Subgroups — #62057

Order 256.

973 conjugacy classes of subgroups.

The subgroup lattice has 601 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3543	C₂	1	1	yes	maximal, characteristic, complemented
2	#3522	C₂	1	1	yes	maximal, characteristic, complemented
3	#3399	C₂	1	1	yes	maximal, characteristic, complemented
4	#3396	C₂	1	1	yes	maximal, characteristic, complemented
5	#3375	C₂	1	1	yes	maximal, characteristic, complemented
6	#3362	C₂	1	1	yes	maximal, characteristic, complemented
7	#3333	C₂	1	1	yes	maximal, characteristic, complemented
8	#3306	C₂	1	2	yes	maximal, complemented
9	#3295	C₂	1	1	yes	maximal, characteristic, complemented
10	#3294	C₂	1	2	yes	maximal, complemented
11	#3287	C₂	1	1	yes	maximal, characteristic, complemented
12	#3282	C₂	1	2	yes	maximal, complemented
13	#3274	C₂	1	1	yes	maximal, characteristic, complemented
14	#3265	C₂	1	2	yes	maximal, complemented
15	#3257	C₂	1	2	yes	maximal, complemented
16	#3247	C₂	1	1	yes	maximal, characteristic, complemented
17	#3224	C₂	1	2	yes	maximal, complemented
18	#3205	C₂	1	1	yes	maximal, characteristic, complemented
19	#3119	C₂	1	2	yes	maximal, complemented
20	#3108	C₂	1	1	yes	maximal, characteristic, complemented
21	#3045	C₂	1	2	yes	maximal, complemented
22	C₂×#460	C₂	1	1	yes	maximal, characteristic, complemented
23	#2994	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×AGL(1,ℤ/8)	C₂²	1	2	yes	complemented
25	C₂×#135	C₂²	1	2	yes	complemented
26	C₂²×SD₁₆	C₂²	1	2	yes	complemented
27	#560	—	2	2	no	—
28	#559	—	2	1	no	—
29	#559	C₂²	1	1	yes	characteristic
30	#559	C₂²	1	1	yes	characteristic, complemented
31	Q₈²	C₂²	1	1	yes	characteristic, complemented
32	#554	—	2	1	no	—
33	#554	C₂²	1	1	yes	characteristic, complemented
34	#550	C₂²	1	1	yes	characteristic
35	#550	C₂²	1	1	yes	characteristic
36	#550	C₂²	1	1	yes	characteristic, complemented
37	#548	C₂²	1	2	yes	complemented
38	#547	—	2	2	no	—
39	#547	C₂²	1	2	yes	complemented
40	#546	—	2	1	no	—
41	#546	C₂²	1	2	yes	—
42	D₄²	—	2	1	no	—
43	D₄²	C₂²	1	2	yes	—
44	D₄²	C₂²	1	1	yes	characteristic
45	#542	—	2	2	no	—
46	#542	C₂²	1	2	yes	complemented
47	#540	—	2	1	no	—
48	#540	C₂²	1	2	yes	—
49	#535	—	2	1	no	—
50	#535	C₂²	1	2	yes	—
51	#534	—	2	2	no	—
52	#532	—	2	1	no	—
53	#532	C₂²	1	1	yes	characteristic, complemented
54	C₂×#127	C₂²	1	1	yes	characteristic
55	#529	—	2	1	no	—
56	#529	C₂²	1	1	yes	characteristic
57	#529	C₂²	1	1	yes	characteristic
58	#520	C₂²	1	2	yes	complemented
59	C₂×C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
