Subgroups — #61493

Order 256.

918 conjugacy classes of subgroups.

The subgroup lattice has 573 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3515	C₂	1	1	yes	maximal, characteristic, complemented
2	#3514	C₂	1	1	yes	maximal, characteristic, complemented
3	#3400	C₂	1	1	yes	maximal, characteristic, complemented
4	#3384	C₂	1	1	yes	maximal, characteristic, complemented
5	#3361	C₂	1	1	yes	maximal, characteristic, complemented
6	#3359	C₂	1	1	yes	maximal, characteristic, complemented
7	#3356	C₂	1	1	yes	maximal, characteristic, complemented
8	#3348	C₂	1	2	yes	maximal, complemented
9	#3303	C₂	1	2	yes	maximal, complemented
10	#3302	C₂	1	1	yes	maximal, characteristic, complemented
11	#3296	C₂	1	2	yes	maximal, complemented
12	#3295	C₂	1	1	yes	maximal, characteristic, complemented
13	#3272	C₂	1	1	yes	maximal, characteristic, complemented
14	#3267	C₂	1	2	yes	maximal, complemented
15	#3178	C₂	1	2	yes	maximal, complemented
16	#3167	C₂	1	1	yes	maximal, characteristic, complemented
17	#3125	C₂	1	2	yes	maximal, complemented
18	#3123	C₂	1	2	yes	maximal, complemented
19	#3116	C₂	1	1	yes	maximal, characteristic, complemented
20	#3115	C₂	1	1	yes	maximal, characteristic, complemented
21	#2966	C₂	1	1	yes	maximal, characteristic, complemented
22	#2946	C₂	1	2	yes	maximal, complemented
23	C₄×#135	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×AGL(1,ℤ/8)	C₂²	1	2	yes	—
25	C₂×#135	C₂²	1	1	yes	characteristic
26	#559	C₂²	1	1	yes	characteristic
27	#557	C₂²	1	1	yes	characteristic, complemented
28	#556	C₂²	1	1	yes	characteristic
29	#555	C₂²	1	2	yes	—
30	#554	C₂²	1	1	yes	characteristic
31	#554	C₂²	1	1	yes	characteristic, complemented
32	#553	—	2	1	no	—
33	#552	—	2	2	no	—
34	#552	—	2	1	no	—
35	#552	C₂²	1	2	yes	complemented
36	#551	—	2	2	no	—
37	D₄×Q₈	C₂²	1	1	yes	characteristic
38	#548	—	2	1	no	—
39	#547	C₂²	1	1	yes	characteristic
40	#547	C₂²	1	2	yes	complemented
41	#546	—	2	1	no	—
42	#546	C₂²	1	2	yes	—
43	D₄²	C₂²	1	1	yes	characteristic
44	#542	C₂²	1	2	yes	—
45	#541	C₂²	1	2	yes	complemented
46	#539	—	2	2	no	—
47	#538	—	2	2	no	—
48	#533	C₂²	1	1	yes	characteristic, complemented
49	#532	C₂²	1	1	yes	characteristic
50	#529	—	2	1	no	—
51	#529	—	2	1	no	—
52	#529	C₂²	1	1	yes	characteristic
53	C₂×#125	—	2	1	no	—
54	C₂×#124	—	2	1	no	—
