Subgroups — #60697

Order 256.

953 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3461	C₂	1	1	yes	maximal, characteristic, complemented
2	#3460	C₂	1	1	yes	maximal, characteristic, complemented
3	#3183	C₂	1	2	yes	maximal, complemented
4	#3182	C₂	1	2	yes	maximal, complemented
5	#3181	C₂	1	2	yes	maximal, complemented
6	#3180	C₂	1	2	yes	maximal, complemented
7	#3179	C₂	1	2	yes	maximal, complemented
8	#3178	C₂	1	2	yes	maximal, complemented
9	#3175	C₂	1	2	yes	maximal, complemented
10	#3174	C₂	1	2	yes	maximal, complemented
11	#3164	C₂	1	1	yes	maximal, characteristic, complemented
12	#3154	C₂	1	1	yes	maximal, characteristic, complemented
13	#3137	C₂	1	1	yes	maximal, characteristic, complemented
14	#3136	C₂	1	1	yes	maximal, characteristic, complemented
15	#3063	C₂	1	1	yes	maximal, characteristic, complemented
16	#3062	C₂	1	1	yes	maximal, characteristic, complemented
17	#3061	C₂	1	1	yes	maximal, characteristic, complemented
18	#3057	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄×#137	C₂	1	1	yes	maximal, characteristic, complemented
20	C₄×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic, complemented
21	#2943	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×#440	C₂	1	1	yes	maximal, characteristic, complemented
23	#2875	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#137	C₂²	1	1	yes	characteristic
25	C₂×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
26	C₂×#135	C₂²	1	1	yes	characteristic
27	C₂²×SD₁₆	C₂²	1	1	yes	characteristic
28	C₂×#131	C₂²	1	1	yes	characteristic
29	C₂×#131	C₂²	1	1	yes	characteristic
30	#544	C₂²	1	1	yes	characteristic
31	#544	C₂²	1	1	yes	characteristic
32	#542	—	2	1	no	—
33	#542	—	2	1	no	—
34	#542	C₂²	1	2	yes	—
35	#542	C₂²	1	2	yes	complemented
36	#541	—	2	1	no	—
37	#541	C₂²	1	2	yes	complemented
38	#540	—	2	1	no	—
39	#540	C₂²	1	2	yes	—
40	#539	—	2	2	no	—
41	#538	—	2	2	no	—
42	#537	C₂²	1	1	yes	characteristic
43	#537	C₂²	1	1	yes	characteristic
44	#536	C₂²	1	1	yes	characteristic
45	#536	C₂²	1	1	yes	characteristic
46	#535	C₂²	1	1	yes	characteristic
47	#535	C₂²	1	1	yes	characteristic
48	#533	—	2	1	no	—
49	#533	C₂²	1	2	yes	complemented
50	#532	—	2	1	no	—
51	#532	C₂²	1	2	yes	—
52	#529	—	2	1	no	—
53	#529	—	2	2	no	—
54	#529	—	2	1	no	—
55	#529	C₂²	1	2	yes	—
56	#529	C₂²	1	2	yes	complemented
57	#525	—	2	2	no	—
58	C₄×#41	C₂²	1	1	yes	characteristic
59	C₄×#41	C₂²	1	1	yes	characteristic
