Subgroups — #62434

Order 256.

950 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3562	C₂	1	2	yes	maximal, complemented
2	#3401	C₂	1	2	yes	maximal, complemented
3	#3396	C₂	1	1	yes	maximal, characteristic, complemented
4	#3393	C₂	1	1	yes	maximal, characteristic, complemented
5	#3287	C₂	1	1	yes	maximal, characteristic, complemented
6	#3285	C₂	1	1	yes	maximal, characteristic, complemented
7	#3285	C₂	1	1	yes	maximal, characteristic, complemented
8	#3283	C₂	1	1	yes	maximal, characteristic, complemented
9	#3280	C₂	1	1	yes	maximal, characteristic, complemented
10	#3280	C₂	1	1	yes	maximal, characteristic, complemented
11	#3275	C₂	1	2	yes	maximal, complemented
12	#3271	C₂	1	2	yes	maximal, complemented
13	#3267	C₂	1	2	yes	maximal, complemented
14	#3222	C₂	1	2	yes	maximal, complemented
15	#3221	C₂	1	2	yes	maximal, complemented
16	#3219	C₂	1	2	yes	maximal, complemented
17	#3177	C₂	1	1	yes	maximal, characteristic, complemented
18	#3176	C₂	1	1	yes	maximal, characteristic, complemented
19	#3168	C₂	1	1	yes	maximal, characteristic, complemented
20	#3156	C₂	1	1	yes	maximal, characteristic, complemented
21	#3155	C₂	1	1	yes	maximal, characteristic, complemented
22	#3147	C₂	1	1	yes	maximal, characteristic, complemented
23	#2966	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#137	C₂²	1	2	yes	complemented
25	C₂×AGL(1,ℤ/8)	C₂²	1	2	yes	—
26	C₂×#135	C₂²	1	1	yes	characteristic
27	C₂×#135	C₂²	1	1	yes	characteristic
28	C₂×#135	C₂²	1	1	yes	characteristic
29	C₂×#135	C₂²	1	2	yes	complemented
30	C₂×#135	C₂²	1	1	yes	characteristic, complemented
31	C₂²×Q₁₆	C₂²	1	1	yes	characteristic, complemented
32	C₂²×D₈	C₂²	1	1	yes	characteristic
33	#562	—	2	2	no	—
34	#560	—	2	2	no	—
35	#559	C₂²	1	2	yes	complemented
36	#556	C₂²	1	2	yes	complemented
37	#553	—	2	2	no	—
38	#551	—	2	2	no	—
39	#550	C₂²	1	2	yes	complemented
40	#548	C₂²	1	2	yes	—
41	#548	C₂²	1	2	yes	complemented
42	#547	C₂²	1	2	yes	—
43	#546	C₂²	1	2	yes	—
44	#546	C₂²	1	2	yes	—
45	#541	C₂²	1	2	yes	—
46	#540	—	2	2	no	—
47	#540	C₂²	1	2	yes	complemented
48	#539	—	2	2	no	—
49	#538	—	2	2	no	—
50	#538	—	2	2	no	—
51	#536	C₂²	1	2	yes	complemented
52	#535	C₂²	1	2	yes	—
53	#532	C₂²	1	2	yes	complemented
54	#529	C₂²	1	1	yes	characteristic
55	#529	C₂²	1	2	yes	complemented
56	#499	C₂²	1	1	yes	characteristic, complemented
57	#497	C₂²	1	2	yes	complemented
58	#497	C₂²	1	2	yes	complemented
59	#496	C₂²	1	2	yes	—
60	#496	C₂²	1	2	yes	—
61	#495	C₂²	1	1	yes	characteristic
62	#495	C₂²	1	1	yes	characteristic
63	#495	C₂²	1	1	yes	characteristic
64	#495	C₂²	1	1	yes	characteristic
65	#495	C₂²	1	1	yes	characteristic, complemented
66	#495	C₂²	1	2	yes	complemented
