Subgroups — #62032

Order 256.

916 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3552	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	#3394	C₂	1	1	yes	maximal, characteristic, complemented
5	#3367	C₂	1	1	yes	maximal, characteristic, complemented
6	#3359	C₂	1	1	yes	maximal, characteristic, complemented
7	#3329	C₂	1	2	yes	maximal, complemented
8	#3328	C₂	1	1	yes	maximal, characteristic, complemented
9	#3321	C₂	1	2	yes	maximal, complemented
10	#3302	C₂	1	1	yes	maximal, characteristic, complemented
11	D₄×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
12	#3275	C₂	1	2	yes	maximal, complemented
13	#3272	C₂	1	1	yes	maximal, characteristic, complemented
14	#3266	C₂	1	2	yes	maximal, complemented
15	#3258	C₂	1	2	yes	maximal, complemented
16	#3251	C₂	1	1	yes	maximal, characteristic, complemented
17	#3225	C₂	1	2	yes	maximal, complemented
18	#3206	C₂	1	1	yes	maximal, characteristic, complemented
19	#3123	C₂	1	2	yes	maximal, complemented
20	#3102	C₂	1	1	yes	maximal, characteristic, complemented
21	#3042	C₂	1	2	yes	maximal, complemented
22	#3039	C₂	1	1	yes	maximal, characteristic, complemented
23	#2993	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#137	C₂²	1	2	yes	—
25	C₂×AGL(1,ℤ/8)	C₂²	1	2	yes	—
26	C₂²×SD₁₆	C₂²	1	2	yes	—
27	#563	—	2	2	no	—
28	#559	C₂²	1	1	yes	characteristic
29	#557	C₂²	1	1	yes	characteristic, complemented
30	#556	C₂²	1	1	yes	characteristic
31	#556	C₂²	1	1	yes	characteristic, complemented
32	#555	C₂²	1	2	yes	—
33	#554	—	2	1	no	—
34	#553	—	2	1	no	—
35	#551	—	2	2	no	—
36	D₄×Q₈	C₂²	1	1	yes	characteristic
37	D₄×Q₈	C₂²	1	1	yes	characteristic
38	D₄×Q₈	C₂²	1	2	yes	complemented
39	#548	—	2	1	no	—
40	#548	C₂²	1	2	yes	complemented
41	#547	C₂²	1	1	yes	characteristic
42	#546	—	2	1	no	—
43	#546	C₂²	1	2	yes	—
44	D₄²	C₂²	1	1	yes	characteristic
45	#544	—	2	1	no	—
46	#542	—	2	1	no	—
47	#542	C₂²	1	2	yes	—
48	#541	C₂²	1	2	yes	complemented
49	#539	—	2	2	no	—
50	#538	—	2	2	no	—
51	#536	C₂²	1	2	yes	complemented
52	#532	C₂²	1	1	yes	characteristic
53	C₂×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
54	#529	—	2	1	no	—
55	#529	C₂²	1	1	yes	characteristic
56	#529	C₂²	1	1	yes	characteristic, complemented