60	C₄×#41	C₂²	1	1	yes	characteristic
61	C₂×C₄×Q₈	C₂²	1	1	yes	characteristic
62	C₂×C₄×D₄	C₂²	1	1	yes	characteristic
63	#501	C₂²	1	2	yes	complemented
64	#501	C₂²	1	2	yes	complemented
65	#500	C₂²	1	2	yes	complemented
66	#499	C₂²	1	2	yes	complemented
67	#497	C₂²	1	2	yes	—
68	#496	C₂²	1	2	yes	—
69	#495	C₂²	1	2	yes	—
70	#492	C₂²	1	2	yes	—
71	#491	C₂²	1	2	yes	complemented
72	#490	C₂²	1	2	yes	—
73	#489	C₂²	1	2	yes	—
74	#489	C₂²	1	2	yes	complemented
75	#488	C₂²	1	2	yes	—
76	#488	C₂²	1	2	yes	complemented
77	#487	C₂²	1	2	yes	complemented
78	#486	C₂²	1	2	yes	—
79	#470	C₂²	1	2	yes	complemented
80	#469	C₂²	1	2	yes	—
81	#468	C₂²	1	2	yes	—
82	#468	C₂²	1	2	yes	—
83	#468	C₂²	1	2	yes	—
84	#468	C₂²	1	2	yes	complemented
85	#468	C₂²	1	2	yes	complemented
86	#468	C₂²	1	2	yes	complemented
87	#467	C₂²	1	2	yes	complemented
88	#467	C₂²	1	2	yes	complemented
89	#466	C₂²	1	2	yes	—
90	#466	C₂²	1	2	yes	complemented
91	#465	C₂²	1	2	yes	—
92	#465	C₂²	1	2	yes	—
93	#465	C₂²	1	2	yes	—
94	#465	C₂²	1	2	yes	complemented
95	#442	C₂²	1	2	yes	—
96	#442	C₂²	1	1	yes	characteristic, complemented
97	#442	C₂²	1	1	yes	characteristic, complemented
98	#441	C₂²	1	1	yes	characteristic, complemented
99	#441	C₂²	1	1	yes	characteristic, complemented
100	#441	C₂²	1	2	yes	complemented
101	#440	C₂²	1	2	yes	—
102	#440	C₂²	1	2	yes	—
103	#440	C₂²	1	2	yes	—
104	#440	C₂²	1	2	yes	—
105	#440	C₂²	1	2	yes	—
106	#440	C₂²	1	1	yes	characteristic, complemented
107	#440	C₂²	1	1	yes	characteristic, complemented
108	#440	C₂²	1	2	yes	complemented
109	#440	C₂²	1	1	yes	characteristic, complemented
110	#440	C₂²	1	1	yes	characteristic, complemented
111	C₄×Q₁₆	C₂²	1	2	yes	complemented
112	C₄×SD₁₆	C₂²	1	2	yes	—
113	C₄×SD₁₆	C₂²	1	2	yes	complemented
114	C₄×D₈	C₂²	1	2	yes	—
115	#428	C₂²	1	1	yes	characteristic
116	#428	C₂²	1	1	yes	characteristic
117	#427	C₂²	1	1	yes	characteristic
118	C₂×#107	C₂²	1	1	yes	characteristic
119	#419	C₂²	1	1	yes	characteristic
120	#418	C₂²	1	1	yes	characteristic
121	#417	C₂²	1	1	yes	characteristic
122	#417	C₂²	1	1	yes	characteristic
123	#416	C₂²	1	1	yes	characteristic
124	#416	C₂²	1	1	yes	characteristic
125	C₂×#103	C₂²	1	1	yes	characteristic
126	C₂×#102	C₂²	1	1	yes	characteristic
127	#405	C₂²	1	1	yes	characteristic
128	#405	C₂²	1	1	yes	characteristic
129	#405	C₂²	1	2	yes	complemented
130	#405	C₂²	1	2	yes	complemented
131	C₄×M₁₆	C₂²	1	1	yes	characteristic