67	#494	C₂²	1	1	yes	characteristic, complemented
68	#494	C₂²	1	1	yes	characteristic, complemented
69	#493	C₂²	1	1	yes	characteristic
70	#493	C₂²	1	1	yes	characteristic
71	#492	C₂²	1	2	yes	complemented
72	#491	C₂²	1	2	yes	complemented
73	#490	C₂²	1	2	yes	complemented
74	#488	C₂²	1	2	yes	complemented
75	#470	C₂²	1	2	yes	—
76	#469	C₂²	1	2	yes	complemented
77	#467	C₂²	1	1	yes	characteristic
78	#467	C₂²	1	1	yes	characteristic
79	#467	C₂²	1	1	yes	characteristic, complemented
80	#466	C₂²	1	1	yes	characteristic
81	#466	C₂²	1	1	yes	characteristic
82	#466	C₂²	1	1	yes	characteristic, complemented
83	#465	C₂²	1	2	yes	complemented
84	#464	C₂²	1	2	yes	complemented
85	#464	C₂²	1	2	yes	complemented
86	#464	C₂²	1	2	yes	complemented
87	#464	C₂²	1	2	yes	complemented
88	#463	C₂²	1	2	yes	—
89	#463	C₂²	1	2	yes	—
90	#463	C₂²	1	2	yes	complemented
91	#463	C₂²	1	2	yes	complemented
92	#461	C₂²	1	2	yes	complemented
93	#461	C₂²	1	2	yes	complemented
94	#460	C₂²	1	2	yes	complemented
95	#460	C₂²	1	2	yes	complemented
96	#452	C₂²	1	2	yes	—
97	#452	C₂²	1	2	yes	—
98	#452	C₂²	1	2	yes	complemented
99	#452	C₂²	1	2	yes	complemented
100	#450	C₂²	1	2	yes	—
101	#450	C₂²	1	2	yes	—
102	#449	C₂²	1	2	yes	—
103	#449	C₂²	1	2	yes	—
104	#449	C₂²	1	2	yes	complemented
105	#449	C₂²	1	2	yes	complemented
106	#448	C₂²	1	2	yes	complemented
107	#448	C₂²	1	2	yes	complemented
108	#446	C₂²	1	1	yes	characteristic, complemented
109	C₈×Q₈	C₂²	1	1	yes	characteristic, complemented
110	#442	C₂²	1	2	yes	complemented
111	#441	C₂²	1	2	yes	complemented
112	C₄×Q₁₆	C₂²	1	1	yes	characteristic, complemented
113	C₄×Q₁₆	C₂²	1	1	yes	characteristic, complemented
114	C₄×Q₁₆	C₂²	1	1	yes	characteristic, complemented
115	C₄×SD₁₆	C₂²	1	2	yes	complemented
116	C₄×D₈	C₂²	1	1	yes	characteristic
117	C₄×D₈	C₂²	1	1	yes	characteristic
118	C₄×D₈	C₂²	1	1	yes	characteristic, complemented
119	#436	C₂²	1	1	yes	characteristic
120	#435	C₂²	1	1	yes	characteristic
121	#435	C₂²	1	1	yes	characteristic, complemented
122	C₈×D₄	C₂²	1	1	yes	characteristic
123	C₈×D₄	C₂²	1	1	yes	characteristic
124	C₈×D₄	C₂²	1	1	yes	characteristic, complemented
125	#433	C₂²	1	1	yes	characteristic
126	#433	C₂²	1	1	yes	characteristic, complemented
127	#432	C₂²	1	1	yes	characteristic, 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	C₂×#41	C₂³	1	2	yes	—
134	C₂×#41	C₂³	1	2	yes	—
135	C₂²×Q₈	C₂³	1	2	yes	—
136	C₂²×D₄	C₂³	1	2	yes	—
137	#137	—	4	4	no	—
138	AGL(1,ℤ/8)	—	4	4	no	—
139	#135	—	4	2	no	—
140	#135	—	4	2	no	—
141	#135	—	4	2	no	—
142	#135	—	4	2	no	—
143	#135	—	4	4	no	—
144	C₂×Q₁₆	—	4	2	no	—
145	C₂×Q₁₆	C₂³	1	1	yes	characteristic
146	C₂×Q₁₆	C₂³	1	1	yes	characteristic
147	C₂×Q₁₆	C₂³	1	1	yes	characteristic
