Subgroups — #60926

Order 256.

918 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	#3510	C₂	1	1	yes	maximal, characteristic, complemented
2	#3460	C₂	1	1	yes	maximal, characteristic, complemented
3	#3263	C₂	1	2	yes	maximal, complemented
4	#3262	C₂	1	2	yes	maximal, complemented
5	#3257	C₂	1	2	yes	maximal, complemented
6	#3257	C₂	1	2	yes	maximal, complemented
7	#3256	C₂	1	2	yes	maximal, complemented
8	#3251	C₂	1	2	yes	maximal, complemented
9	#3250	C₂	1	2	yes	maximal, complemented
10	#3247	C₂	1	2	yes	maximal, complemented
11	#3082	C₂	1	1	yes	maximal, characteristic, complemented
12	#3081	C₂	1	1	yes	maximal, characteristic, complemented
13	#3077	C₂	1	1	yes	maximal, characteristic, complemented
14	#3076	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	#3058	C₂	1	1	yes	maximal, characteristic, complemented
18	#3057	C₂	1	1	yes	maximal, characteristic, complemented
19	#3043	C₂	1	1	yes	maximal, characteristic, complemented
20	#3041	C₂	1	1	yes	maximal, characteristic, complemented
21	#3040	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×#463	C₂	1	1	yes	maximal, characteristic, complemented
23	#2906	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	C₂²×SD₁₆	C₂²	1	1	yes	characteristic
27	C₂²×D₈	C₂²	1	1	yes	characteristic
28	C₂×#131	C₂²	1	1	yes	characteristic
29	C₂×#131	C₂²	1	1	yes	characteristic
30	#559	—	2	1	no	—
31	#559	—	2	1	no	—
32	#556	—	2	1	no	—
33	#556	—	2	1	no	—
34	#551	—	2	2	no	—
35	#551	—	2	2	no	—
36	#544	C₂²	1	1	yes	characteristic
37	#542	—	2	1	no	—
38	#542	C₂²	1	2	yes	complemented
39	#542	C₂²	1	2	yes	complemented
40	#542	C₂²	1	2	yes	complemented
41	#540	—	2	1	no	—
42	#540	C₂²	1	2	yes	complemented
43	#538	—	2	2	no	—
44	#537	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	#535	C₂²	1	1	yes	characteristic
49	#533	C₂²	1	1	yes	characteristic
50	#532	—	2	1	no	—
51	#532	C₂²	1	2	yes	complemented
52	#529	—	2	1	no	—
53	#529	C₂²	1	2	yes	complemented
54	#529	C₂²	1	2	yes	complemented
55	#529	C₂²	1	2	yes	complemented
56	C₂×#124	C₂²	1	1	yes	characteristic
57	#525	—	2	2	no	—
58	#519	C₂²	1	1	yes	characteristic
59	#518	C₂²	1	1	yes	characteristic
60	C₄×#41	C₂²	1	1	yes	characteristic
61	C₄×#41	C₂²	1	1	yes	characteristic
62	C₂×C₄×D₄	C₂²	1	1	yes	characteristic
63	#479	C₂²	1	1	yes	characteristic, complemented
64	#479	C₂²	1	1	yes	characteristic, complemented
65	#479	C₂²	1	2	yes	complemented
66	#479	C₂²	1	2	yes	complemented
67	#478	C₂²	1	1	yes	characteristic, complemented
68	#478	C₂²	1	1	yes	characteristic, complemented
69	#478	C₂²	1	2	yes	complemented
70	#478	C₂²	1	2	yes	complemented
71	#478	C₂²	1	2	yes	complemented