55	#520	C₂²	1	2	yes	complemented
56	#518	C₂²	1	2	yes	—
57	C₄×#41	C₂²	1	1	yes	characteristic
58	C₄×#41	C₂²	1	1	yes	characteristic, complemented
59	#501	C₂²	1	2	yes	complemented
60	#498	C₂²	1	1	yes	characteristic, complemented
61	#497	C₂²	1	2	yes	complemented
62	#492	C₂²	1	1	yes	characteristic
63	#488	C₂²	1	2	yes	complemented
64	#487	C₂²	1	1	yes	characteristic, complemented
65	#487	C₂²	1	2	yes	complemented
66	#486	C₂²	1	1	yes	characteristic
67	#485	C₂²	1	2	yes	complemented
68	#485	C₂²	1	2	yes	complemented
69	#485	C₂²	1	2	yes	complemented
70	#483	C₂²	1	2	yes	complemented
71	#482	C₂²	1	2	yes	complemented
72	#481	C₂²	1	2	yes	—
73	#478	C₂²	1	2	yes	—
74	#478	C₂²	1	2	yes	complemented
75	#477	C₂²	1	1	yes	characteristic, complemented
76	#476	C₂²	1	1	yes	characteristic
77	#476	C₂²	1	2	yes	complemented
78	#475	C₂²	1	2	yes	complemented
79	#475	C₂²	1	1	yes	characteristic, complemented
80	#474	C₂²	1	1	yes	characteristic, complemented
81	#470	C₂²	1	2	yes	complemented
82	#468	C₂²	1	2	yes	—
83	#467	C₂²	1	2	yes	complemented
84	#465	C₂²	1	2	yes	—
85	#465	C₂²	1	2	yes	complemented
86	#465	C₂²	1	2	yes	complemented
87	#464	C₂²	1	2	yes	complemented
88	#463	C₂²	1	2	yes	complemented
89	#462	C₂²	1	1	yes	characteristic, complemented
90	#461	C₂²	1	1	yes	characteristic
91	#461	C₂²	1	2	yes	—
92	#461	C₂²	1	2	yes	complemented
93	#460	C₂²	1	1	yes	characteristic
94	#459	C₂²	1	1	yes	characteristic
95	#452	C₂²	1	2	yes	—
96	#452	C₂²	1	2	yes	complemented
97	#450	C₂²	1	2	yes	—
98	#450	C₂²	1	2	yes	—
99	#449	C₂²	1	2	yes	—
100	#449	C₂²	1	2	yes	complemented
101	#446	C₂²	1	1	yes	characteristic, complemented
102	C₈×Q₈	C₂²	1	1	yes	characteristic, complemented
103	#442	C₂²	1	2	yes	—
104	#442	C₂²	1	2	yes	complemented
105	#441	C₂²	1	2	yes	complemented
106	#440	C₂²	1	2	yes	—
107	#440	C₂²	1	2	yes	complemented
108	#440	C₂²	1	2	yes	complemented
109	C₄×Q₁₆	C₂²	1	1	yes	characteristic, complemented
110	C₄×Q₁₆	C₂²	1	1	yes	characteristic, complemented
111	C₄×SD₁₆	C₂²	1	1	yes	characteristic
112	C₄×SD₁₆	C₂²	1	2	yes	—
113	C₄×SD₁₆	C₂²	1	1	yes	characteristic
114	C₄×SD₁₆	C₂²	1	1	yes	characteristic, complemented
115	C₄×SD₁₆	C₂²	1	2	yes	complemented
116	C₄×SD₁₆	C₂²	1	1	yes	characteristic, complemented
117	C₄×SD₁₆	C₂²	1	2	yes	complemented
118	C₄×D₈	C₂²	1	1	yes	characteristic