57	C₂×#124	—	2	1	no	—
58	#518	C₂²	1	2	yes	—
59	C₄×#41	C₂²	1	1	yes	characteristic
60	#497	C₂²	1	2	yes	complemented
61	#495	C₂²	1	2	yes	complemented
62	#492	C₂²	1	1	yes	characteristic
63	#492	C₂²	1	1	yes	characteristic
64	#489	C₂²	1	2	yes	complemented
65	#487	C₂²	1	1	yes	characteristic, complemented
66	#487	C₂²	1	2	yes	complemented
67	#487	C₂²	1	1	yes	characteristic, complemented
68	#485	C₂²	1	2	yes	complemented
69	#485	C₂²	1	1	yes	characteristic, complemented
70	#485	C₂²	1	2	yes	complemented
71	#482	C₂²	1	1	yes	characteristic, complemented
72	#479	C₂²	1	1	yes	characteristic, complemented
73	#478	C₂²	1	1	yes	characteristic
74	#478	C₂²	1	2	yes	complemented
75	#477	C₂²	1	2	yes	complemented
76	#475	C₂²	1	1	yes	characteristic, complemented
77	#475	C₂²	1	2	yes	complemented
78	#474	C₂²	1	1	yes	characteristic, complemented
79	#470	C₂²	1	2	yes	complemented
80	#469	C₂²	1	2	yes	complemented
81	#468	C₂²	1	2	yes	—
82	#468	C₂²	1	2	yes	complemented
83	#467	C₂²	1	2	yes	complemented
84	#465	C₂²	1	2	yes	—
85	#464	C₂²	1	1	yes	characteristic, complemented
86	#464	C₂²	1	2	yes	complemented
87	#464	C₂²	1	2	yes	complemented
88	#463	C₂²	1	1	yes	characteristic
89	#463	C₂²	1	2	yes	—
90	#463	C₂²	1	2	yes	complemented
91	#463	C₂²	1	2	yes	complemented
92	#462	C₂²	1	1	yes	characteristic, complemented
93	#462	C₂²	1	1	yes	characteristic, complemented
94	#462	C₂²	1	2	yes	complemented
95	#461	C₂²	1	2	yes	—
96	#461	C₂²	1	1	yes	characteristic
97	#461	C₂²	1	1	yes	characteristic
98	#461	C₂²	1	2	yes	—
99	#461	C₂²	1	2	yes	complemented
100	#461	C₂²	1	2	yes	complemented
101	#461	C₂²	1	2	yes	complemented
102	#460	C₂²	1	1	yes	characteristic
103	#459	C₂²	1	1	yes	characteristic
104	#452	C₂²	1	1	yes	characteristic
105	#452	C₂²	1	2	yes	complemented
106	#451	C₂²	1	2	yes	complemented
107	#450	C₂²	1	2	yes	—
108	#450	C₂²	1	2	yes	—
109	#449	C₂²	1	1	yes	characteristic
110	#449	C₂²	1	2	yes	—
111	#448	C₂²	1	2	yes	—
112	#448	C₂²	1	2	yes	complemented
113	#448	C₂²	1	2	yes	complemented
114	#446	C₂²	1	1	yes	characteristic, complemented
115	C₈×Q₈	C₂²	1	1	yes	characteristic, complemented
116	#440	C₂²	1	2	yes	—
117	#440	C₂²	1	2	yes	complemented