60	#496	C₂²	1	2	yes	complemented
61	#495	C₂²	1	2	yes	complemented
62	#493	C₂²	1	1	yes	characteristic
63	#493	C₂²	1	1	yes	characteristic, complemented
64	#489	C₂²	1	2	yes	complemented
65	#486	C₂²	1	1	yes	characteristic
66	#486	C₂²	1	1	yes	characteristic, complemented
67	#486	C₂²	1	2	yes	complemented
68	#483	C₂²	1	1	yes	characteristic, complemented
69	#481	C₂²	1	2	yes	complemented
70	#480	C₂²	1	1	yes	characteristic
71	#480	C₂²	1	2	yes	complemented
72	#479	C₂²	1	1	yes	characteristic, complemented
73	#479	C₂²	1	1	yes	characteristic, complemented
74	#478	C₂²	1	2	yes	complemented
75	#477	C₂²	1	1	yes	characteristic, complemented
76	#476	C₂²	1	1	yes	characteristic, complemented
77	#476	C₂²	1	2	yes	complemented
78	#474	C₂²	1	2	yes	complemented
79	#469	C₂²	1	2	yes	complemented
80	#468	C₂²	1	2	yes	complemented
81	#466	C₂²	1	2	yes	—
82	#466	C₂²	1	2	yes	complemented
83	#465	C₂²	1	2	yes	complemented
84	#465	C₂²	1	2	yes	complemented
85	#464	C₂²	1	1	yes	characteristic, complemented
86	#464	C₂²	1	1	yes	characteristic, complemented
87	#464	C₂²	1	2	yes	complemented
88	#463	C₂²	1	2	yes	complemented
89	#463	C₂²	1	2	yes	complemented
90	#463	C₂²	1	2	yes	complemented
91	#463	C₂²	1	2	yes	complemented
92	#460	C₂²	1	1	yes	characteristic
93	#460	C₂²	1	1	yes	characteristic
94	#460	C₂²	1	1	yes	characteristic, complemented
95	#460	C₂²	1	2	yes	complemented
96	#460	C₂²	1	1	yes	characteristic, complemented
97	#460	C₂²	1	2	yes	complemented
98	#460	C₂²	1	1	yes	characteristic, complemented
99	#460	C₂²	1	2	yes	complemented
100	#459	C₂²	1	2	yes	complemented
101	#459	C₂²	1	1	yes	characteristic, complemented
102	#459	C₂²	1	2	yes	complemented
103	#459	C₂²	1	2	yes	complemented
104	#452	C₂²	1	2	yes	complemented
105	#451	C₂²	1	1	yes	characteristic, complemented
106	#450	C₂²	1	2	yes	complemented
107	#449	C₂²	1	2	yes	complemented
108	#449	C₂²	1	2	yes	complemented
109	#449	C₂²	1	2	yes	complemented
110	#448	C₂²	1	1	yes	characteristic
111	#447	C₂²	1	2	yes	complemented
112	#447	C₂²	1	2	yes	complemented
113	#447	C₂²	1	2	yes	complemented
114	#446	C₂²	1	1	yes	characteristic, complemented
115	C₈×Q₈	C₂²	1	1	yes	characteristic, complemented
116	#442	C₂²	1	2	yes	complemented
117	#440	C₂²	1	2	yes	complemented
118	C₄×Q₁₆	C₂²	1	1	yes	characteristic, complemented
119	C₄×Q₁₆	C₂²	1	1	yes	characteristic, complemented
120	C₄×SD₁₆	C₂²	1	1	yes	characteristic, complemented
121	C₄×SD₁₆	C₂²	1	2	yes	complemented
122	C₄×SD₁₆	C₂²	1	1	yes	characteristic, complemented
