Subgroups — #61973

Order 256.

928 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	#3514	C₂	1	1	yes	maximal, characteristic, complemented
2	#3482	C₂	1	1	yes	maximal, characteristic, complemented
3	#3400	C₂	1	1	yes	maximal, characteristic, complemented
4	#3398	C₂	1	1	yes	maximal, characteristic, complemented
5	#3373	C₂	1	1	yes	maximal, characteristic, complemented
6	#3367	C₂	1	1	yes	maximal, characteristic, complemented
7	#3328	C₂	1	1	yes	maximal, characteristic, complemented
8	#3324	C₂	1	1	yes	maximal, characteristic, complemented
9	#3313	C₂	1	2	yes	maximal, complemented
10	#3311	C₂	1	2	yes	maximal, complemented
11	#3276	C₂	1	1	yes	maximal, characteristic, complemented
12	#3272	C₂	1	1	yes	maximal, characteristic, complemented
13	#3269	C₂	1	2	yes	maximal, complemented
14	#3267	C₂	1	2	yes	maximal, complemented
15	#3252	C₂	1	2	yes	maximal, complemented
16	#3248	C₂	1	1	yes	maximal, characteristic, complemented
17	#3215	C₂	1	2	yes	maximal, complemented
18	#3210	C₂	1	1	yes	maximal, characteristic, complemented
19	#3111	C₂	1	2	yes	maximal, complemented
20	#3102	C₂	1	1	yes	maximal, characteristic, complemented
21	#3040	C₂	1	2	yes	maximal, complemented
22	#3035	C₂	1	1	yes	maximal, characteristic, complemented
23	#2989	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	2	yes	complemented
27	#559	C₂²	1	1	yes	characteristic
28	#557	C₂²	1	1	yes	characteristic, complemented
29	#556	C₂²	1	1	yes	characteristic
30	#556	C₂²	1	1	yes	characteristic
31	#556	C₂²	1	2	yes	complemented
32	#555	—	2	1	no	—
33	#552	—	2	1	no	—
34	#552	—	2	2	no	—
35	#551	—	2	2	no	—
36	D₄×Q₈	C₂²	1	1	yes	characteristic
37	D₄×Q₈	C₂²	1	1	yes	characteristic, complemented
38	#548	—	2	1	no	—
39	#548	C₂²	1	2	yes	—
40	#547	C₂²	1	1	yes	characteristic
41	#547	C₂²	1	2	yes	complemented
42	#546	—	2	1	no	—
43	#546	C₂²	1	2	yes	—
44	D₄²	C₂²	1	1	yes	characteristic
45	#542	—	2	1	no	—
46	#538	—	2	2	no	—
47	#533	C₂²	1	1	yes	characteristic, complemented
48	#533	C₂²	1	2	yes	complemented
49	#532	C₂²	1	1	yes	characteristic
50	#529	—	2	1	no	—
51	#529	—	2	2	no	—
52	#529	C₂²	1	1	yes	characteristic
53	#529	C₂²	1	2	yes	—
54	C₂×#124	C₂²	1	2	yes	—
55	#518	—	2	1	no	—
56	C₄×#41	C₂²	1	1	yes	characteristic
57	C₄×#41	C₂²	1	1	yes	characteristic, complemented
58	C₄×#41	C₂²	1	2	yes	complemented
59	C₂×C₄×Q₈	—	2	1	no	—
60	#497	C₂²	1	2	yes	—
61	#497	C₂²	1	2	yes	complemented
62	#494	C₂²	1	1	yes	characteristic, complemented
63	#492	C₂²	1	1	yes	characteristic
64	#489	C₂²	1	2	yes	—
65	#489	C₂²	1	2	yes	complemented
66	#487	C₂²	1	1	yes	characteristic, complemented
67	#486	C₂²	1	1	yes	characteristic