118	C₄×Q₁₆	C₂²	1	1	yes	characteristic, complemented
119	C₄×SD₁₆	C₂²	1	1	yes	characteristic
120	C₄×SD₁₆	C₂²	1	2	yes	—
121	C₄×SD₁₆	C₂²	1	2	yes	complemented
122	C₄×SD₁₆	C₂²	1	1	yes	characteristic, complemented
123	C₄×D₈	C₂²	1	1	yes	characteristic
124	#436	C₂²	1	1	yes	characteristic
125	#436	C₂²	1	2	yes	complemented
126	#435	C₂²	1	2	yes	complemented
127	C₈×D₄	C₂²	1	1	yes	characteristic
128	#433	C₂²	1	2	yes	complemented
129	#431	C₂²	1	1	yes	characteristic, complemented
130	#424	C₂²	1	2	yes	complemented
131	#423	C₂²	1	1	yes	characteristic, complemented
132	#419	C₂²	1	2	yes	complemented
133	#419	C₂²	1	2	yes	complemented
134	#416	C₂²	1	2	yes	complemented
135	C₂×#41	—	2	1	no	—
136	C₂×#41	C₂³	1	1	yes	characteristic
137	C₂×#41	C₂³	1	2	yes	—
138	C₂²×Q₈	—	2	1	no	—
139	C₂²×Q₈	C₂³	1	2	yes	—
140	C₂²×Q₈	C₂³	1	2	yes	—
141	C₂²×D₄	—	2	1	no	—
142	C₂²×D₄	C₂³	1	2	yes	—
143	#137	—	4	4	no	—
144	AGL(1,ℤ/8)	—	4	4	no	—
145	C₂×Q₁₆	C₂³	1	2	yes	—
146	C₂×Q₁₆	C₂³	1	2	yes	—
147	C₂×Q₁₆	C₂³	1	1	yes	characteristic
148	C₂×SD₁₆	—	4	4	no	—
149	C₂×SD₁₆	C₂³	1	1	yes	characteristic
150	C₂×SD₁₆	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	1	yes	characteristic
157	C₂×SD₁₆	C₂³	1	2	yes	—
158	C₂×D₈	C₂³	1	1	yes	characteristic
159	C₂×D₈	C₂³	1	2	yes	—
160	C₂×M₁₆	C₂³	1	2	yes	—
161	C₂×M₁₆	C₂³	1	2	yes	—
162	C₂²×C₈	C₂³	1	2	yes	—
163	C₄⋊Q₈	—	2	1	no	—
164	C₄⋊Q₈	—	2	2	no	—
165	C₄⋊Q₈	—	2	1	no	—
166	C₄⋊Q₈	—	2	1	no	—
167	C₄⋊Q₈	C₂³	1	2	yes	—
168	C₄⋊Q₈	C₂³	1	1	yes	characteristic
169	C₄⋊Q₈	C₂³	1	1	yes	characteristic
170	C₄⋊Q₈	C₂³	1	2	yes	—
171	C₄⋊Q₈	C₂³	1	1	yes	characteristic
172	C₄⋊Q₈	C₂³	1	2	yes	—
173	#127	C₂³	1	1	yes	characteristic
174	#126	—	2	2	no	—
175	#126	—	2	2	no	—
176	#126	—	2	2	no	—
177	#126	—	2	2	no	—
178	#126	—	2	2	no	—
179	#126	—	2	1	no	—
180	#126	D₄	1	2	yes	—
181	#125	—	2	2	no	—
182	#125	—	2	2	no	—
183	#125	—	2	2	no	—
184	#125	—	2	1	no	—
185	#125	D₄	1	1	yes	characteristic
186	#125	C₂³	1	1	yes	characteristic
187	#124	—	2	1	no	—
188	#124	—	2	1	no	—
189	#124	—	2	2	no	—
190	#124	—	2	2	no	—
191	#124	—	2	2	no	—
192	#124	—	2	2	no	—
193	#124	—	2	1	no	—
194	#124	D₄	1	1	yes	characteristic
195	#124	C₂³	1	1	yes	characteristic
196	#124	C₂³	1	2	yes	—
197	#124	C₂³	1	2	yes	—