123	C₄×D₈	C₂²	1	2	yes	complemented
124	#436	C₂²	1	1	yes	characteristic, complemented
125	#435	C₂²	1	2	yes	complemented
126	C₈×D₄	C₂²	1	2	yes	complemented
127	C₈×D₄	C₂²	1	1	yes	characteristic, complemented
128	#433	C₂²	1	2	yes	complemented
129	#431	C₂²	1	1	yes	characteristic, complemented
130	#424	C₂²	1	2	yes	complemented
131	C₂×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
132	#417	C₂²	1	2	yes	complemented
133	C₂×#102	C₂²	1	2	yes	complemented
134	C₂×#102	C₂²	1	2	yes	complemented
135	C₂×#41	—	2	1	no	—
136	C₂×#41	—	2	2	no	—
137	C₂×#41	—	2	1	no	—
138	C₂×#41	C₂³	1	2	yes	—
139	C₂×#41	C₂³	1	2	yes	—
140	C₂²×Q₈	C₂³	1	1	yes	characteristic
141	C₂²×D₄	—	2	2	no	—
142	C₂²×D₄	—	2	1	no	—
143	C₂²×D₄	—	2	1	no	—
144	C₂²×D₄	—	2	1	no	—
145	C₂²×D₄	C₂³	1	2	yes	—
146	C₂²×D₄	C₂³	1	2	yes	—
147	AGL(1,ℤ/8)	—	4	4	no	—
148	#135	—	4	4	no	—
149	C₂×Q₁₆	C₂³	1	1	yes	characteristic
150	C₂×Q₁₆	C₂³	1	1	yes	characteristic
151	C₂×SD₁₆	—	4	4	no	—
152	C₂×SD₁₆	C₂³	1	2	yes	—
153	C₂×SD₁₆	C₂³	1	2	yes	—
154	C₂×SD₁₆	C₂³	1	1	yes	characteristic
155	C₂×SD₁₆	C₂³	1	2	yes	—
156	C₂×SD₁₆	C₂³	1	2	yes	—
157	C₂×SD₁₆	C₂³	1	2	yes	—
158	C₂×SD₁₆	C₂³	1	1	yes	characteristic
159	C₂×D₈	C₂³	1	2	yes	—
160	C₂×D₈	C₂³	1	2	yes	—
161	C₂×D₈	C₂³	1	2	yes	—
162	C₂×D₈	C₂³	1	2	yes	—
163	C₂×D₈	C₂³	1	2	yes	—
164	C₂×M₁₆	C₂³	1	2	yes	—
165	C₂²×C₈	C₂³	1	2	yes	—
166	C₂²×C₈	C₂³	1	2	yes	—
167	C₄⋊Q₈	—	2	1	no	—
168	C₄⋊Q₈	—	2	2	no	—
169	C₄⋊Q₈	C₂³	1	1	yes	characteristic
170	C₄⋊Q₈	C₂³	1	2	yes	—
171	#127	—	2	1	no	—
172	#127	—	2	1	no	—
173	#127	—	2	1	no	—
174	#127	—	2	1	no	—
175	#127	C₂³	1	2	yes	—
176	#127	C₂³	1	1	yes	characteristic
177	#127	C₂³	1	1	yes	characteristic
178	#127	C₂³	1	1	yes	characteristic
179	#127	C₂³	1	2	yes	—
180	#126	—	2	2	no	—
181	#126	—	2	1	no	—
182	#126	D₄	1	2	yes	—
183	#125	—	2	1	no	—
184	#125	D₄	1	1	yes	characteristic
185	#125	C₂³	1	1	yes	characteristic
186	#124	—	2	1	no	—
187	#124	—	2	1	no	—
188	#124	—	2	2	no	—
189	#124	—	2	2	no	—
190	#124	—	2	1	no	—
191	#124	D₄	1	1	yes	characteristic
192	#124	C₂³	1	1	yes	characteristic
193	#124	C₂³	1	2	yes	—
194	#124	C₂³	1	2	yes	—
195	#123	—	2	1	no	—
196	#123	—	2	2	no	—
197	#123	—	2	2	no	—
198	#123	—	2	2	no	—
199	#123	—	2	2	no	—
200	#123	—	2	2	no	—
201	#123	—	2	2	no	—
202	#123	—	2	2	no	—
203	#123	—	2	2	no	—
204	#123	D₄	1	2	yes	—
205	C₂²⋊Q₈	—	2	2	no	—
206	C₂²⋊Q₈	—	2	2	no	—
207	C₂²⋊Q₈	—	2	2	no	—
208	C₂²⋊Q₈	—	2	2	no	—
209	C₂²⋊Q₈	D₄	1	1	yes	characteristic
210	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
