480	C₂²	1	2	yes	complemented
89	#479	C₂²	1	1	yes	characteristic, complemented
90	#479	C₂²	1	1	yes	characteristic, complemented
91	#479	C₂²	1	2	yes	complemented
92	#479	C₂²	1	2	yes	complemented
93	#478	C₂²	1	2	yes	—
94	#478	C₂²	1	2	yes	—
95	#478	C₂²	1	2	yes	—
96	#478	C₂²	1	2	yes	—
97	#478	C₂²	1	2	yes	—
98	#478	C₂²	1	2	yes	—
99	#478	C₂²	1	1	yes	characteristic, complemented
100	#478	C₂²	1	1	yes	characteristic, complemented
101	#478	C₂²	1	2	yes	complemented
102	#478	C₂²	1	2	yes	complemented
103	#477	C₂²	1	1	yes	characteristic, complemented
104	#476	C₂²	1	2	yes	—
105	#476	C₂²	1	1	yes	characteristic, complemented
106	#475	C₂²	1	1	yes	characteristic, complemented
107	#474	C₂²	1	2	yes	—
108	#474	C₂²	1	1	yes	characteristic, complemented
109	#433	C₂²	1	2	yes	complemented
110	#433	C₂²	1	2	yes	complemented
111	#432	C₂²	1	2	yes	complemented
112	#431	C₂²	1	2	yes	complemented
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	#423	C₂²	1	1	yes	characteristic
122	C₂×C₄⋊C₈	C₂²	1	1	yes	characteristic
123	#418	C₂²	1	1	yes	characteristic
124	#418	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×#102	C₂²	1	1	yes	characteristic
130	C₂×#102	C₂²	1	1	yes	characteristic
131	#408	C₂²	1	1	yes	characteristic
132	#408	C₂²	1	1	yes	characteristic
133	#405	C₂²	1	1	yes	characteristic
134	#405	C₂²	1	1	yes	characteristic
135	C₂×#41	—	2	2	no	—
136	C₂×#41	C₂³	1	1	yes	characteristic
137	C₂×#41	C₂³	1	1	yes	characteristic
138	C₂²×D₄	C₂³	1	1	yes	characteristic
139	C₂³×C₄	—	2	1	no	—
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	1	no	—
145	C₄⋊Q₈	—	2	1	no	—
146	C₄⋊Q₈	—	2	1	no	—
147	C₄⋊Q₈	—	2	2	no	—
148	C₄⋊Q₈	—	2	2	no	—
149	C₄⋊Q₈	C₂³	1	2	yes	—
150	C₄⋊Q₈	C₂³	1	1	yes	characteristic
151	C₄⋊Q₈	C₂³	1	1	yes	characteristic
152	C₄⋊Q₈	C₂³	1	2	yes	—
153	C₄⋊Q₈	C₂³	1	2	yes	—
154	#127	—	2	1	no	—
155	#127	C₂³	1	2	yes	—
156	#126	—	2	2	no	—
157	#126	—	2	2	no	—
158	#125	—	2	1	no	—
159	#125	—	2	1	no	—
160	#125	—	2	1	no	—
161	#125	—	2	2	no	—
162	#125	—	2	2	no	—
163	#125	—	2	1	no	—
164	#125	—	2	1	no	—
165	#125	—	2	2	no	—
166	#125	—	2	2	no	—
167	#125	C₂³	1	2	yes	—
168	#125	C₂³	1	2	yes	—
169	#125	C₂³	1	1	yes	characteristic
170	#125	C₂³	1	2	yes	—
171	#125	C₂³	1	2	yes	—
172	#125	C₂³	1	2	yes	—
173	#125	C₂³	1	1	yes	characteristic
174	#124	—	2	1	no	—
175	#124	—	2	2	no	—
176	#124	—	2	2	no	—
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	C₂²⋊Q₈	—	2	1	no	—
183	C₂²⋊Q₈	—	2	1	no	—
184	C₂²⋊Q₈	—	2	1	no	—