198	#123	—	2	1	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	D₄	1	2	yes	—
206	C₂²⋊Q₈	—	2	1	no	—
207	C₂²⋊Q₈	—	2	1	no	—
208	C₂²⋊Q₈	—	2	2	no	—
209	C₂²⋊Q₈	—	2	2	no	—
210	C₂²⋊Q₈	—	2	2	no	—
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	1	yes	characteristic
218	C₂²⋊Q₈	C₂³	1	2	yes	—
219	C₂²⋊Q₈	C₂³	1	2	yes	—
220	C₂²⋊Q₈	C₂³	1	2	yes	—
221	#121	—	2	2	no	—
222	#121	—	2	2	no	—
223	#121	—	2	1	no	—
224	#121	—	2	1	no	—
225	#121	—	2	1	no	—
226	#121	—	2	2	no	—
227	#121	D₄	1	1	yes	characteristic
228	#121	C₂³	1	1	yes	characteristic
229	#121	C₂³	1	2	yes	—
230	#121	C₂³	1	2	yes	—
231	#120	—	2	2	no	—
232	#120	—	2	2	no	—
233	C₄×Q₈	—	2	1	no	—
234	C₄×Q₈	—	2	1	no	—
235	C₄×Q₈	C₂³	1	1	yes	characteristic
236	C₄×Q₈	C₂³	1	1	yes	characteristic
237	C₄×Q₈	C₂³	1	1	yes	characteristic
238	C₄×Q₈	C₂³	1	2	yes	—
239	C₄×Q₈	C₂³	1	2	yes	—
240	C₄×Q₈	C₂³	1	1	yes	characteristic
241	C₄×D₄	—	2	2	no	—
242	C₄×D₄	—	2	1	no	—
243	C₄×D₄	—	2	1	no	—
244	C₄×D₄	—	2	1	no	—
245	C₄×D₄	—	2	1	no	—
246	C₄×D₄	—	2	2	no	—
247	C₄×D₄	—	2	2	no	—
248	C₄×D₄	—	2	1	no	—
249	C₄×D₄	—	2	2	no	—
250	C₄×D₄	—	2	1	no	—
251	C₄×D₄	C₂³	1	1	yes	characteristic
252	C₄×D₄	C₂³	1	1	yes	characteristic
253	C₄×D₄	C₂³	1	2	yes	—
254	C₄×D₄	C₂³	1	2	yes	—
255	C₄×D₄	C₂³	1	2	yes	—
256	C₄×D₄	C₂³	1	1	yes	characteristic
257	C₄×D₄	C₂³	1	1	yes	characteristic
258	C₄×D₄	C₂³	1	2	yes	—
259	#117	—	2	2	no	—
260	#117	—	2	1	no	—
261	#117	—	2	1	no	—
262	#117	—	2	1	no	—
263	#117	C₂³	1	1	yes	characteristic
264	#117	C₂³	1	2	yes	—
265	#117	C₂³	1	2	yes	—
266	C₂×C₄⋊C₄	—	2	1	no	—
267	C₂×C₄⋊C₄	—	2	1	no	—
268	C₂×C₄⋊C₄	—	2	1	no	—
269	C₂×C₂²⋊C₄	—	2	2	no	—
270	C₂×C₂²⋊C₄	—	2	2	no	—
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	2	yes	—
288	#103	C₂³	1	2	yes	—
289	#103	C₂³	1	2	yes	—
290	#103	C₂³	1	1	yes	characteristic
291	#103	C₂³	1	2	yes	—
292	#103	C₂³	1	2	yes	—
293	#103	C₂³	1	2	yes	—
294	#103	C₂³	1	2	yes	—
295	#103	C₂³	1	1	yes	characteristic
296	#103	C₂³	1	2	yes	—
297	#103	C₂³	1	1	yes	characteristic
298	#103	C₂³	1	1	yes	characteristic
299	#103	C₂³	1	2	yes	—
300	#102	C₂³	1	1	yes	characteristic
301	#102	C₂³	1	2	yes	—
302	#102	C₂³	1	1	yes	characteristic
303	#102	C₂³	1	1	yes	characteristic