211	C₂²⋊Q₈	C₂³	1	2	yes	—
212	#121	—	2	2	no	—
213	#121	—	2	1	no	—
214	#121	—	2	2	no	—
215	#121	—	2	2	no	—
216	#121	—	2	2	no	—
217	#121	—	2	1	no	—
218	#121	—	2	1	no	—
219	#121	—	2	2	no	—
220	#121	—	2	2	no	—
221	#121	—	2	2	no	—
222	#121	—	2	2	no	—
223	#121	—	2	2	no	—
224	#121	—	2	2	no	—
225	#121	D₄	1	1	yes	characteristic
226	#121	C₂³	1	1	yes	characteristic
227	#121	C₂³	1	2	yes	—
228	#121	C₂³	1	2	yes	—
229	#121	C₂³	1	2	yes	—
230	#121	C₂³	1	2	yes	—
231	#120	—	2	2	no	—
232	#120	—	2	2	no	—
233	#120	—	2	2	no	—
234	#120	—	2	2	no	—
235	#120	—	2	2	no	—
236	#120	—	2	2	no	—
237	C₄×Q₈	—	2	1	no	—
238	C₄×Q₈	—	2	1	no	—
239	C₄×Q₈	—	2	1	no	—
240	C₄×Q₈	C₂³	1	1	yes	characteristic
241	C₄×Q₈	C₂³	1	1	yes	characteristic
242	C₄×Q₈	C₂³	1	1	yes	characteristic
243	C₄×Q₈	C₂³	1	1	yes	characteristic
244	C₄×Q₈	C₂³	1	2	yes	—
245	C₄×Q₈	C₂³	1	1	yes	characteristic
246	C₄×Q₈	C₂³	1	1	yes	characteristic
247	C₄×D₄	—	2	1	no	—
248	C₄×D₄	—	2	1	no	—
249	C₄×D₄	—	2	1	no	—
250	C₄×D₄	—	2	1	no	—
251	C₄×D₄	—	2	1	no	—
252	C₄×D₄	—	2	1	no	—
253	C₄×D₄	—	2	2	no	—
254	C₄×D₄	—	2	2	no	—
255	C₄×D₄	—	2	2	no	—
256	C₄×D₄	—	2	1	no	—
257	C₄×D₄	C₂³	1	2	yes	—
258	C₄×D₄	C₂³	1	2	yes	—
259	C₄×D₄	C₂³	1	1	yes	characteristic
260	C₄×D₄	C₂³	1	2	yes	—
261	C₄×D₄	C₂³	1	2	yes	—
262	C₄×D₄	C₂³	1	2	yes	—
263	C₄×D₄	C₂³	1	1	yes	characteristic
264	#117	—	2	2	no	—
265	#117	—	2	1	no	—
266	#117	C₂³	1	2	yes	—
267	C₂×C₄⋊C₄	—	2	1	no	—
268	C₂×C₄⋊C₄	—	2	2	no	—
269	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
270	C₂×C₄⋊C₄	C₂³	1	2	yes	—
271	C₂×C₂²⋊C₄	—	2	2	no	—
272	C₂×C₄²	—	2	1	no	—
273	C₂×C₄²	C₂³	1	1	yes	characteristic
274	#107	C₂³	1	1	yes	characteristic
275	#107	C₂³	1	1	yes	characteristic
276	#107	C₂³	1	2	yes	—
277	#106	C₂³	1	1	yes	characteristic
278	#106	C₂³	1	2	yes	—
279	#106	C₂³	1	1	yes	characteristic
280	C₄⋊C₈	C₂³	1	2	yes	—
281	C₄⋊C₈	C₂³	1	1	yes	characteristic
282	C₄⋊C₈	C₂³	1	1	yes	characteristic
283	C₄⋊C₈	C₂³	1	1	yes	characteristic
284	C₄⋊C₈	C₂³	1	2	yes	—
285	C₄⋊C₈	C₂³	1	2	yes	—
286	C₄⋊C₈	C₂³	1	1	yes	characteristic
287	#103	C₂³	1	1	yes	characteristic
288	#103	C₂³	1	2	yes	—
289	#103	C₂³	1	1	yes	characteristic
290	#103	C₂³	1	1	yes	characteristic
291	#103	C₂³	1	1	yes	characteristic
292	#103	C₂³	1	1	yes	characteristic
293	#103	C₂³	1	1	yes	characteristic
294	#102	C₂³	1	2	yes	—
295	#102	C₂³	1	1	yes	characteristic
296	#102	C₂³	1	2	yes	—
297	#102	C₂³	1	2	yes	—
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	1	yes	characteristic
304	#102	C₂³	1	2	yes	—
305	#102	C₂³	1	2	yes	—