148	C₂×Q₁₆	C₂³	1	2	yes	—
149	C₂×Q₁₆	C₂³	1	2	yes	—
150	C₂×Q₁₆	C₂³	1	2	yes	—
151	C₂×SD₁₆	C₂³	1	2	yes	—
152	C₂×SD₁₆	C₂³	1	2	yes	—
153	C₂×SD₁₆	C₂³	1	2	yes	—
154	C₂×SD₁₆	C₂³	1	2	yes	—
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	2	yes	—
159	C₂×SD₁₆	C₂³	1	2	yes	—
160	C₂×D₈	—	4	2	no	—
161	C₂×D₈	C₂³	1	1	yes	characteristic
162	C₂×D₈	C₂³	1	1	yes	characteristic
163	C₂×D₈	C₂³	1	1	yes	characteristic
164	C₂×D₈	C₂³	1	2	yes	—
165	C₂×D₈	C₂³	1	2	yes	—
166	C₂×D₈	C₂³	1	2	yes	—
167	C₂×M₁₆	C₂³	1	1	yes	characteristic
168	C₂×M₁₆	C₂³	1	1	yes	characteristic
169	C₂²×C₈	C₂³	1	1	yes	characteristic
170	C₂²×C₈	C₂³	1	1	yes	characteristic
171	C₂²×C₈	C₂³	1	1	yes	characteristic
172	C₂²×C₈	C₂³	1	1	yes	characteristic
173	C₄⋊Q₈	C₂³	1	2	yes	—
174	C₄⋊Q₈	C₂³	1	2	yes	—
175	#127	—	2	2	no	—
176	#127	C₂³	1	2	yes	—
177	#127	C₂³	1	2	yes	—
178	#126	—	2	2	no	—
179	#126	—	2	2	no	—
180	#126	—	2	2	no	—
181	#126	—	2	2	no	—
182	#126	—	2	2	no	—
183	#126	D₄	1	1	yes	characteristic
184	#126	D₄	1	1	yes	characteristic
185	#125	—	2	2	no	—
186	#125	—	2	2	no	—
187	#125	D₄	1	1	yes	characteristic
188	#125	C₂³	1	2	yes	—
189	#124	—	2	2	no	—
190	#124	—	2	2	no	—
191	#124	—	2	2	no	—
192	#124	D₄	1	1	yes	characteristic
193	#124	C₂³	1	2	yes	—
194	#124	C₂³	1	2	yes	—
195	#124	C₂³	1	2	yes	—
196	#124	C₂³	1	2	yes	—
197	#124	C₂³	1	2	yes	—
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	—	2	2	no	—
205	#123	—	2	2	no	—
206	#123	—	2	2	no	—
207	#123	—	2	2	no	—
208	#123	—	2	2	no	—
209	#123	D₄	1	1	yes	characteristic
210	#123	D₄	1	1	yes	characteristic
211	C₂²⋊Q₈	—	2	2	no	—
212	C₂²⋊Q₈	—	2	2	no	—
213	C₂²⋊Q₈	—	2	2	no	—
214	C₂²⋊Q₈	—	2	2	no	—
215	C₂²⋊Q₈	—	2	2	no	—
216	C₂²⋊Q₈	D₄	1	1	yes	characteristic
217	C₂²⋊Q₈	C₂³	1	2	yes	—
218	C₂²⋊Q₈	C₂³	1	2	yes	—
219	C₂²⋊Q₈	C₂³	1	2	yes	—
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	—	2	2	no	—
226	#121	—	2	2	no	—
227	#121	—	2	2	no	—
228	#121	—	2	2	no	—
229	#121	—	2	2	no	—
230	#121	—	2	2	no	—
231	#121	—	2	2	no	—
232	#121	—	2	2	no	—
233	#121	D₄	1	1	yes	characteristic
234	#121	C₂³	1	2	yes	—
235	#121	C₂³	1	2	yes	—
236	#121	C₂³	1	2	yes	—
237	#120	—	2	2	no	—
238	#120	—	2	2	no	—
239	#120	—	2	2	no	—
240	#120	—	2	2	no	—
241	C₄×Q₈	C₂³	1	2	yes	—
242	C₄×Q₈	C₂³	1	2	yes	—
243	C₄×Q₈	C₂³	1	2	yes	—
244	C₄×Q₈	C₂³	1	1	yes	characteristic
245	C₄×D₄	—	2	2	no	—
246	C₄×D₄	—	2	2	no	—
247	C₄×D₄	—	2	2	no	—
248	C₄×D₄	—	2	2	no	—
249	C₄×D₄	—	2	2	no	—
250	C₄×D₄	—	2	2	no	—
251	C₄×D₄	—	2	2	no	—
252	C₄×D₄	C₂³	1	2	yes	—
253	C₄×D₄	C₂³	1	2	yes	—
254	C₄×D₄	C₂³	1	2	yes	—
255	C₄×D₄	C₂³	1	1	yes	characteristic
256	C₄×D₄	C₂³	1	1	yes	characteristic
257	C₄×D₄	C₂³	1	1	yes	characteristic
258	#117	—	2	2	no	—
259	#117	—	2	2	no	—