132	C₄×M₁₆	C₂²	1	2	yes	complemented
133	C₂×#97	C₂²	1	1	yes	characteristic
134	C₂×#97	C₂²	1	2	yes	complemented
135	C₂×#41	—	2	2	no	—
136	C₂×#41	C₂³	1	1	yes	characteristic
137	C₂×#41	C₂³	1	1	yes	characteristic
138	C₂×#41	C₂³	1	1	yes	characteristic
139	C₂²×Q₈	C₂³	1	1	yes	characteristic
140	C₂²×D₄	C₂³	1	1	yes	characteristic
141	C₂³×C₄	—	2	1	no	—
142	#137	—	2	4	no	—
143	AGL(1,ℤ/8)	—	2	4	no	—
144	#135	—	2	4	no	—
145	C₂×Q₁₆	C₂³	1	1	yes	characteristic
146	C₂×Q₁₆	C₂³	1	2	yes	—
147	C₂×SD₁₆	—	2	4	no	—
148	C₂×SD₁₆	C₂³	1	2	yes	—
149	C₂×SD₁₆	C₂³	1	2	yes	—
150	C₂×SD₁₆	C₂³	1	1	yes	characteristic
151	C₂×SD₁₆	C₂³	1	1	yes	characteristic
152	C₂×SD₁₆	C₂³	1	2	yes	—
153	C₂×SD₁₆	C₂³	1	2	yes	—
154	C₂×D₈	C₂³	1	1	yes	characteristic
155	C₂×D₈	C₂³	1	2	yes	—
156	#131	—	2	4	no	—
157	#131	—	2	4	no	—
158	C₂×M₁₆	C₂³	1	1	yes	characteristic
159	C₂×M₁₆	C₂³	1	2	yes	—
160	C₂×M₁₆	C₂³	1	2	yes	—
161	C₂×M₁₆	C₂³	1	1	yes	characteristic
162	C₂²×C₈	C₂³	1	1	yes	characteristic
163	C₂²×C₈	C₂³	1	2	yes	—
164	C₂²×C₈	C₂³	1	2	yes	—
165	C₂²×C₈	C₂³	1	1	yes	characteristic
166	C₄⋊Q₈	—	2	1	no	—
167	C₄⋊Q₈	—	2	1	no	—
168	C₄⋊Q₈	—	2	1	no	—
169	C₄⋊Q₈	C₂³	1	2	yes	—
170	C₄⋊Q₈	C₂³	1	2	yes	—
171	C₄⋊Q₈	C₂³	1	2	yes	—
172	#127	—	2	1	no	—
173	#127	C₂³	1	2	yes	—
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	2	no	—
180	#125	—	2	1	no	—
181	#125	—	2	2	no	—
182	#125	—	2	1	no	—
183	#125	—	2	2	no	—
184	#125	—	2	2	no	—
185	#125	C₂³	1	2	yes	—
186	#125	C₂³	1	2	yes	—
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	C₂³	1	2	yes	—
193	#124	C₂³	1	2	yes	—
194	#123	—	2	2	no	—
195	#123	—	2	2	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	C₂²⋊Q₈	—	2	1	no	—
203	C₂²⋊Q₈	—	2	1	no	—
204	C₂²⋊Q₈	—	2	2	no	—
205	C₂²⋊Q₈	—	2	2	no	—
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	C₂³	1	2	yes	—
212	C₂²⋊Q₈	C₂³	1	2	yes	—
213	C₂²⋊Q₈	C₂³	1	2	yes	—
214	C₂²⋊Q₈	C₂³	1	2	yes	—
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	1	no	—
221	#121	—	2	1	no	—
222	#121	—	2	2	no	—
223	#121	—	2	2	no	—
224	#121	C₂³	1	2	yes	—
225	#121	C₂³	1	2	yes	—
226	#121	C₂³	1	2	yes	—
227	#121	C₂³	1	2	yes	—
228	#120	—	2	2	no	—
229	#120	—	2	2	no	—
230	C₄×Q₈	—	2	1	no	—
231	C₄×Q₈	—	2	1	no	—
232	C₄×Q₈	—	2	2	no	—
233	C₄×Q₈	D₄	1	1	yes	characteristic
234	C₄×Q₈	D₄	1	1	yes	characteristic
235	C₄×Q₈	C₂³	1	2	yes	—
236	C₄×Q₈	C₂³	1	2	yes	—
237	C₄×Q₈	C₂³	1	1	yes	characteristic
238	C₄×Q₈	C₂³	1	1	yes	characteristic
239	C₄×Q₈	C₂³	1	1	yes	characteristic