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	2	yes	—
310	C₂²⋊C₈	C₂³	1	2	yes	—
311	#97	C₂³	1	2	yes	—
312	C₄×C₈	C₂³	1	1	yes	characteristic
313	C₄×C₈	C₂³	1	1	yes	characteristic
314	C₄×C₈	C₂³	1	2	yes	—
315	C₂⁴	—	2	2	no	—
316	C₂⁴	—	2	2	no	—
317	#41	—	2	4	no	—
318	#41	—	4	2	no	—
319	#41	—	4	2	no	—
320	#41	—	4	2	no	—
321	#41	—	8	2	no	—
322	#41	—	8	4	no	—
323	#41	—	8	2	no	—
324	C₂×Q₈	—	2	1	no	—
325	C₂×Q₈	—	2	2	no	—
326	C₂×Q₈	—	2	1	no	—
327	C₂×Q₈	—	2	2	no	—
328	C₂×Q₈	—	4	1	no	—
329	C₂×Q₈	C₂×D₄	1	1	yes	characteristic
330	C₂×Q₈	C₂⁴	1	1	yes	characteristic
331	C₂×Q₈	C₂⁴	1	1	yes	characteristic
332	C₂×Q₈	C₂⁴	1	1	yes	characteristic
333	C₂×D₄	—	2	2	no	—
334	C₂×D₄	—	2	1	no	—
335	C₂×D₄	—	2	2	no	—
336	C₂×D₄	—	2	2	no	—
337	C₂×D₄	—	2	2	no	—
338	C₂×D₄	—	2	2	no	—
339	C₂×D₄	—	2	2	no	—
340	C₂×D₄	—	2	1	no	—
341	C₂×D₄	—	2	1	no	—
342	C₂×D₄	—	2	1	no	—
343	C₂×D₄	—	2	2	no	—
344	C₂×D₄	—	2	2	no	—
345	C₂×D₄	—	2	1	no	—
346	C₂×D₄	—	2	2	no	—
347	C₂×D₄	—	2	2	no	—
348	C₂×D₄	—	2	2	no	—
349	C₂×D₄	—	2	2	no	—
350	C₂×D₄	—	2	1	no	—
351	C₂×D₄	—	2	1	no	—
352	C₂×D₄	—	4	2	no	—
353	C₂×D₄	—	4	2	no	—
354	C₂×D₄	—	4	2	no	—
355	C₂×D₄	—	4	2	no	—
356	C₂×D₄	—	8	2	no	—
357	C₂×D₄	—	8	2	no	—
358	C₂×D₄	—	8	2	no	—
359	C₂×D₄	—	8	4	no	—
360	C₂×D₄	C₂×D₄	1	1	yes	characteristic
361	C₂×D₄	C₂×D₄	1	2	yes	—
362	C₂×D₄	C₂⁴	1	1	yes	characteristic
363	C₂×D₄	C₂⁴	1	2	yes	—
364	C₂×D₄	C₂⁴	1	2	yes	—
365	C₂×D₄	C₂⁴	1	2	yes	—
366	C₂²×C₄	—	2	1	no	—
367	C₂²×C₄	—	2	1	no	—
368	C₂²×C₄	—	2	2	no	—
369	C₂²×C₄	—	2	2	no	—
370	C₂²×C₄	—	2	1	no	—
371	C₂²×C₄	—	2	2	no	—
372	C₂²×C₄	—	2	2	no	—
373	C₂²×C₄	—	2	2	no	—
374	C₂²×C₄	—	2	2	no	—
375	C₂²×C₄	—	2	2	no	—
376	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
377	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
378	C₂²×C₄	C₂⁴	1	1	yes	characteristic
379	C₂²×C₄	C₂⁴	1	2	yes	—
380	Q₁₆	—	2	2	no	—
381	Q₁₆	—	4	1	no	—
382	SD₁₆	—	2	4	no	—
383	SD₁₆	—	2	4	no	—
384	SD₁₆	—	2	2	no	—
385	SD₁₆	—	4	2	no	—
386	SD₁₆	—	4	2	no	—
387	SD₁₆	—	4	1	no	—
388	SD₁₆	—	4	2	no	—
389	D₈	—	4	2	no	—
390	D₈	—	4	2	no	—
391	D₈	—	4	2	no	—
392	D₈	—	4	2	no	—
393	D₈	—	4	2	no	—
394	M₁₆	—	4	2	no	—
395	C₂×C₈	—	4	2	no	—
396	C₂×C₈	—	4	2	no	—
397	C₂×C₈	C₂⁴	1	1	yes	characteristic
398	C₂×C₈	C₂⁴	1	1	yes	characteristic
399	C₂×C₈	C₂⁴	1	2	yes	—
400	C₂×C₈	C₂⁴	1	1	yes	characteristic
401	C₂×C₈	C₂⁴	1	1	yes	characteristic
402	C₂×C₈	C₂⁴	1	2	yes	—
403	C₄⋊C₄	—	2	1	no	—
404	C₄⋊C₄	—	2	2	no	—
405	C₄⋊C₄	—	2	2	no	—
406	C₄⋊C₄	—	2	1	no	—
407	C₄⋊C₄	—	2	1	no	—
408	C₄⋊C₄	—	2	1	no	—
409	C₄⋊C₄	—	2	1	no	—