68	#485	C₂²	1	2	yes	complemented
69	#485	C₂²	1	1	yes	characteristic, complemented
70	#482	C₂²	1	1	yes	characteristic
71	#482	C₂²	1	2	yes	—
72	#479	C₂²	1	1	yes	characteristic, complemented
73	#479	C₂²	1	2	yes	complemented
74	#478	C₂²	1	1	yes	characteristic, complemented
75	#477	C₂²	1	2	yes	complemented
76	#476	C₂²	1	2	yes	complemented
77	#475	C₂²	1	1	yes	characteristic, complemented
78	#474	C₂²	1	1	yes	characteristic
79	#470	C₂²	1	2	yes	complemented
80	#470	C₂²	1	2	yes	complemented
81	#468	C₂²	1	2	yes	—
82	#468	C₂²	1	2	yes	—
83	#467	C₂²	1	2	yes	complemented
84	#465	C₂²	1	2	yes	—
85	#464	C₂²	1	1	yes	characteristic
86	#464	C₂²	1	2	yes	—
87	#464	C₂²	1	2	yes	—
88	#464	C₂²	1	2	yes	complemented
89	#464	C₂²	1	2	yes	complemented
90	#464	C₂²	1	2	yes	complemented
91	#464	C₂²	1	2	yes	complemented
92	#463	C₂²	1	1	yes	characteristic
93	#463	C₂²	1	2	yes	—
94	#463	C₂²	1	2	yes	complemented
95	#463	C₂²	1	2	yes	complemented
96	#462	C₂²	1	1	yes	characteristic, complemented
97	#462	C₂²	1	2	yes	complemented
98	#462	C₂²	1	1	yes	characteristic, complemented
99	#461	C₂²	1	1	yes	characteristic
100	#461	C₂²	1	1	yes	characteristic, 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, complemented
105	#452	C₂²	1	2	yes	complemented
106	#452	C₂²	1	2	yes	complemented
107	#452	C₂²	1	2	yes	complemented
108	#451	C₂²	1	2	yes	complemented
109	#451	C₂²	1	2	yes	complemented
110	#450	C₂²	1	2	yes	—
111	#450	C₂²	1	2	yes	—
112	#449	C₂²	1	1	yes	characteristic
113	#449	C₂²	1	2	yes	—
114	#446	C₂²	1	1	yes	characteristic, complemented
115	#446	C₂²	1	1	yes	characteristic, complemented
116	#442	C₂²	1	2	yes	complemented
117	#441	C₂²	1	2	yes	complemented
118	#440	C₂²	1	2	yes	complemented
119	#440	C₂²	1	2	yes	complemented
120	C₄×Q₁₆	C₂²	1	1	yes	characteristic, complemented
121	C₄×SD₁₆	C₂²	1	1	yes	characteristic
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	1	yes	characteristic
126	#435	C₂²	1	2	yes	complemented
127	#435	C₂²	1	2	yes	complemented
128	#432	C₂²	1	2	yes	complemented
129	#431	C₂²	1	1	yes	characteristic, complemented
130	#423	C₂²	1	2	yes	complemented
131	C₂×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
132	#419	C₂²	1	2	yes	complemented
133	#418	C₂²	1	2	yes	—
134	#416	C₂²	1	2	yes	complemented
135	C₂×#41	D₄	1	1	yes	characteristic
136	C₂×#41	C₂³	1	2	yes	—
137	C₂×#41	C₂³	1	1	yes	characteristic
138	C₂×#41	C₂³	1	2	yes	—
139	C₂²×Q₈	—	2	1	no	—
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	#135	—	4	4	no	—
146	C₂×Q₁₆	C₂³	1	2	yes	—
147	C₂×Q₁₆	C₂³	1	2	yes	—
148	C₂×Q₁₆	C₂³	1	2	yes	—
149	C₂×Q₁₆	C₂³	1	1	yes	characteristic
150	C₂×Q₁₆	C₂³	1	2	yes	—