304	#102	C₂³	1	1	yes	characteristic
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	#41	—	2	2	no	—
317	#41	—	4	1	no	—
318	#41	—	4	2	no	—
319	#41	—	4	2	no	—
320	#41	—	8	2	no	—
321	C₂×Q₈	—	2	1	no	—
322	C₂×Q₈	—	2	2	no	—
323	C₂×Q₈	—	2	2	no	—
324	C₂×Q₈	—	2	2	no	—
325	C₂×Q₈	—	4	2	no	—
326	C₂×Q₈	—	4	2	no	—
327	C₂×Q₈	—	4	2	no	—
328	C₂×Q₈	—	4	2	no	—
329	C₂×Q₈	—	8	2	no	—
330	C₂×Q₈	C₂×D₄	1	1	yes	characteristic
331	C₂×Q₈	C₂⁴	1	1	yes	characteristic
332	C₂×Q₈	C₂⁴	1	2	yes	—
333	C₂×Q₈	C₂⁴	1	2	yes	—
334	C₂×Q₈	C₂⁴	1	1	yes	characteristic
335	C₂×D₄	—	2	4	no	—
336	C₂×D₄	—	2	1	no	—
337	C₂×D₄	—	2	1	no	—
338	C₂×D₄	—	2	2	no	—
339	C₂×D₄	—	2	2	no	—
340	C₂×D₄	—	2	2	no	—
341	C₂×D₄	—	2	2	no	—
342	C₂×D₄	—	2	1	no	—
343	C₂×D₄	—	2	1	no	—
344	C₂×D₄	—	4	2	no	—
345	C₂×D₄	—	8	2	no	—
346	C₂×D₄	C₂×D₄	1	1	yes	characteristic
347	C₂×D₄	C₂×D₄	1	2	yes	—
348	C₂×D₄	C₂⁴	1	1	yes	characteristic
349	C₂×D₄	C₂⁴	1	2	yes	—
350	C₂×D₄	C₂⁴	1	1	yes	characteristic
351	C₂²×C₄	—	2	2	no	—
352	C₂²×C₄	—	2	2	no	—
353	C₂²×C₄	—	2	1	no	—
354	C₂²×C₄	—	2	1	no	—
355	C₂²×C₄	—	2	1	no	—
356	C₂²×C₄	—	2	1	no	—
357	C₂²×C₄	—	2	2	no	—
358	C₂²×C₄	—	2	2	no	—
359	C₂²×C₄	—	2	2	no	—
360	C₂²×C₄	—	2	2	no	—
361	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
362	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
363	C₂²×C₄	C₂⁴	1	1	yes	characteristic
364	C₂²×C₄	C₂⁴	1	2	yes	—
365	Q₁₆	—	4	1	no	—
366	Q₁₆	—	4	2	no	—
367	Q₁₆	—	4	2	no	—
368	SD₁₆	—	2	2	no	—
369	SD₁₆	—	2	4	no	—
370	SD₁₆	—	2	4	no	—
371	SD₁₆	—	4	2	no	—
372	SD₁₆	—	4	2	no	—
373	SD₁₆	—	4	2	no	—
374	SD₁₆	—	4	1	no	—
375	SD₁₆	—	4	2	no	—
376	SD₁₆	—	4	2	no	—
377	D₈	—	2	2	no	—
378	D₈	—	4	2	no	—
379	M₁₆	—	4	2	no	—
380	M₁₆	—	4	2	no	—
381	C₂×C₈	—	4	2	no	—
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	2	yes	—
386	C₂×C₈	C₂⁴	1	1	yes	characteristic
387	C₂×C₈	C₂⁴	1	2	yes	—
388	C₄⋊C₄	—	2	1	no	—
389	C₄⋊C₄	—	2	1	no	—
390	C₄⋊C₄	—	2	1	no	—
391	C₄⋊C₄	—	2	2	no	—
392	C₄⋊C₄	—	2	2	no	—
393	C₄⋊C₄	—	2	2	no	—
394	C₄⋊C₄	—	2	1	no	—
395	C₄⋊C₄	—	2	1	no	—
396	C₄⋊C₄	—	2	1	no	—
397	C₄⋊C₄	—	2	2	no	—
398	C₄⋊C₄	—	2	1	no	—
399	C₄⋊C₄	—	2	1	no	—
400	C₄⋊C₄	—	2	1	no	—
401	C₄⋊C₄	—	2	2	no	—
402	C₄⋊C₄	—	2	2	no	—
403	C₄⋊C₄	—	2	1	no	—
404	C₄⋊C₄	—	2	2	no	—
405	C₄⋊C₄	—	2	2	no	—