410	C₄⋊C₄	—	2	1	no	—
411	C₄⋊C₄	—	2	1	no	—
412	C₄⋊C₄	—	2	1	no	—
413	C₄⋊C₄	—	2	1	no	—
414	C₄⋊C₄	—	2	2	no	—
415	C₄⋊C₄	—	2	2	no	—
416	C₄⋊C₄	—	2	1	no	—
417	C₄⋊C₄	C₂×D₄	1	2	yes	—
418	C₄⋊C₄	C₂×D₄	1	2	yes	—
419	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
420	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
421	C₄⋊C₄	C₂×D₄	1	2	yes	—
422	C₄⋊C₄	C₂×D₄	1	2	yes	—
423	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
424	C₄⋊C₄	C₂⁴	1	2	yes	—
425	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
426	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
427	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
428	C₂²⋊C₄	—	2	1	no	—
429	C₂²⋊C₄	—	2	2	no	—
430	C₂²⋊C₄	—	2	2	no	—
431	C₂²⋊C₄	—	2	2	no	—
432	C₂²⋊C₄	—	2	2	no	—
433	C₂²⋊C₄	—	2	2	no	—
434	C₂²⋊C₄	—	2	1	no	—
435	C₂²⋊C₄	—	2	1	no	—
436	C₂²⋊C₄	—	2	1	no	—
437	C₂²⋊C₄	—	2	2	no	—
438	C₂²⋊C₄	—	2	2	no	—
439	C₂²⋊C₄	—	2	2	no	—
440	C₂²⋊C₄	—	2	2	no	—
441	C₂²⋊C₄	—	2	2	no	—
442	C₂²⋊C₄	—	2	2	no	—
443	C₂²⋊C₄	—	2	1	no	—
444	C₂²⋊C₄	—	2	2	no	—
445	C₂²⋊C₄	—	2	2	no	—
446	C₂²⋊C₄	C₂×D₄	1	2	yes	—
447	C₂²⋊C₄	C₂×D₄	1	2	yes	—
448	C₂²⋊C₄	C₂×D₄	1	2	yes	—
449	C₂²⋊C₄	C₂×D₄	1	2	yes	—
450	C₂²⋊C₄	C₂×D₄	1	2	yes	—
451	C₄²	—	2	1	no	—
452	C₄²	—	2	1	no	—
453	C₄²	—	2	1	no	—
454	C₄²	—	2	1	no	—
455	C₄²	—	2	1	no	—
456	C₄²	—	2	2	no	—
457	C₄²	C₂×D₄	1	1	yes	characteristic
458	C₄²	C₂×D₄	1	1	yes	characteristic
459	C₄²	C₂⁴	1	1	yes	characteristic
460	C₄²	C₂⁴	1	2	yes	—
461	C₄²	C₂⁴	1	1	yes	characteristic
462	C₂³	—	2	2	no	—
463	C₂³	—	2	2	no	—
464	C₂³	—	2	1	no	—
465	C₂³	—	2	2	no	—
466	C₂³	—	4	4	no	—
467	C₂³	—	8	2	no	—
468	C₂³	—	8	2	no	—
469	C₂³	—	8	2	no	—
470	C₂³	—	8	2	no	—
471	C₂³	—	8	2	no	—
472	C₂³	C₂²×D₄	1	2	yes	—
473	C₂³	C₂²×D₄	1	1	yes	characteristic
474	Q₈	—	2	2	no	—
475	Q₈	—	2	1	no	—
476	Q₈	—	2	1	no	—
477	Q₈	—	2	1	no	—
478	Q₈	—	2	1	no	—
479	Q₈	—	2	1	no	—
480	Q₈	—	4	2	no	—
481	Q₈	—	8	1	no	—
482	Q₈	—	8	2	no	—
483	Q₈	H(5,𝔽₂)	1	2	yes	—
484	D₄	—	2	4	no	—
485	D₄	—	2	2	no	—
486	D₄	—	2	2	no	—
487	D₄	—	2	1	no	—
488	D₄	—	2	2	no	—
489	D₄	—	2	2	no	—
490	D₄	—	2	2	no	—
491	D₄	—	2	2	no	—
492	D₄	—	2	2	no	—
493	D₄	—	2	1	no	—
494	D₄	—	4	4	no	—
495	D₄	—	4	2	no	—
496	D₄	—	4	4	no	—
497	D₄	—	4	2	no	—
498	D₄	—	4	2	no	—
499	D₄	—	4	2	no	—
500	D₄	—	8	2	no	—
501	D₄	—	8	2	no	—
502	D₄	—	8	2	no	—
503	D₄	—	8	1	no	—
504	D₄	—	8	1	no	—
505	D₄	—	8	2	no	—
506	D₄	—	8	2	no	—
507	D₄	—	8	1	no	—
508	D₄	—	8	2	no	—
509	D₄	—	8	2	no	—
510	D₄	—	8	2	no	—
511	D₄	—	8	2	no	—
512	D₄	—	8	2	no	—
513	C₂×C₄	—	2	2	no	—
514	C₂×C₄	—	2	1	no	—