240	C₄×Q₈	C₂³	1	1	yes	characteristic
241	C₄×D₄	—	2	1	no	—
242	C₄×D₄	—	2	1	no	—
243	C₄×D₄	—	2	1	no	—
244	C₄×D₄	—	2	1	no	—
245	C₄×D₄	—	2	2	no	—
246	C₄×D₄	—	2	2	no	—
247	C₄×D₄	—	2	1	no	—
248	C₄×D₄	—	2	1	no	—
249	C₄×D₄	—	2	2	no	—
250	C₄×D₄	D₄	1	2	yes	—
251	C₄×D₄	D₄	1	2	yes	—
252	C₄×D₄	D₄	1	1	yes	characteristic
253	C₄×D₄	D₄	1	1	yes	characteristic
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	1	yes	characteristic
259	C₄×D₄	C₂³	1	1	yes	characteristic
260	#117	—	2	2	no	—
261	#117	—	2	1	no	—
262	#117	—	2	1	no	—
263	#117	—	2	2	no	—
264	#117	—	2	2	no	—
265	#117	C₂³	1	1	yes	characteristic
266	#117	C₂³	1	1	yes	characteristic
267	#117	C₂³	1	1	yes	characteristic
268	#117	C₂³	1	2	yes	—
269	C₂×C₄⋊C₄	—	2	1	no	—
270	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
271	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
272	C₂×C₂²⋊C₄	—	2	1	no	—
273	C₂×C₄²	—	2	1	no	—
274	C₂×C₄²	—	2	1	no	—
275	C₂×C₄²	—	2	1	no	—
276	C₂×C₄²	C₂³	1	1	yes	characteristic
277	C₂×C₄²	C₂³	1	2	yes	—
278	#107	C₂³	1	2	yes	—
279	#107	C₂³	1	2	yes	—
280	#107	C₂³	1	1	yes	characteristic
281	#107	C₂³	1	1	yes	characteristic
282	#107	C₂³	1	2	yes	—
283	#107	C₂³	1	2	yes	—
284	#106	C₂³	1	1	yes	characteristic
285	#106	C₂³	1	1	yes	characteristic
286	#106	C₂³	1	2	yes	—
287	#106	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	1	yes	characteristic
292	#103	C₂³	1	1	yes	characteristic
293	#103	C₂³	1	1	yes	characteristic
294	#103	C₂³	1	2	yes	—
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	1	yes	characteristic
302	#102	C₂³	1	1	yes	characteristic
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	#102	C₂³	1	2	yes	—
308	#97	C₂³	1	1	yes	characteristic
309	#97	C₂³	1	1	yes	characteristic
310	#97	C₂³	1	1	yes	characteristic
311	#97	C₂³	1	1	yes	characteristic
312	#97	C₂³	1	2	yes	—
313	#97	C₂³	1	2	yes	—
314	#97	C₂³	1	2	yes	—
315	C₄×C₈	C₂³	1	2	yes	—
316	C₄×C₈	C₂³	1	2	yes	—
317	C₄×C₈	C₂³	1	2	yes	—
318	C₂⁴	—	2	1	no	—
319	#41	—	2	2	no	—
320	#41	—	2	2	no	—
321	#41	—	2	2	no	—
322	#41	—	2	2	no	—
323	#41	—	2	2	no	—
324	#41	—	2	2	no	—
325	#41	—	8	4	no	—
326	C₂×Q₈	—	2	1	no	—
327	C₂×Q₈	—	2	2	no	—
328	C₂×Q₈	—	2	2	no	—
329	C₂×Q₈	—	2	2	no	—
330	C₂×Q₈	—	2	2	no	—
331	C₂×Q₈	C₂×D₄	1	1	yes	characteristic
332	C₂×Q₈	C₂⁴	1	1	yes	characteristic
333	C₂×Q₈	C₂⁴	1	2	yes	—
334	C₂×Q₈	C₂⁴	1	1	yes	characteristic
335	C₂×D₄	—	2	1	no	—
336	C₂×D₄	—	2	1	no	—
337	C₂×D₄	—	2	2	no	—