119	C₄×D₈	C₂²	1	1	yes	characteristic
120	C₄×D₈	C₂²	1	2	yes	complemented
121	#436	C₂²	1	1	yes	characteristic
122	#435	C₂²	1	2	yes	complemented
123	C₈×D₄	C₂²	1	1	yes	characteristic
124	C₈×D₄	C₂²	1	2	yes	complemented
125	#433	C₂²	1	2	yes	complemented
126	#432	C₂²	1	1	yes	characteristic, complemented
127	#428	C₂²	1	2	yes	complemented
128	#427	C₂²	1	1	yes	characteristic, complemented
129	#416	C₂²	1	1	yes	characteristic
130	#416	C₂²	1	1	yes	characteristic, complemented
131	#416	C₂²	1	2	yes	complemented
132	C₂×#102	C₂²	1	2	yes	—
133	#405	C₂²	1	2	yes	complemented
134	C₂×C₄×C₈	C₂²	1	1	yes	characteristic, complemented
135	C₂×#41	—	2	1	no	—
136	C₂×#41	C₂³	1	1	yes	characteristic
137	C₂×#41	C₂³	1	1	yes	characteristic
138	C₂×#41	C₂³	1	2	yes	—
139	C₂²×Q₈	—	2	1	no	—
140	C₂²×D₄	—	2	1	no	—
141	C₂²×D₄	C₂³	1	2	yes	—
142	AGL(1,ℤ/8)	—	2	8	no	—
143	#135	—	2	4	no	—
144	C₂×Q₁₆	C₂³	1	1	yes	characteristic
145	C₂×Q₁₆	C₂³	1	2	yes	—
146	C₂×SD₁₆	C₂³	1	1	yes	characteristic
147	C₂×SD₁₆	C₂³	1	1	yes	characteristic
148	C₂×SD₁₆	C₂³	1	2	yes	—
149	C₂×SD₁₆	C₂³	1	2	yes	—
150	C₂×SD₁₆	C₂³	1	2	yes	—
151	C₂×SD₁₆	C₂³	1	2	yes	—
152	C₂×D₈	C₂³	1	2	yes	—
153	C₂×D₈	C₂³	1	1	yes	characteristic
154	C₂×M₁₆	C₂³	1	2	yes	—
155	C₂²×C₈	C₂³	1	1	yes	characteristic
156	C₂²×C₈	C₂³	1	1	yes	characteristic
157	C₂²×C₈	C₂³	1	2	yes	—
158	C₄⋊Q₈	C₂³	1	1	yes	characteristic
159	C₄⋊Q₈	C₂³	1	2	yes	—
160	C₄⋊Q₈	C₂³	1	1	yes	characteristic
161	C₄⋊Q₈	C₂³	1	1	yes	characteristic
162	C₄⋊Q₈	C₂³	1	2	yes	—
163	#127	C₂³	1	1	yes	characteristic
164	#126	—	2	2	no	—
165	#126	—	2	2	no	—
166	#126	—	2	2	no	—
167	#126	—	2	2	no	—
168	#126	—	2	2	no	—
169	#126	D₄	1	2	yes	—
170	#125	—	2	2	no	—
171	#125	—	2	2	no	—
172	#125	—	2	1	no	—
173	#125	—	2	1	no	—
174	#125	—	2	2	no	—
175	#125	—	2	2	no	—
176	#125	—	2	1	no	—
177	#125	D₄	1	1	yes	characteristic
178	#125	C₂³	1	2	yes	—
179	#124	—	2	1	no	—
180	#124	—	2	1	no	—
181	#124	—	2	2	no	—
182	#124	—	2	2	no	—
183	#124	—	2	2	no	—
184	#124	—	2	1	no	—
185	#124	D₄	1	1	yes	characteristic
186	#124	C₂³	1	2	yes	—
187	#123	—	2	2	no	—
188	#123	—	2	2	no	—
189	#123	—	2	2	no	—
190	#123	—	2	2	no	—
191	#123	—	2	2	no	—
192	#123	—	2	2	no	—
193	#123	—	2	2	no	—
194	#123	D₄	1	2	yes	—
195	C₂²⋊Q₈	—	2	1	no	—
196	C₂²⋊Q₈	—	2	1	no	—
197	C₂²⋊Q₈	—	2	1	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	1	yes	characteristic