260	#117	C₂³	1	1	yes	characteristic
261	#117	C₂³	1	1	yes	characteristic
262	C₂×C₄⋊C₄	—	2	2	no	—
263	C₂×C₂²⋊C₄	—	2	2	no	—
264	C₂×C₂²⋊C₄	—	2	2	no	—
265	C₂×C₄²	C₂³	1	1	yes	characteristic
266	#107	C₂³	1	1	yes	characteristic
267	#107	C₂³	1	1	yes	characteristic
268	#106	C₂³	1	2	yes	—
269	C₄⋊C₈	C₂³	1	1	yes	characteristic
270	C₄⋊C₈	C₂³	1	1	yes	characteristic
271	C₄⋊C₈	C₂³	1	1	yes	characteristic
272	C₄⋊C₈	C₂³	1	1	yes	characteristic
273	C₄⋊C₈	C₂³	1	1	yes	characteristic
274	C₄⋊C₈	C₂³	1	1	yes	characteristic
275	#103	C₂³	1	2	yes	—
276	#103	C₂³	1	2	yes	—
277	#103	C₂³	1	2	yes	—
278	#103	C₂³	1	2	yes	—
279	#103	C₂³	1	2	yes	—
280	#103	C₂³	1	2	yes	—
281	#102	C₂³	1	2	yes	—
282	#102	C₂³	1	2	yes	—
283	#102	C₂³	1	2	yes	—
284	#102	C₂³	1	2	yes	—
285	#102	C₂³	1	2	yes	—
286	#102	C₂³	1	2	yes	—
287	C₂²⋊C₈	C₂³	1	1	yes	characteristic
288	C₂²⋊C₈	C₂³	1	1	yes	characteristic
289	C₂²⋊C₈	C₂³	1	1	yes	characteristic
290	C₂²⋊C₈	C₂³	1	1	yes	characteristic
291	C₂²⋊C₈	C₂³	1	1	yes	characteristic
292	C₂²⋊C₈	C₂³	1	1	yes	characteristic
293	#97	C₂³	1	1	yes	characteristic
294	#97	C₂³	1	1	yes	characteristic
295	#97	C₂³	1	1	yes	characteristic
296	#97	C₂³	1	1	yes	characteristic
297	C₄×C₈	C₂³	1	1	yes	characteristic
298	C₄×C₈	C₂³	1	1	yes	characteristic
299	C₄×C₈	C₂³	1	1	yes	characteristic
300	C₄×C₈	C₂³	1	1	yes	characteristic
301	C₄×C₈	C₂³	1	1	yes	characteristic
302	C₄×C₈	C₂³	1	1	yes	characteristic
303	C₂⁴	—	2	2	no	—
304	#41	—	4	2	no	—
305	#41	—	4	2	no	—
306	#41	—	4	2	no	—
307	#41	—	4	2	no	—
308	#41	—	4	2	no	—
309	#41	—	4	2	no	—
310	#41	—	4	2	no	—
311	#41	—	4	2	no	—
312	C₂×Q₈	—	2	2	no	—
313	C₂×Q₈	—	4	2	no	—
314	C₂×Q₈	—	4	2	no	—
315	C₂×Q₈	C₂×D₄	1	1	yes	characteristic
316	C₂×Q₈	C₂⁴	1	2	yes	—
317	C₂×Q₈	C₂⁴	1	2	yes	—
318	C₂×Q₈	C₂⁴	1	2	yes	—
319	C₂×D₄	—	2	2	no	—
320	C₂×D₄	—	2	2	no	—
321	C₂×D₄	—	2	2	no	—
322	C₂×D₄	—	2	2	no	—
323	C₂×D₄	—	2	2	no	—
324	C₂×D₄	—	2	2	no	—
325	C₂×D₄	—	2	2	no	—
326	C₂×D₄	—	2	2	no	—
327	C₂×D₄	—	2	2	no	—
328	C₂×D₄	—	2	2	no	—
329	C₂×D₄	—	2	2	no	—
330	C₂×D₄	—	2	2	no	—
331	C₂×D₄	—	4	2	no	—
332	C₂×D₄	—	4	2	no	—
333	C₂×D₄	C₂×D₄	1	1	yes	characteristic
334	C₂×D₄	C₂×D₄	1	1	yes	characteristic
335	C₂×D₄	C₂×D₄	1	1	yes	characteristic
336	C₂×D₄	C₂⁴	1	2	yes	—
337	C₂×D₄	C₂⁴	1	2	yes	—
338	C₂×D₄	C₂⁴	1	2	yes	—
339	C₂²×C₄	—	2	2	no	—
340	C₂²×C₄	—	2	2	no	—
341	C₂²×C₄	—	2	2	no	—
342	C₂²×C₄	—	2	2	no	—
343	C₂²×C₄	—	2	2	no	—
344	C₂²×C₄	—	2	2	no	—
345	C₂²×C₄	—	2	2	no	—
346	C₂²×C₄	—	2	2	no	—
347	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
348	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
349	C₂²×C₄	C₂⁴	1	1	yes	characteristic
350	C₂²×C₄	C₂⁴	1	1	yes	characteristic
351	C₂²×C₄	C₂⁴	1	1	yes	characteristic