406	C₄⋊C₄	—	2	2	no	—
407	C₄⋊C₄	—	2	2	no	—
408	C₄⋊C₄	—	2	1	no	—
409	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
410	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
411	C₄⋊C₄	C₂×D₄	1	2	yes	—
412	C₄⋊C₄	C₂×D₄	1	2	yes	—
413	C₄⋊C₄	C₂×D₄	1	2	yes	—
414	C₄⋊C₄	C₂×D₄	1	2	yes	—
415	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
416	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
417	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
418	C₄⋊C₄	C₂⁴	1	2	yes	—
419	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
420	C₂²⋊C₄	—	2	2	no	—
421	C₂²⋊C₄	—	2	2	no	—
422	C₂²⋊C₄	—	2	1	no	—
423	C₂²⋊C₄	—	2	1	no	—
424	C₂²⋊C₄	—	2	2	no	—
425	C₂²⋊C₄	—	2	2	no	—
426	C₂²⋊C₄	—	2	1	no	—
427	C₂²⋊C₄	—	2	2	no	—
428	C₂²⋊C₄	—	2	2	no	—
429	C₂²⋊C₄	—	2	2	no	—
430	C₂²⋊C₄	—	2	2	no	—
431	C₂²⋊C₄	—	2	2	no	—
432	C₂²⋊C₄	—	2	1	no	—
433	C₂²⋊C₄	—	2	2	no	—
434	C₂²⋊C₄	—	2	2	no	—
435	C₂²⋊C₄	—	2	1	no	—
436	C₂²⋊C₄	—	2	1	no	—
437	C₂²⋊C₄	—	2	2	no	—
438	C₂²⋊C₄	—	2	1	no	—
439	C₂²⋊C₄	—	2	2	no	—
440	C₂²⋊C₄	—	2	1	no	—
441	C₂²⋊C₄	C₂×D₄	1	2	yes	—
442	C₂²⋊C₄	C₂×D₄	1	2	yes	—
443	C₂²⋊C₄	C₂×D₄	1	2	yes	—
444	C₂²⋊C₄	C₂×D₄	1	2	yes	—
445	C₂²⋊C₄	C₂×D₄	1	2	yes	—
446	C₄²	—	2	1	no	—
447	C₄²	—	2	1	no	—
448	C₄²	—	2	1	no	—
449	C₄²	—	2	2	no	—
450	C₄²	—	2	1	no	—
451	C₄²	—	2	2	no	—
452	C₄²	—	2	2	no	—
453	C₄²	C₂×D₄	1	1	yes	characteristic
454	C₄²	C₂×D₄	1	1	yes	characteristic
455	C₄²	C₂⁴	1	1	yes	characteristic
456	C₄²	C₂⁴	1	2	yes	—
457	C₄²	C₂⁴	1	1	yes	characteristic
458	C₂³	—	2	1	no	—
459	C₂³	—	2	1	no	—
460	C₂³	—	2	2	no	—
461	C₂³	—	4	4	no	—
462	C₂³	—	8	2	no	—
463	C₂³	—	8	2	no	—
464	C₂³	C₂²×D₄	1	2	yes	—
465	C₂³	C₂²×D₄	1	1	yes	characteristic
466	Q₈	—	2	2	no	—
467	Q₈	—	2	1	no	—
468	Q₈	—	2	2	no	—
469	Q₈	—	2	2	no	—
470	Q₈	—	2	1	no	—
471	Q₈	—	2	1	no	—
472	Q₈	—	2	2	no	—
473	Q₈	—	2	2	no	—
474	Q₈	—	2	1	no	—
475	Q₈	—	4	2	no	—
476	Q₈	—	8	2	no	—
477	Q₈	—	8	2	no	—
478	Q₈	—	8	2	no	—
479	D₄	—	2	2	no	—
480	D₄	—	2	1	no	—
481	D₄	—	2	2	no	—
482	D₄	—	2	1	no	—
483	D₄	—	2	2	no	—
484	D₄	—	2	1	no	—
485	D₄	—	4	2	no	—
486	D₄	—	4	4	no	—
487	D₄	—	4	2	no	—
488	D₄	—	4	2	no	—
489	D₄	—	4	2	no	—
490	D₄	—	8	1	no	—
491	D₄	—	8	2	no	—
492	D₄	—	8	2	no	—
493	D₄	—	8	2	no	—
494	D₄	H(5,𝔽₂)	1	2	yes	—