185	C₂²⋊Q₈	—	2	2	no	—
186	C₂²⋊Q₈	—	2	2	no	—
187	C₂²⋊Q₈	—	2	2	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	—	2	2	no	—
193	C₂²⋊Q₈	—	2	2	no	—
194	C₂²⋊Q₈	—	2	2	no	—
195	C₂²⋊Q₈	C₂³	1	2	yes	—
196	#121	—	2	2	no	—
197	#121	—	2	1	no	—
198	#121	—	2	2	no	—
199	#121	—	2	1	no	—
200	#121	—	2	1	no	—
201	#121	—	2	2	no	—
202	#121	—	2	2	no	—
203	#121	C₂³	1	2	yes	—
204	#121	C₂³	1	2	yes	—
205	#121	C₂³	1	2	yes	—
206	#120	—	2	2	no	—
207	#120	—	2	2	no	—
208	C₄×Q₈	—	2	1	no	—
209	C₄×Q₈	—	2	1	no	—
210	C₄×Q₈	—	2	1	no	—
211	C₄×Q₈	—	2	1	no	—
212	C₄×Q₈	—	2	2	no	—
213	C₄×Q₈	—	2	2	no	—
214	C₄×Q₈	D₄	1	1	yes	characteristic
215	C₄×Q₈	D₄	1	1	yes	characteristic
216	C₄×Q₈	C₂³	1	1	yes	characteristic
217	C₄×Q₈	C₂³	1	1	yes	characteristic
218	C₄×D₄	—	2	2	no	—
219	C₄×D₄	—	2	2	no	—
220	C₄×D₄	—	2	1	no	—
221	C₄×D₄	—	2	1	no	—
222	C₄×D₄	—	2	1	no	—
223	C₄×D₄	—	2	1	no	—
224	C₄×D₄	—	2	2	no	—
225	C₄×D₄	—	2	1	no	—
226	C₄×D₄	—	2	1	no	—
227	C₄×D₄	—	2	2	no	—
228	C₄×D₄	D₄	1	2	yes	—
229	C₄×D₄	D₄	1	1	yes	characteristic
230	C₄×D₄	D₄	1	2	yes	—
231	C₄×D₄	D₄	1	1	yes	characteristic
232	C₄×D₄	C₂³	1	2	yes	—
233	C₄×D₄	C₂³	1	2	yes	—
234	C₄×D₄	C₂³	1	1	yes	characteristic
235	C₄×D₄	C₂³	1	1	yes	characteristic
236	#117	—	2	1	no	—
237	#117	—	2	2	no	—
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	#117	C₂³	1	2	yes	—
243	#117	C₂³	1	1	yes	characteristic
244	#117	C₂³	1	2	yes	—
245	C₂×C₄⋊C₄	—	2	1	no	—
246	C₂×C₄⋊C₄	—	2	1	no	—
247	C₂×C₄⋊C₄	—	2	2	no	—
248	C₂×C₄⋊C₄	—	2	2	no	—
249	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
250	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
251	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
252	C₂×C₄⋊C₄	C₂³	1	2	yes	—
253	C₂×C₄⋊C₄	C₂³	1	2	yes	—
254	C₂×C₂²⋊C₄	—	2	1	no	—
255	C₂×C₄²	—	2	1	no	—
256	C₂×C₄²	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
279	C₄⋊C₈	C₂³	1	1	yes	characteristic
280	C₄⋊C₈	C₂³	1	1	yes	characteristic
281	C₄⋊C₈	C₂³	1	1	yes	characteristic
282	C₄⋊C₈	C₂³	1	2	yes	—
283	C₄⋊C₈	C₂³	1	2	yes	—
284	#103	C₂³	1	1	yes	characteristic
285	#103	C₂³	1	1	yes	characteristic
286	#103	C₂³	1	1	yes	characteristic
287	#103	C₂³	1	1	yes	characteristic
288	#103	C₂³	1	2	yes	—
289	#103	C₂³	1	2	yes	—
290	#102	C₂³	1	2	yes	—
291	#102	C₂³	1	2	yes	—
292	#102	C₂³	1	2	yes	—
293	#102	C₂³	1	2	yes	—
294	#102	C₂³	1	1	yes	characteristic
295	#102	C₂³	1	1	yes	characteristic
296	#102	C₂³	1	1	yes	characteristic
297	#102	C₂³	1	1	yes	characteristic
298	#102	C₂³	1	2	yes	—
299	#102	C₂³	1	2	yes	—