203	C₂²⋊Q₈	C₂³	1	2	yes	—
204	C₂²⋊Q₈	C₂³	1	2	yes	—
205	C₂²⋊Q₈	C₂³	1	2	yes	—
206	C₂²⋊Q₈	C₂³	1	2	yes	—
207	#121	—	2	1	no	—
208	#121	—	2	2	no	—
209	#121	—	2	2	no	—
210	#121	—	2	1	no	—
211	#121	—	2	1	no	—
212	#121	—	2	2	no	—
213	#121	D₄	1	1	yes	characteristic
214	#121	C₂³	1	2	yes	—
215	#121	C₂³	1	2	yes	—
216	#120	—	2	2	no	—
217	#120	—	2	2	no	—
218	C₄×Q₈	—	2	1	no	—
219	C₄×Q₈	—	2	1	no	—
220	C₄×Q₈	—	2	1	no	—
221	C₄×Q₈	C₂³	1	1	yes	characteristic
222	C₄×Q₈	C₂³	1	1	yes	characteristic
223	C₄×Q₈	C₂³	1	1	yes	characteristic
224	C₄×Q₈	C₂³	1	1	yes	characteristic
225	C₄×Q₈	C₂³	1	2	yes	—
226	C₄×Q₈	C₂³	1	2	yes	—
227	C₄×Q₈	C₂³	1	1	yes	characteristic
228	C₄×D₄	—	2	1	no	—
229	C₄×D₄	—	2	1	no	—
230	C₄×D₄	—	2	1	no	—
231	C₄×D₄	—	2	1	no	—
232	C₄×D₄	—	2	1	no	—
233	C₄×D₄	—	2	2	no	—
234	C₄×D₄	—	2	2	no	—
235	C₄×D₄	—	2	1	no	—
236	C₄×D₄	—	2	2	no	—
237	C₄×D₄	—	2	2	no	—
238	C₄×D₄	—	2	1	no	—
239	C₄×D₄	C₂³	1	1	yes	characteristic
240	C₄×D₄	C₂³	1	1	yes	characteristic
241	C₄×D₄	C₂³	1	1	yes	characteristic
242	C₄×D₄	C₂³	1	1	yes	characteristic
243	C₄×D₄	C₂³	1	2	yes	—
244	C₄×D₄	C₂³	1	2	yes	—
245	C₄×D₄	C₂³	1	2	yes	—
246	C₄×D₄	C₂³	1	2	yes	—
247	C₄×D₄	C₂³	1	1	yes	characteristic
248	C₄×D₄	C₂³	1	2	yes	—
249	#117	—	2	1	no	—
250	#117	—	2	2	no	—
251	#117	—	2	2	no	—
252	#117	—	2	2	no	—
253	#117	—	2	1	no	—
254	#117	—	2	1	no	—
255	#117	C₂³	1	1	yes	characteristic
256	#117	C₂³	1	1	yes	characteristic
257	#117	C₂³	1	2	yes	—
258	#117	C₂³	1	2	yes	—
259	C₂×C₄⋊C₄	—	2	2	no	—
260	C₂×C₄⋊C₄	—	2	1	no	—
261	C₂×C₄⋊C₄	—	2	2	no	—
262	C₂×C₄⋊C₄	—	2	1	no	—
263	C₂×C₄⋊C₄	C₂³	1	2	yes	—
264	C₂×C₂²⋊C₄	—	2	2	no	—
265	C₂×C₂²⋊C₄	—	2	2	no	—
266	C₂×C₂²⋊C₄	—	2	2	no	—
267	C₂×C₄²	—	2	1	no	—
268	C₂×C₄²	—	2	1	no	—
269	C₂×C₄²	C₂³	1	1	yes	characteristic
270	#107	C₂³	1	1	yes	characteristic
271	#107	C₂³	1	1	yes	characteristic
272	#107	C₂³	1	2	yes	—
273	#107	C₂³	1	2	yes	—
274	#106	C₂³	1	1	yes	characteristic
275	#106	C₂³	1	1	yes	characteristic
276	#106	C₂³	1	2	yes	—
277	#106	C₂³	1	2	yes	—
278	#106	C₂³	1	2	yes	—
279	#106	C₂³	1	2	yes	—
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	2	yes	—
287	#103	C₂³	1	1	yes	characteristic
288	#103	C₂³	1	1	yes	characteristic
289	#103	C₂³	1	2	yes	—
290	#103	C₂³	1	2	yes	—
291	#103	C₂³	1	2	yes	—
292	#103	C₂³	1	2	yes	—