338	C₂×D₄	—	2	2	no	—
339	C₂×D₄	—	2	2	no	—
340	C₂×D₄	—	2	2	no	—
341	C₂×D₄	—	2	1	no	—
342	C₂×D₄	—	2	2	no	—
343	C₂×D₄	—	2	2	no	—
344	C₂×D₄	—	2	2	no	—
345	C₂×D₄	—	2	2	no	—
346	C₂×D₄	C₂×D₄	1	2	yes	—
347	C₂×D₄	C₂×D₄	1	1	yes	characteristic
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	1	no	—
352	C₂²×C₄	—	2	1	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	1	no	—
358	C₂²×C₄	—	2	2	no	—
359	C₂²×C₄	—	2	1	no	—
360	C₂²×C₄	—	2	1	no	—
361	C₂²×C₄	—	2	2	no	—
362	C₂²×C₄	—	8	2	no	—
363	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
364	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
365	C₂²×C₄	C₂×D₄	1	2	yes	—
366	C₂²×C₄	C₂×D₄	1	2	yes	—
367	C₂²×C₄	C₂⁴	1	2	yes	—
368	C₂²×C₄	C₂⁴	1	1	yes	characteristic
369	Q₁₆	—	2	2	no	—
370	Q₁₆	—	2	4	no	—
371	SD₁₆	—	2	4	no	—
372	SD₁₆	—	2	4	no	—
373	SD₁₆	—	2	2	no	—
374	SD₁₆	—	2	2	no	—
375	SD₁₆	—	2	4	no	—
376	SD₁₆	—	2	4	no	—
377	D₈	—	2	2	no	—
378	D₈	—	2	4	no	—
379	M₁₆	—	2	2	no	—
380	M₁₆	—	2	4	no	—
381	M₁₆	—	2	4	no	—
382	M₁₆	#41	1	4	yes	complemented
383	C₂×C₈	—	2	2	no	—
384	C₂×C₈	—	2	4	no	—
385	C₂×C₈	—	2	4	no	—
386	C₂×C₈	#41	1	4	yes	complemented
387	C₂×C₈	C₂⁴	1	2	yes	—
388	C₂×C₈	C₂⁴	1	1	yes	characteristic
389	C₂×C₈	C₂⁴	1	1	yes	characteristic
390	C₂×C₈	C₂⁴	1	2	yes	—
391	C₂×C₈	C₂⁴	1	1	yes	characteristic
392	C₂×C₈	C₂⁴	1	1	yes	characteristic
393	C₄⋊C₄	—	2	2	no	—
394	C₄⋊C₄	—	2	2	no	—
395	C₄⋊C₄	—	2	1	no	—
396	C₄⋊C₄	—	2	1	no	—
397	C₄⋊C₄	—	2	1	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	2	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	2	no	—
409	C₄⋊C₄	—	2	2	no	—
410	C₄⋊C₄	—	2	2	no	—
411	C₄⋊C₄	—	2	2	no	—
412	C₄⋊C₄	—	2	2	no	—
413	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
414	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
415	C₄⋊C₄	C₂×D₄	1	2	yes	—
416	C₄⋊C₄	C₂×D₄	1	2	yes	—
417	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
418	C₄⋊C₄	C₂⁴	1	2	yes	—
419	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
420	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
421	C₄⋊C₄	C₂⁴	1	2	yes	—
422	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
423	C₂²⋊C₄	—	2	2	no	—
424	C₂²⋊C₄	—	2	2	no	—
425	C₂²⋊C₄	—	2	1	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	1	no	—
432	C₂²⋊C₄	—	2	1	no	—
433	C₂²⋊C₄	—	2	1	no	—
434	C₂²⋊C₄	—	2	1	no	—
435	C₂²⋊C₄	—	2	2	no	—
436	C₂²⋊C₄	—	2	2	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	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	2	no	—