72	#478	C₂²	1	2	yes	complemented
73	#477	C₂²	1	1	yes	characteristic, complemented
74	#477	C₂²	1	2	yes	complemented
75	#476	C₂²	1	1	yes	characteristic, complemented
76	#476	C₂²	1	2	yes	complemented
77	#476	C₂²	1	2	yes	complemented
78	#475	C₂²	1	1	yes	characteristic, complemented
79	#475	C₂²	1	2	yes	complemented
80	#474	C₂²	1	1	yes	characteristic, complemented
81	#474	C₂²	1	2	yes	complemented
82	#474	C₂²	1	2	yes	complemented
83	#470	C₂²	1	2	yes	complemented
84	#469	C₂²	1	2	yes	—
85	#469	C₂²	1	2	yes	—
86	#469	C₂²	1	2	yes	complemented
87	#468	C₂²	1	2	yes	complemented
88	#468	C₂²	1	2	yes	complemented
89	#468	C₂²	1	2	yes	complemented
90	#468	C₂²	1	2	yes	complemented
91	#467	C₂²	1	2	yes	complemented
92	#466	C₂²	1	2	yes	—
93	#466	C₂²	1	2	yes	—
94	#466	C₂²	1	2	yes	complemented
95	#465	C₂²	1	2	yes	complemented
96	#465	C₂²	1	2	yes	complemented
97	#465	C₂²	1	2	yes	complemented
98	#465	C₂²	1	2	yes	complemented
99	#464	C₂²	1	2	yes	complemented
100	#464	C₂²	1	2	yes	complemented
101	#464	C₂²	1	2	yes	complemented
102	#464	C₂²	1	2	yes	complemented
103	#463	C₂²	1	2	yes	—
104	#463	C₂²	1	2	yes	—
105	#463	C₂²	1	2	yes	—
106	#463	C₂²	1	2	yes	—
107	#463	C₂²	1	2	yes	—
108	#463	C₂²	1	2	yes	—
109	#463	C₂²	1	2	yes	complemented
110	#463	C₂²	1	2	yes	complemented
111	#460	C₂²	1	2	yes	complemented
112	#460	C₂²	1	2	yes	complemented
113	#459	C₂²	1	2	yes	—
114	#459	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	#427	C₂²	1	1	yes	characteristic
119	#424	C₂²	1	1	yes	characteristic
120	#424	C₂²	1	1	yes	characteristic
121	#424	C₂²	1	2	yes	complemented
122	#424	C₂²	1	2	yes	complemented
123	#423	C₂²	1	1	yes	characteristic
124	#423	C₂²	1	2	yes	complemented
125	C₂×C₄⋊C₈	C₂²	1	1	yes	characteristic
126	C₂×C₄⋊C₈	C₂²	1	2	yes	complemented
127	#419	C₂²	1	1	yes	characteristic
128	#418	C₂²	1	1	yes	characteristic
129	#418	C₂²	1	1	yes	characteristic
130	#418	C₂²	1	1	yes	characteristic
131	#416	C₂²	1	1	yes	characteristic
132	#416	C₂²	1	1	yes	characteristic
133	C₂×#103	C₂²	1	1	yes	characteristic
134	C₂×#102	C₂²	1	1	yes	characteristic
135	C₂×#41	—	2	2	no	—
136	C₂×#41	C₂³	1	1	yes	characteristic
137	C₂×#41	C₂³	1	1	yes	characteristic
138	C₂²×Q₈	C₂³	1	1	yes	characteristic
139	C₂²×D₄	C₂³	1	1	yes	characteristic
140	C₂²×D₄	C₂³	1	1	yes	characteristic
141	C₂³×C₄	—	2	1	no	—
142	#137	—	4	2	no	—
143	AGL(1,ℤ/8)	—	4	2	no	—
144	C₂×Q₁₆	C₂³	1	2	yes	—
145	C₂×SD₁₆	—	4	2	no	—
146	C₂×SD₁₆	C₂³	1	2	yes	—
147	C₂×SD₁₆	C₂³	1	2	yes	—
148	C₂×SD₁₆	C₂³	1	2	yes	—
149	C₂×SD₁₆	C₂³	1	2	yes	—
150	C₂×D₈	—	4	2	no	—
151	C₂×D₈	C₂³	1	2	yes	—
152	C₂×D₈	C₂³	1	2	yes	—
153	C₂×D₈	C₂³	1	2	yes	—
154	#131	—	4	2	no	—