515	C₂×C₄	—	2	2	no	—
516	C₂×C₄	—	2	1	no	—
517	C₂×C₄	—	2	2	no	—
518	C₂×C₄	—	2	1	no	—
519	C₂×C₄	—	2	2	no	—
520	C₂×C₄	—	2	1	no	—
521	C₂×C₄	—	2	1	no	—
522	C₂×C₄	—	2	1	no	—
523	C₂×C₄	—	2	1	no	—
524	C₂×C₄	—	2	1	no	—
525	C₂×C₄	—	2	2	no	—
526	C₂×C₄	—	2	1	no	—
527	C₂×C₄	—	4	4	no	—
528	C₂×C₄	—	4	2	no	—
529	C₂×C₄	—	4	2	no	—
530	C₂×C₄	—	4	2	no	—
531	C₂×C₄	—	8	2	no	—
532	C₂×C₄	—	8	2	no	—
533	C₂×C₄	—	8	2	no	—
534	C₂×C₄	—	8	2	no	—
535	C₂×C₄	—	8	2	no	—
536	C₂×C₄	—	8	2	no	—
537	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
538	C₂×C₄	C₂²×D₄	1	2	yes	—
539	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
540	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
541	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
542	C₂×C₄	C₂²×D₄	1	2	yes	—
543	C₂×C₄	C₂²×D₄	1	2	yes	—
544	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
545	C₂×C₄	C₂⁵	1	1	yes	characteristic
546	C₈	—	2	1	no	—
547	C₈	—	2	2	no	—
548	C₈	—	2	2	no	—
549	C₈	—	2	1	no	—
550	C₈	—	2	1	no	—
551	C₈	—	2	1	no	—
552	C₂²	—	2	1	no	—
553	C₂²	—	2	1	no	—
554	C₂²	—	2	2	no	—
555	C₂²	—	2	2	no	—
556	C₂²	—	2	2	no	—
557	C₂²	—	4	2	no	—
558	C₂²	—	4	2	no	—
559	C₂²	—	4	1	no	—
560	C₂²	—	4	2	no	—
561	C₂²	—	4	2	no	—
562	C₂²	—	4	2	no	—
563	C₂²	—	4	1	no	—
564	C₂²	—	4	2	no	—
565	C₂²	—	4	1	no	—
566	C₂²	—	4	2	no	—
567	C₂²	—	4	2	no	—
568	C₂²	—	4	2	no	—
569	C₂²	—	16	4	no	—
570	C₂²	—	16	4	no	—
571	C₂²	#576	1	2	yes	—
572	C₂²	C₂³×D₄	1	1	yes	characteristic
573	C₄	—	2	2	no	—
574	C₄	—	2	1	no	—
575	C₄	—	2	2	no	—
576	C₄	—	2	1	no	—
577	C₄	—	2	1	no	—
578	C₄	—	2	2	no	—
579	C₄	—	2	1	no	—
580	C₄	—	2	2	no	—
581	C₄	—	4	1	no	—
582	C₄	—	4	1	no	—
583	C₄	—	4	1	no	—
584	C₄	—	4	1	no	—
585	C₄	—	4	1	no	—
586	C₄	—	4	2	no	—
587	C₄	—	4	1	no	—
588	C₄	#577	1	2	yes	—
589	C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
590	C₄	#585	1	1	yes	characteristic
591	C₂	—	2	2	no	—
592	C₂	—	4	2	no	—
593	C₂	—	8	2	no	—
594	C₂	—	8	2	no	—
595	C₂	—	8	2	no	—
596	C₂	—	8	1	no	—
597	C₂	#3488	1	1	yes	characteristic
598	C₂	C₂×#576	1	1	yes	characteristic
599	C₂	C₂×#577	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. #3543	C₂	semidirect
2. #3522	C₂	semidirect
3. #3399	C₂	semidirect
4. #3396	C₂	semidirect
5. #3375	C₂	semidirect
6. #3362	C₂	semidirect
7. #3333	C₂	semidirect
8. #3306	C₂	semidirect
9. #3295	C₂	semidirect
10. #3294	C₂	semidirect
11. #3287	C₂	semidirect
12. #3282	C₂	semidirect
13. #3274	C₂	semidirect
14. #3265	C₂	semidirect
15. #3257	C₂	semidirect
16. #3247	C₂	semidirect
17. #3224	C₂	semidirect