448	C₄²	—	2	1	no	—
449	C₄²	—	2	1	no	—
450	C₄²	—	2	1	no	—
451	C₄²	—	2	1	no	—
452	C₄²	—	2	1	no	—
453	C₄²	—	2	2	no	—
454	C₄²	C₂×D₄	1	1	yes	characteristic
455	C₄²	C₂×D₄	1	1	yes	characteristic
456	C₄²	C₂×D₄	1	2	yes	—
457	C₄²	C₂×D₄	1	2	yes	—
458	C₄²	C₂⁴	1	1	yes	characteristic
459	C₄²	C₂⁴	1	2	yes	—
460	C₄²	C₂⁴	1	1	yes	characteristic
461	C₂³	—	2	1	no	—
462	C₂³	—	2	2	no	—
463	C₂³	—	2	1	no	—
464	C₂³	—	4	2	no	—
465	C₂³	—	8	1	no	—
466	C₂³	—	8	1	no	—
467	C₂³	C₂²×D₄	1	2	yes	—
468	C₂³	C₂²×D₄	1	1	yes	characteristic
469	Q₈	—	2	2	no	—
470	Q₈	—	2	2	no	—
471	Q₈	—	2	1	no	—
472	Q₈	—	2	2	no	—
473	Q₈	—	2	1	no	—
474	Q₈	—	2	1	no	—
475	Q₈	—	2	1	no	—
476	Q₈	—	4	2	no	—
477	Q₈	—	8	2	no	—
478	Q₈	—	8	2	no	—
479	D₄	—	2	4	no	—
480	D₄	—	2	2	no	—
481	D₄	—	2	1	no	—
482	D₄	—	2	2	no	—
483	D₄	—	2	1	no	—
484	D₄	—	2	1	no	—
485	D₄	—	2	2	no	—
486	D₄	—	2	1	no	—
487	D₄	—	4	2	no	—
488	D₄	—	4	2	no	—
489	D₄	—	4	2	no	—
490	D₄	—	8	2	no	—
491	D₄	—	8	2	no	—
492	D₄	—	8	2	no	—
493	D₄	—	8	2	no	—
494	D₄	—	8	2	no	—
495	D₄	—	8	2	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	2	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	2	no	—
507	C₂×C₄	—	4	1	no	—
508	C₂×C₄	—	4	1	no	—
509	C₂×C₄	—	4	2	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	2	no	—
515	C₂×C₄	—	4	2	no	—
516	C₂×C₄	—	4	2	no	—
517	C₂×C₄	—	8	1	no	—
518	C₂×C₄	—	8	1	no	—
519	C₂×C₄	—	8	2	no	—
520	C₂×C₄	—	8	1	no	—
521	C₂×C₄	—	8	1	no	—
522	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
523	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
524	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
525	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
526	C₂×C₄	C₂²×D₄	1	2	yes	—
527	C₂×C₄	C₂²×D₄	1	2	yes	—
528	C₂×C₄	C₂²×D₄	1	2	yes	—
529	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
530	C₂×C₄	C₂×#41	1	2	yes	—
531	C₂×C₄	C₂×#41	1	2	yes	—
532	C₂×C₄	C₂⁵	1	1	yes	characteristic
533	C₈	—	2	1	no	—
534	C₈	—	2	1	no	—
535	C₈	—	2	2	no	—
536	C₈	C₂×#41	1	2	yes	—
537	C₈	C₂×#41	1	4	yes	—
538	C₈	C₂×#41	1	2	yes	—
539	C₂²	—	2	1	no	—
540	C₂²	—	2	1	no	—
541	C₂²	—	2	2	no	—
542	C₂²	—	2	2	no	—
543	C₂²	—	2	2	no	—
544	C₂²	—	4	2	no	—
545	C₂²	—	4	1	no	—
546	C₂²	—	4	1	no	—
547	C₂²	—	4	1	no	—
548	C₂²	—	4	1	no	—
549	C₂²	—	4	2	no	—
550	C₂²	—	4	1	no	—
551	C₂²	—	4	1	no	—
552	C₂²	—	4	2	no	—
553	C₂²	—	8	4	no	—
554	C₂²	#532	1	2	yes	—
555	C₂²	C₂³×D₄	1	1	yes	characteristic
556	C₄	—	2	1	no	—
557	C₄	—	2	1	no	—