151	C₂×SD₁₆	C₂³	1	2	yes	—
152	C₂×SD₁₆	C₂³	1	1	yes	characteristic
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	2	yes	—
159	C₂×D₈	C₂³	1	1	yes	characteristic
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	C₂³	1	1	yes	characteristic
165	C₄⋊Q₈	C₂³	1	1	yes	characteristic
166	C₄⋊Q₈	C₂³	1	2	yes	—
167	C₄⋊Q₈	C₂³	1	1	yes	characteristic
168	C₄⋊Q₈	C₂³	1	2	yes	—
169	#127	C₂³	1	1	yes	characteristic
170	#126	—	2	2	no	—
171	#126	—	2	2	no	—
172	#126	—	2	2	no	—
173	#126	—	2	2	no	—
174	#126	—	2	2	no	—
175	#126	—	2	1	no	—
176	#125	—	2	1	no	—
177	#125	—	2	2	no	—
178	#125	—	2	2	no	—
179	#125	—	2	1	no	—
180	#125	C₂³	1	1	yes	characteristic
181	#124	—	2	1	no	—
182	#124	—	2	1	no	—
183	#124	—	2	2	no	—
184	#124	—	2	2	no	—
185	#124	—	2	2	no	—
186	#124	—	2	2	no	—
187	#124	C₂³	1	1	yes	characteristic
188	#124	C₂³	1	2	yes	—
189	#124	C₂³	1	2	yes	—
190	#124	C₂³	1	2	yes	—
191	#123	—	2	1	no	—
192	#123	—	2	2	no	—
193	#123	—	2	2	no	—
194	#123	—	2	2	no	—
195	#123	—	2	2	no	—
196	#123	—	2	2	no	—
197	#123	—	2	2	no	—
198	C₂²⋊Q₈	—	2	1	no	—
199	C₂²⋊Q₈	—	2	1	no	—
200	C₂²⋊Q₈	—	2	2	no	—
201	C₂²⋊Q₈	—	2	1	no	—
202	C₂²⋊Q₈	—	2	2	no	—
203	C₂²⋊Q₈	—	2	2	no	—
204	C₂²⋊Q₈	—	2	2	no	—
205	C₂²⋊Q₈	C₂³	1	2	yes	—
206	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
207	C₂²⋊Q₈	C₂³	1	2	yes	—
208	C₂²⋊Q₈	C₂³	1	2	yes	—
209	C₂²⋊Q₈	C₂³	1	2	yes	—
210	#121	—	2	1	no	—
211	#121	—	2	2	no	—
212	#121	—	2	2	no	—
213	#121	—	2	1	no	—
214	#121	—	2	1	no	—
215	#121	—	2	1	no	—
216	#121	—	2	2	no	—
217	#121	C₂³	1	2	yes	—
218	#121	C₂³	1	1	yes	characteristic
219	#120	—	2	2	no	—
220	#120	—	2	2	no	—
221	C₄×Q₈	—	2	1	no	—
222	C₄×Q₈	—	2	1	no	—
223	C₄×Q₈	—	2	2	no	—
224	C₄×Q₈	—	2	1	no	—
225	C₄×Q₈	—	2	2	no	—
226	C₄×Q₈	D₄	1	1	yes	characteristic
227	C₄×Q₈	C₂³	1	1	yes	characteristic
228	C₄×Q₈	C₂³	1	2	yes	—
229	C₄×Q₈	C₂³	1	1	yes	characteristic
230	C₄×Q₈	C₂³	1	2	yes	—
231	C₄×Q₈	C₂³	1	2	yes	—
232	C₄×Q₈	C₂³	1	1	yes	characteristic
233	C₄×Q₈	C₂³	1	1	yes	characteristic
234	C₄×D₄	—	2	1	no	—
235	C₄×D₄	—	2	2	no	—
236	C₄×D₄	—	2	1	no	—
237	C₄×D₄	—	2	1	no	—
238	C₄×D₄	—	2	2	no	—
239	C₄×D₄	—	2	2	no	—
240	C₄×D₄	—	2	1	no	—
241	C₄×D₄	—	2	1	no	—
242	C₄×D₄	—	2	2	no	—
243	C₄×D₄	—	2	1	no	—
244	C₄×D₄	—	2	1	no	—
245	C₄×D₄	D₄	1	1	yes	characteristic
246	C₄×D₄	D₄	1	2	yes	—
247	C₄×D₄	C₂³	1	1	yes	characteristic
248	C₄×D₄	C₂³	1	1	yes	characteristic
249	C₄×D₄	C₂³	1	2	yes	—
250	C₄×D₄	C₂³	1	1	yes	characteristic
251	C₄×D₄	C₂³	1	2	yes	—
252	C₄×D₄	C₂³	1	1	yes	characteristic
253	C₄×D₄	C₂³	1	2	yes	—
254	#117	—	2	2	no	—
255	#117	—	2	1	no	—
256	#117	—	2	1	no	—
257	#117	—	2	2	no	—
258	#117	—	2	1	no	—
259	#117	—	2	1	no	—