352	Q₁₆	—	2	2	no	—
353	Q₁₆	—	2	2	no	—
354	Q₁₆	—	2	2	no	—
355	Q₁₆	—	2	4	no	—
356	Q₁₆	—	4	2	no	—
357	Q₁₆	—	4	2	no	—
358	SD₁₆	—	2	4	no	—
359	SD₁₆	—	4	2	no	—
360	SD₁₆	—	4	2	no	—
361	SD₁₆	—	4	2	no	—
362	SD₁₆	—	4	2	no	—
363	SD₁₆	—	4	2	no	—
364	SD₁₆	—	4	2	no	—
365	SD₁₆	—	4	2	no	—
366	SD₁₆	—	4	2	no	—
367	D₈	—	2	2	no	—
368	D₈	—	2	2	no	—
369	D₈	—	2	2	no	—
370	D₈	—	2	4	no	—
371	D₈	—	4	2	no	—
372	D₈	—	4	2	no	—
373	M₁₆	—	2	2	no	—
374	M₁₆	—	2	2	no	—
375	C₂×C₈	—	2	2	no	—
376	C₂×C₈	—	2	2	no	—
377	C₂×C₈	—	2	2	no	—
378	C₂×C₈	—	2	2	no	—
379	C₂×C₈	C₂⁴	1	1	yes	characteristic
380	C₂×C₈	C₂⁴	1	1	yes	characteristic
381	C₂×C₈	C₂⁴	1	1	yes	characteristic
382	C₂×C₈	C₂⁴	1	1	yes	characteristic
383	C₂×C₈	C₂⁴	1	1	yes	characteristic
384	C₂×C₈	C₂⁴	1	1	yes	characteristic
385	C₂×C₈	C₂⁴	1	1	yes	characteristic
386	C₂×C₈	C₂⁴	1	1	yes	characteristic
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	2	no	—
393	C₄⋊C₄	—	2	2	no	—
394	C₄⋊C₄	—	2	2	no	—
395	C₄⋊C₄	—	2	2	no	—
396	C₄⋊C₄	—	2	2	no	—
397	C₄⋊C₄	—	2	2	no	—
398	C₄⋊C₄	—	2	2	no	—
399	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
400	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
401	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
402	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
403	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
404	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
405	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
406	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
407	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
408	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
409	C₄⋊C₄	C₂⁴	1	2	yes	—
410	C₄⋊C₄	C₂⁴	1	2	yes	—
411	C₂²⋊C₄	—	2	2	no	—
412	C₂²⋊C₄	—	2	2	no	—
413	C₂²⋊C₄	—	2	2	no	—
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	2	no	—
419	C₂²⋊C₄	—	2	2	no	—
420	C₂²⋊C₄	—	2	2	no	—
421	C₂²⋊C₄	—	2	2	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	2	no	—
428	C₂²⋊C₄	—	2	2	no	—
429	C₂²⋊C₄	—	2	2	no	—
430	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
431	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
432	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
433	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
434	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
435	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
436	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
437	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
438	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
439	C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
440	C₄²	—	2	2	no	—
441	C₄²	—	2	2	no	—
442	C₄²	—	2	2	no	—
443	C₄²	C₂×D₄	1	1	yes	characteristic