300	#102	C₂³	1	2	yes	—
301	#102	C₂³	1	2	yes	—
302	#102	C₂³	1	2	yes	—
303	#102	C₂³	1	2	yes	—
304	C₂²⋊C₈	C₂³	1	2	yes	—
305	C₂²⋊C₈	C₂³	1	2	yes	—
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	—	2	1	no	—
313	#41	—	2	2	no	—
314	#41	—	2	2	no	—
315	#41	—	2	2	no	—
316	#41	—	2	2	no	—
317	#41	—	8	4	no	—
318	C₂×Q₈	—	2	1	no	—
319	C₂×Q₈	—	2	2	no	—
320	C₂×Q₈	—	2	1	no	—
321	C₂×Q₈	—	2	2	no	—
322	C₂×Q₈	—	2	2	no	—
323	C₂×Q₈	C₂×D₄	1	1	yes	characteristic
324	C₂×Q₈	C₂⁴	1	1	yes	characteristic
325	C₂×D₄	—	2	1	no	—
326	C₂×D₄	—	2	2	no	—
327	C₂×D₄	—	2	2	no	—
328	C₂×D₄	—	2	2	no	—
329	C₂×D₄	—	2	1	no	—
330	C₂×D₄	—	2	2	no	—
331	C₂×D₄	—	2	2	no	—
332	C₂×D₄	—	2	2	no	—
333	C₂×D₄	—	2	2	no	—
334	C₂×D₄	C₂×D₄	1	2	yes	—
335	C₂×D₄	C₂×D₄	1	1	yes	characteristic
336	C₂×D₄	C₂⁴	1	2	yes	—
337	C₂×D₄	C₂⁴	1	1	yes	characteristic
338	C₂²×C₄	—	2	1	no	—
339	C₂²×C₄	—	2	2	no	—
340	C₂²×C₄	—	2	2	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	1	no	—
347	C₂²×C₄	—	2	2	no	—
348	C₂²×C₄	—	8	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	2	yes	—
352	C₂²×C₄	C₂×D₄	1	2	yes	—
353	C₂²×C₄	C₂⁴	1	2	yes	—
354	C₂²×C₄	C₂⁴	1	1	yes	characteristic
355	M₁₆	—	2	2	no	—
356	M₁₆	—	2	2	no	—
357	C₂×C₈	—	2	2	no	—
358	C₂×C₈	—	2	2	no	—
359	C₂×C₈	C₂⁴	1	1	yes	characteristic
360	C₂×C₈	C₂⁴	1	1	yes	characteristic
361	C₂×C₈	C₂⁴	1	2	yes	—
362	C₂×C₈	C₂⁴	1	2	yes	—
363	C₂×C₈	C₂⁴	1	1	yes	characteristic
364	C₂×C₈	C₂⁴	1	1	yes	characteristic
365	C₄⋊C₄	—	2	2	no	—
366	C₄⋊C₄	—	2	1	no	—
367	C₄⋊C₄	—	2	2	no	—
368	C₄⋊C₄	—	2	1	no	—
369	C₄⋊C₄	—	2	2	no	—
370	C₄⋊C₄	—	2	2	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	2	no	—
377	C₄⋊C₄	—	2	2	no	—
378	C₄⋊C₄	—	2	1	no	—
379	C₄⋊C₄	—	2	1	no	—
380	C₄⋊C₄	—	2	1	no	—
381	C₄⋊C₄	—	2	1	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	—	2	1	no	—
387	C₄⋊C₄	—	2	1	no	—
388	C₄⋊C₄	—	2	1	no	—
389	C₄⋊C₄	—	2	2	no	—
390	C₄⋊C₄	—	2	1	no	—
391	C₄⋊C₄	—	2	2	no	—
392	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
393	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
394	C₄⋊C₄	C₂×D₄	1	2	yes	—
395	C₄⋊C₄	C₂×D₄	1	2	yes	—
396	C₄⋊C₄	C₂⁴	1	2	yes	—
397	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
398	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
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	2	yes	—
403	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
404	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
405	C₂²⋊C₄	—	2	1	no	—
406	C₂²⋊C₄	—	2	2	no	—
407	C₂²⋊C₄	—	2	2	no	—