260	#117	—	2	2	no	—
261	#117	D₄	1	2	yes	—
262	#117	D₄	1	1	yes	characteristic
263	#117	C₂³	1	2	yes	—
264	#117	C₂³	1	1	yes	characteristic
265	C₂×C₄⋊C₄	—	2	1	no	—
266	C₂×C₄⋊C₄	—	2	2	no	—
267	C₂×C₂²⋊C₄	—	2	2	no	—
268	C₂×C₂²⋊C₄	—	2	2	no	—
269	C₂×C₂²⋊C₄	—	2	2	no	—
270	C₂×C₄²	—	2	1	no	—
271	C₂×C₄²	—	2	2	no	—
272	C₂×C₄²	C₂³	1	2	yes	—
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	1	yes	characteristic
279	#106	C₂³	1	2	yes	—
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	1	yes	characteristic
290	#103	C₂³	1	2	yes	—
291	#103	C₂³	1	2	yes	—
292	#103	C₂³	1	1	yes	characteristic
293	#103	C₂³	1	1	yes	characteristic
294	#103	C₂³	1	1	yes	characteristic
295	#103	C₂³	1	2	yes	—
296	#103	C₂³	1	2	yes	—
297	#103	C₂³	1	2	yes	—
298	#102	C₂³	1	2	yes	—
299	#102	C₂³	1	2	yes	—
300	#102	C₂³	1	1	yes	characteristic
301	#102	C₂³	1	2	yes	—
302	#102	C₂³	1	2	yes	—
303	#102	C₂³	1	1	yes	characteristic
304	#102	C₂³	1	1	yes	characteristic
305	#102	C₂³	1	1	yes	characteristic
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	#97	C₂³	1	2	yes	—
313	C₄×C₈	C₂³	1	1	yes	characteristic
314	C₄×C₈	C₂³	1	1	yes	characteristic
315	C₂⁴	—	2	2	no	—
316	#41	—	2	2	no	—
317	#41	—	2	4	no	—
318	#41	—	4	2	no	—
319	#41	—	4	2	no	—
320	#41	—	4	1	no	—
321	#41	—	4	2	no	—
322	#41	—	4	2	no	—
323	C₂×Q₈	—	2	2	no	—
324	C₂×Q₈	—	2	1	no	—
325	C₂×Q₈	—	2	2	no	—
326	C₂×Q₈	—	4	2	no	—
327	C₂×Q₈	—	4	2	no	—
328	C₂×Q₈	—	4	4	no	—
329	C₂×Q₈	C₂×D₄	1	1	yes	characteristic
330	C₂×Q₈	C₂⁴	1	1	yes	characteristic
331	C₂×Q₈	C₂⁴	1	2	yes	—
332	C₂×Q₈	C₂⁴	1	1	yes	characteristic
333	C₂×Q₈	C₂⁴	1	2	yes	—
334	C₂×D₄	—	2	2	no	—
335	C₂×D₄	—	2	2	no	—
336	C₂×D₄	—	2	1	no	—
337	C₂×D₄	—	2	1	no	—
338	C₂×D₄	—	2	2	no	—
339	C₂×D₄	—	2	1	no	—
340	C₂×D₄	—	2	1	no	—
341	C₂×D₄	—	2	2	no	—
342	C₂×D₄	—	4	2	no	—
343	C₂×D₄	—	4	2	no	—
344	C₂×D₄	—	4	4	no	—
345	C₂×D₄	C₂×D₄	1	1	yes	characteristic
346	C₂×D₄	C₂×D₄	1	2	yes	—
347	C₂×D₄	C₂⁴	1	1	yes	characteristic
348	C₂×D₄	C₂⁴	1	2	yes	—
349	C₂×D₄	C₂⁴	1	1	yes	characteristic
350	C₂²×C₄	—	2	2	no	—
351	C₂²×C₄	—	2	1	no	—
352	C₂²×C₄	—	2	1	no	—
353	C₂²×C₄	—	2	2	no	—
354	C₂²×C₄	—	2	2	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	C₂×D₄	1	1	yes	characteristic
360	C₂²×C₄	C₂×D₄	1	2	yes	—
361	C₂²×C₄	C₂×D₄	1	2	yes	—
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	Q₁₆	—	4	2	no	—
369	Q₁₆	—	4	2	no	—
370	SD₁₆	—	2	4	no	—
371	SD₁₆	—	2	2	no	—
372	SD₁₆	—	4	2	no	—
373	SD₁₆	—	4	1	no	—
374	SD₁₆	—	4	2	no	—
375	SD₁₆	—	4	2	no	—
376	SD₁₆	—	4	2	no	—
377	D₈	—	2	4	no	—
378	D₈	—	2	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	1	yes	characteristic
386	C₂×C₈	C₂⁴	1	2	yes	—
387	C₂×C₈	C₂⁴	1	2	yes	—