495	C₂×C₄	—	2	2	no	—
496	C₂×C₄	—	2	2	no	—
497	C₂×C₄	—	2	1	no	—
498	C₂×C₄	—	2	2	no	—
499	C₂×C₄	—	2	1	no	—
500	C₂×C₄	—	2	1	no	—
501	C₂×C₄	—	2	1	no	—
502	C₂×C₄	—	2	1	no	—
503	C₂×C₄	—	2	1	no	—
504	C₂×C₄	—	2	1	no	—
505	C₂×C₄	—	2	2	no	—
506	C₂×C₄	—	2	1	no	—
507	C₂×C₄	—	2	2	no	—
508	C₂×C₄	—	2	2	no	—
509	C₂×C₄	—	4	1	no	—
510	C₂×C₄	—	4	2	no	—
511	C₂×C₄	—	4	2	no	—
512	C₂×C₄	—	4	2	no	—
513	C₂×C₄	—	8	1	no	—
514	C₂×C₄	—	8	2	no	—
515	C₂×C₄	—	8	2	no	—
516	C₂×C₄	—	8	2	no	—
517	C₂×C₄	—	8	2	no	—
518	C₂×C₄	—	8	2	no	—
519	C₂×C₄	—	8	2	no	—
520	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
521	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
522	C₂×C₄	C₂²×D₄	1	2	yes	—
523	C₂×C₄	C₂²×D₄	1	2	yes	—
524	C₂×C₄	C₂²×D₄	1	2	yes	—
525	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
526	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
527	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
528	C₂×C₄	C₂⁵	1	1	yes	characteristic
529	C₈	—	2	1	no	—
530	C₈	—	2	2	no	—
531	C₈	—	2	1	no	—
532	C₈	—	2	2	no	—
533	C₈	—	2	1	no	—
534	C₈	—	2	1	no	—
535	C₂²	—	2	1	no	—
536	C₂²	—	2	2	no	—
537	C₂²	—	2	1	no	—
538	C₂²	—	2	2	no	—
539	C₂²	—	2	2	no	—
540	C₂²	—	2	1	no	—
541	C₂²	—	2	2	no	—
542	C₂²	—	4	1	no	—
543	C₂²	—	4	1	no	—
544	C₂²	—	4	2	no	—
545	C₂²	—	4	1	no	—
546	C₂²	—	4	1	no	—
547	C₂²	—	4	2	no	—
548	C₂²	—	4	1	no	—
549	C₂²	—	4	2	no	—
550	C₂²	—	16	4	no	—
551	C₂²	C₂³×D₄	1	1	yes	characteristic
552	C₄	—	2	1	no	—
553	C₄	—	2	1	no	—
554	C₄	—	2	2	no	—
555	C₄	—	2	1	no	—
556	C₄	—	2	2	no	—
557	C₄	—	2	1	no	—
558	C₄	—	2	2	no	—
559	C₄	—	4	1	no	—
560	C₄	—	4	1	no	—
561	C₄	—	4	1	no	—
562	C₄	—	4	2	no	—
563	C₄	—	4	1	no	—
564	C₄	—	4	2	no	—
565	C₄	—	4	1	no	—
566	C₄	—	4	1	no	—
567	C₄	—	4	2	no	—
568	C₄	#577	1	2	yes	—
569	C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
570	C₄	#585	1	1	yes	characteristic
571	C₂	—	4	1	no	—
572	C₂	—	4	2	no	—
573	C₂	—	4	2	no	—
574	C₂	—	8	1	no	—
575	C₂	—	8	2	no	—
576	C₂	#3488	1	1	yes	characteristic
577	C₂	C₂×#577	1	1	yes	characteristic
578	C₂	#3586	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. #3552	C₂	semidirect
2. #3514	C₂	semidirect
3. #3400	C₂	semidirect
4. #3394	C₂	semidirect
5. #3367	C₂	semidirect