293	#103	C₂³	1	2	yes	—
294	#102	C₂³	1	1	yes	characteristic
295	#102	C₂³	1	2	yes	—
296	#102	C₂³	1	2	yes	—
297	#102	C₂³	1	2	yes	—
298	#102	C₂³	1	1	yes	characteristic
299	#102	C₂³	1	1	yes	characteristic
300	#102	C₂³	1	1	yes	characteristic
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	#97	C₂³	1	2	yes	—
308	#97	C₂³	1	2	yes	—
309	C₄×C₈	C₂³	1	1	yes	characteristic
310	C₄×C₈	C₂³	1	1	yes	characteristic
311	C₄×C₈	C₂³	1	1	yes	characteristic
312	C₄×C₈	C₂³	1	1	yes	characteristic
313	C₄×C₈	C₂³	1	2	yes	—
314	C₂⁴	—	2	2	no	—
315	#41	—	2	2	no	—
316	#41	—	2	2	no	—
317	#41	—	2	4	no	—
318	#41	—	4	2	no	—
319	#41	—	4	1	no	—
320	#41	—	4	1	no	—
321	#41	—	8	2	no	—
322	C₂×Q₈	—	2	1	no	—
323	C₂×Q₈	—	2	1	no	—
324	C₂×Q₈	—	2	2	no	—
325	C₂×Q₈	—	8	2	no	—
326	C₂×Q₈	C₂×D₄	1	1	yes	characteristic
327	C₂×Q₈	C₂⁴	1	1	yes	characteristic
328	C₂×Q₈	C₂⁴	1	2	yes	—
329	C₂×Q₈	C₂⁴	1	1	yes	characteristic
330	C₂×D₄	—	2	4	no	—
331	C₂×D₄	—	2	1	no	—
332	C₂×D₄	—	2	2	no	—
333	C₂×D₄	—	2	1	no	—
334	C₂×D₄	—	2	2	no	—
335	C₂×D₄	—	2	2	no	—
336	C₂×D₄	—	2	2	no	—
337	C₂×D₄	—	2	1	no	—
338	C₂×D₄	—	2	1	no	—
339	C₂×D₄	—	4	2	no	—
340	C₂×D₄	—	8	2	no	—
341	C₂×D₄	C₂×D₄	1	1	yes	characteristic
342	C₂×D₄	C₂×D₄	1	2	yes	—
343	C₂×D₄	C₂⁴	1	2	yes	—
344	C₂×D₄	C₂⁴	1	1	yes	characteristic
345	C₂×D₄	C₂⁴	1	1	yes	characteristic
346	C₂²×C₄	—	2	2	no	—
347	C₂²×C₄	—	2	1	no	—
348	C₂²×C₄	—	2	1	no	—
349	C₂²×C₄	—	2	1	no	—
350	C₂²×C₄	—	2	1	no	—
351	C₂²×C₄	—	2	2	no	—
352	C₂²×C₄	—	2	1	no	—
353	C₂²×C₄	—	2	1	no	—
354	C₂²×C₄	—	2	2	no	—
355	C₂²×C₄	—	2	2	no	—
356	C₂²×C₄	—	2	2	no	—
357	C₂²×C₄	—	2	2	no	—
358	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
359	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
360	C₂²×C₄	C₂⁴	1	1	yes	characteristic
361	C₂²×C₄	C₂⁴	1	2	yes	—
362	Q₁₆	—	2	2	no	—
363	Q₁₆	—	4	2	no	—
364	SD₁₆	—	2	2	no	—
365	SD₁₆	—	2	2	no	—
366	SD₁₆	—	2	4	no	—
367	SD₁₆	—	2	4	no	—
368	SD₁₆	—	4	2	no	—
369	SD₁₆	—	4	2	no	—
370	D₈	—	2	4	no	—
371	D₈	#41	1	4	yes	complemented
372	M₁₆	—	2	4	no	—
373	C₂×C₈	—	2	2	no	—
374	C₂×C₈	—	4	1	no	—
375	C₂×C₈	—	4	2	no	—
376	C₂×C₈	C₂⁴	1	1	yes	characteristic
377	C₂×C₈	C₂⁴	1	1	yes	characteristic
378	C₂×C₈	C₂⁴	1	1	yes	characteristic
379	C₂×C₈	C₂⁴	1	2	yes	—
380	C₂×C₈	C₂⁴	1	2	yes	—
381	C₂×C₈	C₂⁴	1	1	yes	characteristic
382	C₄⋊C₄	—	2	2	no	—
383	C₄⋊C₄	—	2	1	no	—
384	C₄⋊C₄	—	2	1	no	—