388	C₄⋊C₄	—	2	2	no	—
389	C₄⋊C₄	—	2	1	no	—
390	C₄⋊C₄	—	2	2	no	—
391	C₄⋊C₄	—	2	2	no	—
392	C₄⋊C₄	—	2	2	no	—
393	C₄⋊C₄	—	2	1	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	2	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	1	no	—
406	C₄⋊C₄	—	2	1	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	2	yes	—
411	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
412	C₄⋊C₄	C₂×D₄	1	2	yes	—
413	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
414	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
415	C₄⋊C₄	C₂⁴	1	2	yes	—
416	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
417	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
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	1	no	—
424	C₂²⋊C₄	—	2	1	no	—
425	C₂²⋊C₄	—	2	2	no	—
426	C₂²⋊C₄	—	2	1	no	—
427	C₂²⋊C₄	—	2	1	no	—
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	2	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	C₂×D₄	1	2	yes	—
441	C₂²⋊C₄	C₂×D₄	1	2	yes	—
442	C₂²⋊C₄	C₂×D₄	1	2	yes	—
443	C₄²	—	2	1	no	—
444	C₄²	—	2	2	no	—
445	C₄²	—	2	1	no	—
446	C₄²	—	2	2	no	—
447	C₄²	—	2	2	no	—
448	C₄²	—	2	1	no	—
449	C₄²	—	2	2	no	—
450	C₄²	—	2	1	no	—
451	C₄²	C₂×D₄	1	1	yes	characteristic
452	C₄²	C₂×D₄	1	2	yes	—
453	C₄²	C₂×D₄	1	2	yes	—
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	1	no	—
470	Q₈	—	2	2	no	—
471	Q₈	—	2	2	no	—
472	Q₈	—	2	1	no	—
473	Q₈	—	2	1	no	—
474	Q₈	—	2	2	no	—
475	Q₈	—	4	4	no	—
476	Q₈	—	4	2	no	—
477	Q₈	—	8	2	no	—
478	D₄	—	2	2	no	—
479	D₄	—	2	1	no	—
480	D₄	—	2	2	no	—
481	D₄	—	2	1	no	—
482	D₄	—	2	1	no	—
483	D₄	—	2	2	no	—
484	D₄	—	4	2	no	—
485	D₄	—	4	4	no	—
486	D₄	—	4	2	no	—
487	D₄	—	4	4	no	—
488	D₄	—	4	2	no	—
489	D₄	—	8	1	no	—
490	D₄	—	8	2	no	—
491	D₄	—	8	1	no	—
492	D₄	—	8	2	no	—
493	D₄	H(5,𝔽₂)	1	2	yes	—
494	C₂×C₄	—	2	2	no	—
495	C₂×C₄	—	2	1	no	—
496	C₂×C₄	—	2	2	no	—
497	C₂×C₄	—	2	2	no	—
498	C₂×C₄	—	2	1	no	—
499	C₂×C₄	—	2	1	no	—
500	C₂×C₄	—	2	1	no	—
501	C₂×C₄	—	2	2	no	—
502	C₂×C₄	—	2	1	no	—
503	C₂×C₄	—	2	2	no	—
504	C₂×C₄	—	2	1	no	—
505	C₂×C₄	—	2	1	no	—
506	C₂×C₄	—	2	1	no	—
507	C₂×C₄	—	2	2	no	—
508	C₂×C₄	—	4	2	no	—
509	C₂×C₄	—	4	1	no	—
510	C₂×C₄	—	4	2	no	—
511	C₂×C₄	—	4	2	no	—
512	C₂×C₄	—	4	4	no	—
513	C₂×C₄	—	4	2	no	—
514	C₂×C₄	—	4	4	no	—
515	C₂×C₄	—	4	2	no	—
516	C₂×C₄	—	4	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	2	no	—
530	C₈	—	2	2	no	—
531	C₈	—	2	1	no	—
532	C₈	—	2	1	no	—
533	C₈	—	2	1	no	—
534	C₈	—	2	1	no	—
535	C₂²	—	2	1	no	—
536	C₂²	—	2	2	no	—
537	C₂²	—	2	2	no	—
538	C₂²	—	2	1	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	2	no	—
547	C₂²	—	4	1	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	2	no	—