444	C₄²	C₂×D₄	1	1	yes	characteristic
445	C₄²	C₂⁴	1	1	yes	characteristic
446	C₄²	C₂⁴	1	1	yes	characteristic
447	C₄²	C₂⁴	1	1	yes	characteristic
448	C₄²	C₂⁴	1	1	yes	characteristic
449	C₂³	—	2	2	no	—
450	C₂³	—	2	2	no	—
451	C₂³	—	2	2	no	—
452	C₂³	—	8	2	no	—
453	C₂³	—	8	2	no	—
454	C₂³	—	8	2	no	—
455	C₂³	C₂²×D₄	1	1	yes	characteristic
456	C₂³	C₂²×D₄	1	1	yes	characteristic
457	C₂³	C₂²×D₄	1	1	yes	characteristic
458	Q₈	—	2	2	no	—
459	Q₈	—	2	2	no	—
460	Q₈	—	2	2	no	—
461	Q₈	—	2	2	no	—
462	Q₈	—	2	2	no	—
463	Q₈	—	2	2	no	—
464	Q₈	—	4	1	no	—
465	Q₈	—	8	2	no	—
466	D₄	—	2	2	no	—
467	D₄	—	2	2	no	—
468	D₄	—	2	2	no	—
469	D₄	—	2	2	no	—
470	D₄	—	2	2	no	—
471	D₄	—	2	2	no	—
472	D₄	—	4	1	no	—
473	D₄	—	4	1	no	—
474	D₄	—	4	1	no	—
475	D₄	—	8	2	no	—
476	D₄	—	8	2	no	—
477	D₄	—	8	2	no	—
478	D₄	—	8	2	no	—
479	D₄	—	8	2	no	—
480	D₄	—	8	2	no	—
481	D₄	—	8	2	no	—
482	D₄	—	8	2	no	—
483	D₄	—	8	2	no	—
484	D₄	—	8	2	no	—
485	D₄	—	8	2	no	—
486	D₄	—	8	2	no	—
487	C₂×C₄	—	2	1	no	—
488	C₂×C₄	—	2	1	no	—
489	C₂×C₄	—	2	1	no	—
490	C₂×C₄	—	2	1	no	—
491	C₂×C₄	—	2	1	no	—
492	C₂×C₄	—	2	1	no	—
493	C₂×C₄	—	2	2	no	—
494	C₂×C₄	—	2	2	no	—
495	C₂×C₄	—	2	2	no	—
496	C₂×C₄	—	2	2	no	—
497	C₂×C₄	—	2	2	no	—
498	C₂×C₄	—	4	1	no	—
499	C₂×C₄	—	4	1	no	—
500	C₂×C₄	—	8	2	no	—
501	C₂×C₄	—	8	2	no	—
502	C₂×C₄	—	8	2	no	—
503	C₂×C₄	—	8	2	no	—
504	C₂×C₄	—	8	2	no	—
505	C₂×C₄	—	8	2	no	—
506	C₂×C₄	—	8	2	no	—
507	C₂×C₄	—	8	2	no	—
508	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
509	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
510	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
511	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
512	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
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	1	yes	characteristic
517	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
518	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
519	C₂×C₄	C₂⁵	1	1	yes	characteristic
520	C₈	—	2	1	no	—
521	C₈	—	2	1	no	—
522	C₈	—	2	1	no	—
523	C₈	—	2	1	no	—
524	C₈	—	2	1	no	—
525	C₈	—	2	1	no	—
526	C₈	H(5,𝔽₂)	1	2	yes	—
527	C₈	H(5,𝔽₂)	1	2	yes	—
528	C₂²	—	2	1	no	—
529	C₂²	—	2	1	no	—
530	C₂²	—	2	1	no	—
531	C₂²	—	2	1	no	—
532	C₂²	—	2	1	no	—
533	C₂²	—	2	1	no	—
534	C₂²	—	2	1	no	—
535	C₂²	—	2	1	no	—
536	C₂²	—	2	1	no	—
537	C₂²	—	4	2	no	—
538	C₂²	—	4	2	no	—
539	C₂²	—	4	2	no	—
540	C₂²	—	4	2	no	—
541	C₂²	—	4	2	no	—
542	C₂²	—	4	2	no	—
543	C₂²	—	4	2	no	—
544	C₂²	—	4	2	no	—
545	C₂²	—	4	2	no	—
546	C₂²	—	16	4	no	—
547	C₂²	C₂³×D₄	1	1	yes	characteristic
548	C₄	—	2	1	no	—
549	C₄	—	2	1	no	—
550	C₄	—	2	1	no	—
551	C₄	—	2	1	no	—
552	C₄	—	2	1	no	—
553	C₄	—	2	1	no	—
554	C₄	—	2	1	no	—
555	C₄	—	2	1	no	—
556	C₄	—	2	1	no	—