408	C₂²⋊C₄	—	2	1	no	—
409	C₂²⋊C₄	—	2	1	no	—
410	C₂²⋊C₄	—	2	2	no	—
411	C₂²⋊C₄	—	2	2	no	—
412	C₂²⋊C₄	—	2	2	no	—
413	C₂²⋊C₄	—	2	1	no	—
414	C₂²⋊C₄	—	2	1	no	—
415	C₂²⋊C₄	—	2	2	no	—
416	C₂²⋊C₄	—	2	2	no	—
417	C₂²⋊C₄	—	2	2	no	—
418	C₂²⋊C₄	—	2	2	no	—
419	C₂²⋊C₄	—	2	2	no	—
420	C₂²⋊C₄	C₂×D₄	1	2	yes	—
421	C₂²⋊C₄	C₂×D₄	1	2	yes	—
422	C₂²⋊C₄	C₂×D₄	1	2	yes	—
423	C₄²	—	2	1	no	—
424	C₄²	—	2	1	no	—
425	C₄²	—	2	1	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	2	yes	—
432	C₄²	C₂×D₄	1	1	yes	characteristic
433	C₄²	C₂×D₄	1	2	yes	—
434	C₄²	C₂⁴	1	2	yes	—
435	C₄²	C₂⁴	1	1	yes	characteristic
436	C₄²	C₂⁴	1	1	yes	characteristic
437	C₂³	—	2	2	no	—
438	C₂³	—	2	1	no	—
439	C₂³	—	4	2	no	—
440	C₂³	—	8	1	no	—
441	C₂³	—	8	1	no	—
442	C₂³	C₂²×D₄	1	2	yes	—
443	C₂³	C₂²×D₄	1	1	yes	characteristic
444	Q₈	—	2	2	no	—
445	Q₈	—	2	1	no	—
446	Q₈	—	2	1	no	—
447	Q₈	—	8	1	no	—
448	Q₈	—	8	2	no	—
449	Q₈	—	8	1	no	—
450	Q₈	—	8	2	no	—
451	Q₈	—	8	2	no	—
452	D₄	—	2	4	no	—
453	D₄	—	2	2	no	—
454	D₄	—	2	2	no	—
455	D₄	—	2	2	no	—
456	D₄	—	2	1	no	—
457	D₄	—	2	1	no	—
458	D₄	—	4	2	no	—
459	D₄	—	4	2	no	—
460	D₄	—	8	2	no	—
461	D₄	—	8	2	no	—
462	D₄	—	8	2	no	—
463	D₄	—	8	2	no	—
464	D₄	—	8	2	no	—
465	C₂×C₄	—	2	2	no	—
466	C₂×C₄	—	2	2	no	—
467	C₂×C₄	—	2	1	no	—
468	C₂×C₄	—	2	1	no	—
469	C₂×C₄	—	2	1	no	—
470	C₂×C₄	—	2	1	no	—
471	C₂×C₄	—	2	1	no	—
472	C₂×C₄	—	2	2	no	—
473	C₂×C₄	—	2	1	no	—
474	C₂×C₄	—	2	2	no	—
475	C₂×C₄	—	2	1	no	—
476	C₂×C₄	—	2	2	no	—
477	C₂×C₄	—	4	1	no	—
478	C₂×C₄	—	4	1	no	—
479	C₂×C₄	—	4	2	no	—
480	C₂×C₄	—	4	2	no	—
481	C₂×C₄	—	4	4	no	—
482	C₂×C₄	—	4	2	no	—
483	C₂×C₄	—	4	2	no	—
484	C₂×C₄	—	8	1	no	—
485	C₂×C₄	—	8	2	no	—
486	C₂×C₄	—	8	1	no	—
487	C₂×C₄	—	8	2	no	—
488	C₂×C₄	—	8	1	no	—
489	C₂×C₄	—	8	2	no	—
490	C₂×C₄	—	8	1	no	—
491	C₂×C₄	C₂²×D₄	1	2	yes	—
492	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
493	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
494	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
495	C₂×C₄	C₂²×D₄	1	2	yes	—
496	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
497	C₂×C₄	C₂²×D₄	1	2	yes	—
498	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
499	C₂×C₄	2₋¹⁺⁴	1	2	yes	—
500	C₂×C₄	2₋¹⁺⁴	1	2	yes	—
501	C₂×C₄	C₂⁵	1	1	yes	characteristic
502	C₈	—	2	1	no	—
503	C₈	—	2	1	no	—
504	C₈	—	2	1	no	—
505	C₈	—	2	1	no	—
506	C₈	—	2	2	no	—
507	C₈	—	2	2	no	—
508	C₂²	—	2	1	no	—
509	C₂²	—	2	1	no	—
510	C₂²	—	2	2	no	—
511	C₂²	—	2	2	no	—
512	C₂²	—	2	2	no	—
513	C₂²	—	4	1	no	—
514	C₂²	—	4	2	no	—
515	C₂²	—	4	2	no	—