554	C₄	—	2	1	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	2	no	—
564	C₄	—	4	1	no	—
565	C₄	—	4	1	no	—
566	C₄	—	4	2	no	—
567	C₄	—	4	1	no	—
568	C₄	#575	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	2	no	—
575	C₂	—	8	1	no	—
576	C₂	#3488	1	1	yes	characteristic
577	C₂	C₂×#575	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 ◁ 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. #3514	C₂	semidirect
2. #3482	C₂	semidirect
3. #3400	C₂	semidirect
4. #3398	C₂	semidirect
5. #3373	C₂	semidirect
6. #3367	C₂	semidirect
7. #3328	C₂	semidirect
8. #3324	C₂	semidirect
9. #3313	C₂	semidirect
10. #3311	C₂	semidirect
11. #3276	C₂	semidirect
12. #3272	C₂	semidirect
13. #3269	C₂	semidirect
14. #3267	C₂	semidirect
15. #3252	C₂	semidirect
16. #3248	C₂	semidirect
17. #3215	C₂	semidirect
18. #3210	C₂	semidirect
19. #3111	C₂	semidirect
20. #3102	C₂	semidirect
21. #3040	C₂	semidirect
22. #3035	C₂	semidirect
23. #2989	C₂	semidirect
24. C₂×#137	C₂²	semidirect
26. C₂×#135	C₂²	semidirect
28. #557	C₂²	semidirect
31. #556	C₂²	semidirect
37. D₄×Q₈	C₂²	semidirect
41. #547	C₂²	semidirect
47. #533	C₂²	semidirect
48. #533	C₂²	semidirect
57. C₄×#41	C₂²	semidirect
58. C₄×#41	C₂²	semidirect
61. #497	C₂²	semidirect
62. #494	C₂²	semidirect
65. #489	C₂²	semidirect
66. #487	C₂²	semidirect
68. #485	C₂²	semidirect
69. #485	C₂²	semidirect
72. #479	C₂²	semidirect
73. #479	C₂²	semidirect
74. #478	C₂²	semidirect
75. #477	C₂²	semidirect
76. #476	C₂²	semidirect
77. #475	C₂²	semidirect
79. #470	C₂²	semidirect
80. #470	C₂²	semidirect
83. #467	C₂²	semidirect
88. #464	C₂²	semidirect
89. #464	C₂²	semidirect
90. #464	C₂²	semidirect
91. #464	C₂²	semidirect
94. #463	C₂²	semidirect
95. #463	C₂²	semidirect
96. #462	C₂²	semidirect
97. #462	C₂²	semidirect
98. #462	C₂²	semidirect
100. #461	C₂²	semidirect
101. #461	C₂²	semidirect
104. #452	C₂²	semidirect
105. #452	C₂²	semidirect
106. #452	C₂²	semidirect
107. #452	C₂²	semidirect
108. #451	C₂²	semidirect
109. #451	C₂²	semidirect
114. #446	C₂²	semidirect
115. #446	C₂²	semidirect
116. #442	C₂²	semidirect
117. #441	C₂²	semidirect
118. #440	C₂²	semidirect
119. #440	C₂²	semidirect
120. C₄×Q₁₆	C₂²	semidirect
122. C₄×SD₁₆	C₂²	semidirect
126. #435	C₂²	semidirect
127. #435	C₂²	semidirect
128. #432	C₂²	semidirect
129. #431	C₂²	semidirect
130. #423	C₂²	semidirect
131. C₂×C₄⋊C₈	C₂²	semidirect
132. #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
#3514	2
#3482	2
#3400	2
#3398	2
#3373	2
#3367	2
#3328	2
#3324	2
#3313	2
#3311	2
#3276	2
#3272	2
#3269	2
#3267	2
#3252	2
#3248	2
#3215	2
#3210	2
#3111	2
#3102	2
#3040	2
#3035	2
#2989	2