385	C₄⋊C₄	—	2	2	no	—
386	C₄⋊C₄	—	2	2	no	—
387	C₄⋊C₄	—	2	2	no	—
388	C₄⋊C₄	—	2	2	no	—
389	C₄⋊C₄	—	2	2	no	—
390	C₄⋊C₄	—	2	2	no	—
391	C₄⋊C₄	—	2	2	no	—
392	C₄⋊C₄	—	2	1	no	—
393	C₄⋊C₄	—	2	1	no	—
394	C₄⋊C₄	—	2	1	no	—
395	C₄⋊C₄	—	2	1	no	—
396	C₄⋊C₄	—	2	2	no	—
397	C₄⋊C₄	—	2	2	no	—
398	C₄⋊C₄	—	2	1	no	—
399	C₄⋊C₄	—	2	2	no	—
400	C₄⋊C₄	—	2	1	no	—
401	C₄⋊C₄	—	2	2	no	—
402	C₄⋊C₄	C₂×D₄	1	2	yes	—
403	C₄⋊C₄	C₂×D₄	1	2	yes	—
404	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
405	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
406	C₄⋊C₄	C₂×D₄	1	2	yes	—
407	C₄⋊C₄	C₂×D₄	1	2	yes	—
408	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
409	C₄⋊C₄	C₂⁴	1	2	yes	—
410	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
411	C₄⋊C₄	C₂⁴	1	2	yes	—
412	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
413	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
414	C₂²⋊C₄	—	2	2	no	—
415	C₂²⋊C₄	—	2	2	no	—
416	C₂²⋊C₄	—	2	2	no	—
417	C₂²⋊C₄	—	2	2	no	—
418	C₂²⋊C₄	—	2	1	no	—
419	C₂²⋊C₄	—	2	1	no	—
420	C₂²⋊C₄	—	2	2	no	—
421	C₂²⋊C₄	—	2	1	no	—
422	C₂²⋊C₄	—	2	2	no	—
423	C₂²⋊C₄	—	2	2	no	—
424	C₂²⋊C₄	—	2	2	no	—
425	C₂²⋊C₄	—	2	2	no	—
426	C₂²⋊C₄	—	2	2	no	—
427	C₂²⋊C₄	—	2	1	no	—
428	C₂²⋊C₄	—	2	1	no	—
429	C₂²⋊C₄	—	2	1	no	—
430	C₂²⋊C₄	—	2	2	no	—
431	C₂²⋊C₄	—	2	2	no	—
432	C₂²⋊C₄	—	2	2	no	—
433	C₂²⋊C₄	C₂×D₄	1	2	yes	—
434	C₂²⋊C₄	C₂×D₄	1	2	yes	—
435	C₂²⋊C₄	C₂×D₄	1	2	yes	—
436	C₂²⋊C₄	C₂×D₄	1	2	yes	—
437	C₂²⋊C₄	C₂×D₄	1	2	yes	—
438	C₄²	—	2	1	no	—
439	C₄²	—	2	1	no	—
440	C₄²	—	2	1	no	—
441	C₄²	—	2	1	no	—
442	C₄²	—	2	1	no	—
443	C₄²	—	2	1	no	—
444	C₄²	—	2	2	no	—
445	C₄²	—	2	2	no	—
446	C₄²	—	2	2	no	—
447	C₄²	C₂×D₄	1	1	yes	characteristic
448	C₄²	C₂×D₄	1	1	yes	characteristic
449	C₄²	C₂⁴	1	1	yes	characteristic
450	C₄²	C₂⁴	1	1	yes	characteristic
451	C₄²	C₂⁴	1	2	yes	—
452	C₂³	—	2	1	no	—
453	C₂³	—	2	1	no	—
454	C₂³	—	2	2	no	—
455	C₂³	—	4	4	no	—
456	C₂³	—	8	2	no	—
457	C₂³	—	8	2	no	—
458	C₂³	C₂²×D₄	1	2	yes	—
459	C₂³	C₂²×D₄	1	1	yes	characteristic
460	Q₈	—	2	2	no	—
461	Q₈	—	2	2	no	—
462	Q₈	—	2	1	no	—
463	Q₈	—	2	1	no	—
464	Q₈	—	2	1	no	—
465	Q₈	—	2	2	no	—
466	Q₈	—	2	1	no	—
467	Q₈	—	4	2	no	—
468	Q₈	—	8	1	no	—
469	Q₈	—	8	2	no	—
470	D₄	—	2	2	no	—
471	D₄	—	2	2	no	—
472	D₄	—	2	1	no	—
473	D₄	—	2	1	no	—
474	D₄	—	2	2	no	—
475	D₄	—	4	2	no	—
476	D₄	—	4	4	no	—