516	C₂²	—	4	1	no	—
517	C₂²	—	4	1	no	—
518	C₂²	—	4	2	no	—
519	C₂²	—	8	4	no	—
520	C₂²	#536	1	2	yes	—
521	C₂²	C₂³×D₄	1	1	yes	characteristic
522	C₄	—	2	1	no	—
523	C₄	—	2	1	no	—
524	C₄	—	2	2	no	—
525	C₄	—	2	1	no	—
526	C₄	—	2	1	no	—
527	C₄	—	2	2	no	—
528	C₄	—	2	2	no	—
529	C₄	—	4	2	no	—
530	C₄	—	4	1	no	—
531	C₄	—	4	1	no	—
532	C₄	—	4	1	no	—
533	C₄	—	4	2	no	—
534	C₄	—	4	1	no	—
535	C₄	—	4	2	no	—
536	C₄	—	4	1	no	—
537	C₄	—	4	1	no	—
538	C₄	—	4	1	no	—
539	C₄	#536	1	2	yes	—
540	C₄	C₂×2₋¹⁺⁴	1	1	yes	characteristic
541	C₄	C₂×2₋¹⁺⁴	1	1	yes	characteristic
542	C₂	—	2	2	no	—
543	C₂	—	4	2	no	—
544	C₂	—	8	1	no	—
545	C₂	—	8	2	no	—
546	C₂	C₂×#536	1	1	yes	characteristic
547	C₂	#3584	1	1	yes	characteristic
548	C₂	#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵
prime radical	#3460	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₄×#41 ◁ G
LECS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #3504	C₂	semidirect
3. #3244	C₂	semidirect
4. #3243	C₂	semidirect
5. #3241	C₂	semidirect
6. #3241	C₂	semidirect
7. #3240	C₂	semidirect
8. #3234	C₂	semidirect
9. #3232	C₂	semidirect
10. #3228	C₂	semidirect
11. #3164	C₂	semidirect
12. #3163	C₂	semidirect
13. #3136	C₂	semidirect
14. #3136	C₂	semidirect
15. #3099	C₂	semidirect
16. #3098	C₂	semidirect
17. #3096	C₂	semidirect
18. #3096	C₂	semidirect
19. #3080	C₂	semidirect
20. #3077	C₂	semidirect
21. #3076	C₂	semidirect
22. C₂×#478	C₂	semidirect
23. #2925	C₂	semidirect
33. #544	C₂²	semidirect
34. #544	C₂²	semidirect
44. #533	C₂²	semidirect
50. C₂×#125	C₂²	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
73. #485	C₂²	semidirect
74. #485	C₂²	semidirect
75. #484	C₂²	semidirect
76. #483	C₂²	semidirect
81. #482	C₂²	semidirect
82. #482	C₂²	semidirect
85. #481	C₂²	semidirect
88. #480	C₂²	semidirect
89. #479	C₂²	semidirect
90. #479	C₂²	semidirect
91. #479	C₂²	semidirect
92. #479	C₂²	semidirect
99. #478	C₂²	semidirect
100. #478	C₂²	semidirect
101. #478	C₂²	semidirect
102. #478	C₂²	semidirect
103. #477	C₂²	semidirect
105. #476	C₂²	semidirect
106. #475	C₂²	semidirect
108. #474	C₂²	semidirect
109. #433	C₂²	semidirect
110. #433	C₂²	semidirect
111. #432	C₂²	semidirect
112. #431	C₂²	semidirect

Maximal subgroups

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

subgroup	index
#3504	2
#3460	2
#3244	2
#3243	2
#3241	2
#3240	2
#3234	2
#3232	2
#3228	2
#3164	2
#3163	2
#3136	2
#3099	2
#3098	2
#3096	2
#3080	2
#3077	2
#3076	2
C₂×#478	2
#2925	2