557	C₄	—	2	1	no	—
558	C₄	—	2	1	no	—
559	C₄	—	4	2	no	—
560	C₄	—	4	2	no	—
561	C₄	—	4	2	no	—
562	C₄	—	4	2	no	—
563	C₄	—	4	2	no	—
564	C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
565	C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
566	C₂	—	4	1	no	—
567	C₂	—	4	1	no	—
568	C₂	—	4	1	no	—
569	C₂	—	8	2	no	—
570	C₂	—	8	2	no	—
571	C₂	—	8	2	no	—
572	C₂	#3498	1	1	yes	characteristic
573	C₂	#3584	1	1	yes	characteristic
574	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. #3562	C₂	semidirect
2. #3401	C₂	semidirect
3. #3396	C₂	semidirect
4. #3393	C₂	semidirect
5. #3287	C₂	semidirect
6. #3285	C₂	semidirect
7. #3285	C₂	semidirect
8. #3283	C₂	semidirect
9. #3280	C₂	semidirect
10. #3280	C₂	semidirect
11. #3275	C₂	semidirect
12. #3271	C₂	semidirect
13. #3267	C₂	semidirect
14. #3222	C₂	semidirect
15. #3221	C₂	semidirect
16. #3219	C₂	semidirect
17. #3177	C₂	semidirect
18. #3176	C₂	semidirect
19. #3168	C₂	semidirect
20. #3156	C₂	semidirect
21. #3155	C₂	semidirect
22. #3147	C₂	semidirect
23. #2966	C₂	semidirect
24. C₂×#137	C₂²	semidirect
29. C₂×#135	C₂²	semidirect
30. C₂×#135	C₂²	semidirect
31. C₂²×Q₁₆	C₂²	semidirect
35. #559	C₂²	semidirect
36. #556	C₂²	semidirect
39. #550	C₂²	semidirect
41. #548	C₂²	semidirect
47. #540	C₂²	semidirect
51. #536	C₂²	semidirect
53. #532	C₂²	semidirect
55. #529	C₂²	semidirect
56. #499	C₂²	semidirect
57. #497	C₂²	semidirect
58. #497	C₂²	semidirect
65. #495	C₂²	semidirect
66. #495	C₂²	semidirect
67. #494	C₂²	semidirect
68. #494	C₂²	semidirect
71. #492	C₂²	semidirect
72. #491	C₂²	semidirect
73. #490	C₂²	semidirect
74. #488	C₂²	semidirect
76. #469	C₂²	semidirect
79. #467	C₂²	semidirect
82. #466	C₂²	semidirect
83. #465	C₂²	semidirect
84. #464	C₂²	semidirect
85. #464	C₂²	semidirect
86. #464	C₂²	semidirect
87. #464	C₂²	semidirect
90. #463	C₂²	semidirect
91. #463	C₂²	semidirect
92. #461	C₂²	semidirect
93. #461	C₂²	semidirect
94. #460	C₂²	semidirect
95. #460	C₂²	semidirect
98. #452	C₂²	semidirect
99. #452	C₂²	semidirect
104. #449	C₂²	semidirect
105. #449	C₂²	semidirect
106. #448	C₂²	semidirect
107. #448	C₂²	semidirect
108. #446	C₂²	semidirect
109. C₈×Q₈	C₂²	semidirect
110. #442	C₂²	semidirect
111. #441	C₂²	semidirect
112. C₄×Q₁₆	C₂²	semidirect
113. C₄×Q₁₆	C₂²	semidirect
114. C₄×Q₁₆	C₂²	semidirect
115. C₄×SD₁₆	C₂²	semidirect
118. C₄×D₈	C₂²	semidirect
121. #435	C₂²	semidirect
124. C₈×D₄	C₂²	semidirect
126. #433	C₂²	semidirect
127. #432	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
#3562	2
#3401	2
#3396	2
#3393	2
#3287	2
#3285	2
#3283	2
#3280	2
#3275	2
#3271	2
#3267	2
#3222	2
#3221	2
#3219	2
#3177	2
#3176	2
#3168	2
#3156	2
#3155	2
#3147	2
#2966	2