477	D₄	—	4	2	no	—
478	D₄	—	4	2	no	—
479	D₄	—	4	4	no	—
480	D₄	—	4	2	no	—
481	D₄	—	8	1	no	—
482	D₄	—	8	2	no	—
483	D₄	—	8	2	no	—
484	D₄	C₂×#41	1	2	yes	—
485	D₄	C₂×#41	1	2	yes	—
486	C₂×C₄	—	2	2	no	—
487	C₂×C₄	—	2	1	no	—
488	C₂×C₄	—	2	2	no	—
489	C₂×C₄	—	2	2	no	—
490	C₂×C₄	—	2	1	no	—
491	C₂×C₄	—	2	1	no	—
492	C₂×C₄	—	2	1	no	—
493	C₂×C₄	—	2	1	no	—
494	C₂×C₄	—	2	1	no	—
495	C₂×C₄	—	2	1	no	—
496	C₂×C₄	—	2	1	no	—
497	C₂×C₄	—	2	2	no	—
498	C₂×C₄	—	2	2	no	—
499	C₂×C₄	—	2	2	no	—
500	C₂×C₄	—	4	1	no	—
501	C₂×C₄	—	4	2	no	—
502	C₂×C₄	—	4	2	no	—
503	C₂×C₄	—	4	4	no	—
504	C₂×C₄	—	4	2	no	—
505	C₂×C₄	—	4	2	no	—
506	C₂×C₄	—	8	1	no	—
507	C₂×C₄	—	8	1	no	—
508	C₂×C₄	—	8	2	no	—
509	C₂×C₄	—	8	2	no	—
510	C₂×C₄	—	8	2	no	—
511	C₂×C₄	—	8	2	no	—
512	C₂×C₄	—	8	2	no	—
513	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
514	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
515	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
516	C₂×C₄	C₂²×D₄	1	2	yes	—
517	C₂×C₄	C₂²×D₄	1	2	yes	—
518	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
519	C₂×C₄	C₂²×D₄	1	2	yes	—
520	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
521	C₂×C₄	C₂⁵	1	1	yes	characteristic
522	C₈	—	2	1	no	—
523	C₈	—	2	2	no	—
524	C₈	—	2	1	no	—
525	C₈	—	2	1	no	—
526	C₈	—	2	2	no	—
527	C₈	C₂×#41	1	2	yes	—
528	C₂²	—	2	1	no	—
529	C₂²	—	2	2	no	—
530	C₂²	—	2	1	no	—
531	C₂²	—	2	2	no	—
532	C₂²	—	2	2	no	—
533	C₂²	—	2	2	no	—
534	C₂²	—	2	1	no	—
535	C₂²	—	2	2	no	—
536	C₂²	—	4	1	no	—
537	C₂²	—	4	1	no	—
538	C₂²	—	4	1	no	—
539	C₂²	—	4	1	no	—
540	C₂²	—	4	2	no	—
541	C₂²	—	4	2	no	—
542	C₂²	—	4	2	no	—
543	C₂²	—	16	4	no	—
544	C₂²	C₂³×D₄	1	1	yes	characteristic
545	C₄	—	2	1	no	—
546	C₄	—	2	1	no	—
547	C₄	—	2	2	no	—
548	C₄	—	2	1	no	—
549	C₄	—	2	2	no	—
550	C₄	—	2	1	no	—
551	C₄	—	2	2	no	—
552	C₄	—	4	1	no	—
553	C₄	—	4	1	no	—
554	C₄	—	4	2	no	—
555	C₄	—	4	1	no	—
556	C₄	—	4	2	no	—
557	C₄	—	4	1	no	—
558	C₄	—	4	1	no	—
559	C₄	—	4	1	no	—
560	C₄	—	4	2	no	—
561	C₄	#577	1	2	yes	—
562	C₄	C₂²×#41	1	1	yes	characteristic
563	C₄	#585	1	1	yes	characteristic
564	C₂	—	4	1	no	—
565	C₂	—	4	2	no	—
566	C₂	—	4	2	no	—
567	C₂	—	4	2	no	—
568	C₂	—	8	2	no	—
569	C₂	D₄×#41	1	1	yes	characteristic
570	C₂	C₂×#577	1	1	yes	characteristic
571	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. #3515	C₂	semidirect
2. #3514	C₂	semidirect