558	C₄	—	2	2	no	—
559	C₄	—	2	1	no	—
560	C₄	—	2	1	no	—
561	C₄	—	2	2	no	—
562	C₄	—	2	2	no	—
563	C₄	—	4	2	no	—
564	C₄	—	4	1	no	—
565	C₄	—	4	2	no	—
566	C₄	—	4	1	no	—
567	C₄	—	4	1	no	—
568	C₄	—	4	1	no	—
569	C₄	—	4	1	no	—
570	C₄	—	4	1	no	—
571	C₄	—	4	2	no	—
572	C₄	#532	1	2	yes	—
573	C₄	C₂²×#41	1	1	yes	characteristic
574	C₄	C₂²×#41	1	1	yes	characteristic
575	C₂	—	2	2	no	—
576	C₂	—	4	2	no	—
577	C₂	—	8	1	no	—
578	C₂	—	8	1	no	—
579	C₂	—	8	2	no	—
580	C₂	C₂×#532	1	1	yes	characteristic
581	C₂	#3585	1	1	yes	characteristic
582	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. #3461	C₂	semidirect
2. #3460	C₂	semidirect
3. #3183	C₂	semidirect
4. #3182	C₂	semidirect
5. #3181	C₂	semidirect
6. #3180	C₂	semidirect
7. #3179	C₂	semidirect
8. #3178	C₂	semidirect
9. #3175	C₂	semidirect
10. #3174	C₂	semidirect
11. #3164	C₂	semidirect
12. #3154	C₂	semidirect
13. #3137	C₂	semidirect
14. #3136	C₂	semidirect
15. #3063	C₂	semidirect
16. #3062	C₂	semidirect
17. #3061	C₂	semidirect
18. #3057	C₂	semidirect
19. C₄×#137	C₂	semidirect
20. C₄×AGL(1,ℤ/8)	C₂	semidirect
21. #2943	C₂	semidirect
22. C₂×#440	C₂	semidirect
23. #2875	C₂	semidirect
35. #542	C₂²	semidirect
37. #541	C₂²	semidirect
49. #533	C₂²	semidirect
56. #529	C₂²	semidirect
63. #501	C₂²	semidirect
64. #501	C₂²	semidirect
65. #500	C₂²	semidirect
66. #499	C₂²	semidirect
71. #491	C₂²	semidirect
74. #489	C₂²	semidirect
76. #488	C₂²	semidirect
77. #487	C₂²	semidirect
79. #470	C₂²	semidirect
84. #468	C₂²	semidirect
85. #468	C₂²	semidirect
86. #468	C₂²	semidirect
87. #467	C₂²	semidirect
88. #467	C₂²	semidirect
90. #466	C₂²	semidirect
94. #465	C₂²	semidirect
96. #442	C₂²	semidirect
97. #442	C₂²	semidirect
98. #441	C₂²	semidirect
99. #441	C₂²	semidirect
100. #441	C₂²	semidirect
106. #440	C₂²	semidirect
107. #440	C₂²	semidirect
108. #440	C₂²	semidirect
109. #440	C₂²	semidirect
110. #440	C₂²	semidirect
111. C₄×Q₁₆	C₂²	semidirect
113. C₄×SD₁₆	C₂²	semidirect
129. #405	C₂²	semidirect
130. #405	C₂²	semidirect
132. C₄×M₁₆	C₂²	semidirect
134. C₂×#97	C₂²	semidirect
382. M₁₆	#41	semidirect
386. C₂×C₈	#41	semidirect

Maximal subgroups

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

subgroup	index
#3461	2
#3460	2
#3183	2
#3182	2
#3181	2
#3180	2
#3179	2
#3178	2
#3175	2
#3174	2
#3164	2
#3154	2
#3137	2
#3136	2
#3063	2
#3062	2
#3061	2
#3057	2
C₄×#137	2
C₄×AGL(1,ℤ/8)	2
#2943	2
C₂×#440	2
#2875	2