18. #3205	C₂	semidirect
19. #3119	C₂	semidirect
20. #3108	C₂	semidirect
21. #3045	C₂	semidirect
22. C₂×#460	C₂	semidirect
23. #2994	C₂	semidirect
24. C₂×AGL(1,ℤ/8)	C₂²	semidirect
25. C₂×#135	C₂²	semidirect
26. C₂²×SD₁₆	C₂²	semidirect
30. #559	C₂²	semidirect
31. Q₈²	C₂²	semidirect
33. #554	C₂²	semidirect
36. #550	C₂²	semidirect
37. #548	C₂²	semidirect
39. #547	C₂²	semidirect
46. #542	C₂²	semidirect
53. #532	C₂²	semidirect
58. #520	C₂²	semidirect
59. C₂×C₄×Q₈	C₂²	semidirect
60. #496	C₂²	semidirect
61. #495	C₂²	semidirect
63. #493	C₂²	semidirect
64. #489	C₂²	semidirect
66. #486	C₂²	semidirect
67. #486	C₂²	semidirect
68. #483	C₂²	semidirect
69. #481	C₂²	semidirect
71. #480	C₂²	semidirect
72. #479	C₂²	semidirect
73. #479	C₂²	semidirect
74. #478	C₂²	semidirect
75. #477	C₂²	semidirect
76. #476	C₂²	semidirect
77. #476	C₂²	semidirect
78. #474	C₂²	semidirect
79. #469	C₂²	semidirect
80. #468	C₂²	semidirect
82. #466	C₂²	semidirect
83. #465	C₂²	semidirect
84. #465	C₂²	semidirect
85. #464	C₂²	semidirect
86. #464	C₂²	semidirect
87. #464	C₂²	semidirect
88. #463	C₂²	semidirect
89. #463	C₂²	semidirect
90. #463	C₂²	semidirect
91. #463	C₂²	semidirect
94. #460	C₂²	semidirect
95. #460	C₂²	semidirect
96. #460	C₂²	semidirect
97. #460	C₂²	semidirect
98. #460	C₂²	semidirect
99. #460	C₂²	semidirect
100. #459	C₂²	semidirect
101. #459	C₂²	semidirect
102. #459	C₂²	semidirect
103. #459	C₂²	semidirect
104. #452	C₂²	semidirect
105. #451	C₂²	semidirect
106. #450	C₂²	semidirect
107. #449	C₂²	semidirect
108. #449	C₂²	semidirect
109. #449	C₂²	semidirect
111. #447	C₂²	semidirect
112. #447	C₂²	semidirect
113. #447	C₂²	semidirect
114. #446	C₂²	semidirect
115. C₈×Q₈	C₂²	semidirect
116. #442	C₂²	semidirect
117. #440	C₂²	semidirect
118. C₄×Q₁₆	C₂²	semidirect
119. C₄×Q₁₆	C₂²	semidirect
120. C₄×SD₁₆	C₂²	semidirect
121. C₄×SD₁₆	C₂²	semidirect
122. C₄×SD₁₆	C₂²	semidirect
123. C₄×D₈	C₂²	semidirect
124. #436	C₂²	semidirect
125. #435	C₂²	semidirect
126. C₈×D₄	C₂²	semidirect
127. C₈×D₄	C₂²	semidirect
128. #433	C₂²	semidirect
129. #431	C₂²	semidirect
130. #424	C₂²	semidirect
131. C₂×C₄⋊C₈	C₂²	semidirect
132. #417	C₂²	semidirect
133. C₂×#102	C₂²	semidirect
134. C₂×#102	C₂²	semidirect

Maximal subgroups

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

subgroup	index
#3543	2
#3522	2
#3399	2
#3396	2
#3375	2
#3362	2
#3333	2
#3306	2
#3295	2
#3294	2
#3287	2
#3282	2
#3274	2
#3265	2
#3257	2
#3247	2
#3224	2
#3205	2
#3119	2
#3108	2
#3045	2
C₂×#460	2
#2994	2