3. #3400	C₂	semidirect
4. #3384	C₂	semidirect
5. #3361	C₂	semidirect
6. #3359	C₂	semidirect
7. #3356	C₂	semidirect
8. #3348	C₂	semidirect
9. #3303	C₂	semidirect
10. #3302	C₂	semidirect
11. #3296	C₂	semidirect
12. #3295	C₂	semidirect
13. #3272	C₂	semidirect
14. #3267	C₂	semidirect
15. #3178	C₂	semidirect
16. #3167	C₂	semidirect
17. #3125	C₂	semidirect
18. #3123	C₂	semidirect
19. #3116	C₂	semidirect
20. #3115	C₂	semidirect
21. #2966	C₂	semidirect
22. #2946	C₂	semidirect
23. C₄×#135	C₂	semidirect
27. #557	C₂²	semidirect
31. #554	C₂²	semidirect
35. #552	C₂²	semidirect
40. #547	C₂²	semidirect
45. #541	C₂²	semidirect
48. #533	C₂²	semidirect
55. #520	C₂²	semidirect
58. C₄×#41	C₂²	semidirect
59. #501	C₂²	semidirect
60. #498	C₂²	semidirect
61. #497	C₂²	semidirect
63. #488	C₂²	semidirect
64. #487	C₂²	semidirect
65. #487	C₂²	semidirect
67. #485	C₂²	semidirect
68. #485	C₂²	semidirect
69. #485	C₂²	semidirect
70. #483	C₂²	semidirect
71. #482	C₂²	semidirect
74. #478	C₂²	semidirect
75. #477	C₂²	semidirect
77. #476	C₂²	semidirect
78. #475	C₂²	semidirect
79. #475	C₂²	semidirect
80. #474	C₂²	semidirect
81. #470	C₂²	semidirect
83. #467	C₂²	semidirect
85. #465	C₂²	semidirect
86. #465	C₂²	semidirect
87. #464	C₂²	semidirect
88. #463	C₂²	semidirect
89. #462	C₂²	semidirect
92. #461	C₂²	semidirect
96. #452	C₂²	semidirect
100. #449	C₂²	semidirect
101. #446	C₂²	semidirect
102. C₈×Q₈	C₂²	semidirect
104. #442	C₂²	semidirect
105. #441	C₂²	semidirect
107. #440	C₂²	semidirect
108. #440	C₂²	semidirect
109. C₄×Q₁₆	C₂²	semidirect
110. C₄×Q₁₆	C₂²	semidirect
114. C₄×SD₁₆	C₂²	semidirect
115. C₄×SD₁₆	C₂²	semidirect
116. C₄×SD₁₆	C₂²	semidirect
117. C₄×SD₁₆	C₂²	semidirect
120. C₄×D₈	C₂²	semidirect
122. #435	C₂²	semidirect
124. C₈×D₄	C₂²	semidirect
125. #433	C₂²	semidirect
126. #432	C₂²	semidirect
127. #428	C₂²	semidirect
128. #427	C₂²	semidirect
130. #416	C₂²	semidirect
131. #416	C₂²	semidirect
133. #405	C₂²	semidirect
134. C₂×C₄×C₈	C₂²	semidirect
371. D₈	#41	semidirect

Maximal subgroups

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

subgroup	index
#3515	2
#3514	2
#3400	2
#3384	2
#3361	2
#3359	2
#3356	2
#3348	2
#3303	2
#3302	2
#3296	2
#3295	2
#3272	2
#3267	2
#3178	2
#3167	2
#3125	2
#3123	2
#3116	2
#3115	2
#2966	2
#2946	2
C₄×#135	2