6. #3359	C₂	semidirect
7. #3329	C₂	semidirect
8. #3328	C₂	semidirect
9. #3321	C₂	semidirect
10. #3302	C₂	semidirect
11. D₄×SD₁₆	C₂	semidirect
12. #3275	C₂	semidirect
13. #3272	C₂	semidirect
14. #3266	C₂	semidirect
15. #3258	C₂	semidirect
16. #3251	C₂	semidirect
17. #3225	C₂	semidirect
18. #3206	C₂	semidirect
19. #3123	C₂	semidirect
20. #3102	C₂	semidirect
21. #3042	C₂	semidirect
22. #3039	C₂	semidirect
23. #2993	C₂	semidirect
29. #557	C₂²	semidirect
31. #556	C₂²	semidirect
38. D₄×Q₈	C₂²	semidirect
40. #548	C₂²	semidirect
48. #541	C₂²	semidirect
51. #536	C₂²	semidirect
53. C₂×C₄⋊Q₈	C₂²	semidirect
56. #529	C₂²	semidirect
60. #497	C₂²	semidirect
61. #495	C₂²	semidirect
64. #489	C₂²	semidirect
65. #487	C₂²	semidirect
66. #487	C₂²	semidirect
67. #487	C₂²	semidirect
68. #485	C₂²	semidirect
69. #485	C₂²	semidirect
70. #485	C₂²	semidirect
71. #482	C₂²	semidirect
72. #479	C₂²	semidirect
74. #478	C₂²	semidirect
75. #477	C₂²	semidirect
76. #475	C₂²	semidirect
77. #475	C₂²	semidirect
78. #474	C₂²	semidirect
79. #470	C₂²	semidirect
80. #469	C₂²	semidirect
82. #468	C₂²	semidirect
83. #467	C₂²	semidirect
85. #464	C₂²	semidirect
86. #464	C₂²	semidirect
87. #464	C₂²	semidirect
90. #463	C₂²	semidirect
91. #463	C₂²	semidirect
92. #462	C₂²	semidirect
93. #462	C₂²	semidirect
94. #462	C₂²	semidirect
99. #461	C₂²	semidirect
100. #461	C₂²	semidirect
101. #461	C₂²	semidirect
105. #452	C₂²	semidirect
106. #451	C₂²	semidirect
112. #448	C₂²	semidirect
113. #448	C₂²	semidirect
114. #446	C₂²	semidirect
115. C₈×Q₈	C₂²	semidirect
117. #440	C₂²	semidirect
118. C₄×Q₁₆	C₂²	semidirect
121. C₄×SD₁₆	C₂²	semidirect
122. C₄×SD₁₆	C₂²	semidirect
125. #436	C₂²	semidirect
126. #435	C₂²	semidirect
128. #433	C₂²	semidirect
129. #431	C₂²	semidirect
130. #424	C₂²	semidirect
131. #423	C₂²	semidirect
132. #419	C₂²	semidirect
133. #419	C₂²	semidirect
134. #416	C₂²	semidirect

Maximal subgroups

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

subgroup	index
#3552	2
#3514	2
#3400	2
#3394	2
#3367	2
#3359	2
#3329	2
#3328	2
#3321	2
#3302	2
D₄×SD₁₆	2
#3275	2
#3272	2
#3266	2
#3258	2
#3251	2
#3225	2
#3206	2
#3123	2
#3102	2
#3042	2
#3039	2
#2993	2