155	#131	—	4	2	no	—
156	C₂×M₁₆	C₂³	1	1	yes	characteristic
157	C₂×M₁₆	C₂³	1	1	yes	characteristic
158	C₂×M₁₆	C₂³	1	2	yes	—
159	C₂×M₁₆	C₂³	1	2	yes	—
160	C₂²×C₈	C₂³	1	1	yes	characteristic
161	C₂²×C₈	C₂³	1	1	yes	characteristic
162	C₂²×C₈	C₂³	1	2	yes	—
163	C₂²×C₈	C₂³	1	2	yes	—
164	C₄⋊Q₈	—	2	1	no	—
165	C₄⋊Q₈	—	2	1	no	—
166	C₄⋊Q₈	C₂³	1	2	yes	—
167	C₄⋊Q₈	C₂³	1	1	yes	characteristic
168	C₄⋊Q₈	C₂³	1	1	yes	characteristic
169	#127	—	2	1	no	—
170	#127	—	2	1	no	—
171	#127	C₂³	1	2	yes	—
172	#126	—	2	2	no	—
173	#126	—	2	2	no	—
174	#126	—	2	2	no	—
175	#126	—	2	2	no	—
176	#126	—	2	2	no	—
177	#126	—	2	2	no	—
178	#125	—	2	1	no	—
179	#125	C₂³	1	1	yes	characteristic
180	#125	C₂³	1	1	yes	characteristic
181	#125	C₂³	1	2	yes	—
182	#124	—	2	1	no	—
183	#124	—	2	1	no	—
184	#124	—	2	1	no	—
185	#124	—	2	2	no	—
186	#124	—	2	2	no	—
187	#124	—	2	2	no	—
188	#124	—	2	1	no	—
189	#124	—	2	1	no	—
190	#124	—	2	2	no	—
191	#124	C₂³	1	2	yes	—
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	#123	—	2	2	no	—
203	C₂²⋊Q₈	—	2	1	no	—
204	C₂²⋊Q₈	—	2	1	no	—
205	C₂²⋊Q₈	—	2	1	no	—
206	C₂²⋊Q₈	—	2	2	no	—
207	C₂²⋊Q₈	—	2	2	no	—
208	C₂²⋊Q₈	—	2	2	no	—
209	C₂²⋊Q₈	—	2	2	no	—
210	C₂²⋊Q₈	C₂³	1	2	yes	—
211	C₂²⋊Q₈	C₂³	1	2	yes	—
212	C₂²⋊Q₈	C₂³	1	2	yes	—
213	#121	—	2	2	no	—
214	#121	—	2	1	no	—
215	#121	—	2	2	no	—
216	#121	—	2	1	no	—
217	#121	—	2	1	no	—
218	#121	—	2	2	no	—
219	#121	—	2	2	no	—
220	#121	C₂³	1	2	yes	—
221	#121	C₂³	1	2	yes	—
222	#121	C₂³	1	2	yes	—
223	#121	C₂³	1	2	yes	—
224	#121	C₂³	1	2	yes	—
225	#120	—	2	2	no	—
226	#120	—	2	2	no	—
227	#120	—	2	2	no	—
228	C₄×Q₈	—	2	1	no	—
229	C₄×Q₈	—	2	1	no	—
230	C₄×Q₈	—	2	1	no	—
231	C₄×Q₈	—	2	1	no	—
232	C₄×Q₈	D₄	1	1	yes	characteristic
233	C₄×Q₈	D₄	1	1	yes	characteristic
234	C₄×Q₈	C₂³	1	1	yes	characteristic
235	C₄×Q₈	C₂³	1	1	yes	characteristic
236	C₄×Q₈	C₂³	1	2	yes	—
237	C₄×Q₈	C₂³	1	2	yes	—
238	C₄×D₄	—	2	1	no	—
239	C₄×D₄	—	2	1	no	—
240	C₄×D₄	—	2	2	no	—
241	C₄×D₄	—	2	2	no	—
242	C₄×D₄	—	2	2	no	—
243	C₄×D₄	—	2	1	no	—
244	C₄×D₄	—	2	1	no	—
245	C₄×D₄	—	2	1	no	—
246	C₄×D₄	—	2	1	no	—
247	C₄×D₄	—	2	2	no	—
248	C₄×D₄	D₄	1	2	yes	—
249	C₄×D₄	D₄	1	1	yes	characteristic
250	C₄×D₄	D₄	1	2	yes	—
251	C₄×D₄	D₄	1	1	yes	characteristic
252	C₄×D₄	C₂³	1	2	yes	—
253	C₄×D₄	C₂³	1	2	yes	—
254	C₄×D₄	C₂³	1	1	yes	characteristic
255	C₄×D₄	C₂³	1	1	yes	characteristic
256	C₄×D₄	C₂³	1	2	yes	—
257	C₄×D₄	C₂³	1	2	yes	—
258	#117	—	2	2	no	—
259	#117	—	2	1	no	—
260	#117	—	2	2	no	—
261	#117	—	2	2	no	—
262	#117	—	2	2	no	—
263	#117	C₂³	1	1	yes	characteristic
264	#117	C₂³	1	1	yes	characteristic
265	#117	C₂³	1	1	yes	characteristic
266	#117	C₂³	1	1	yes	characteristic
267	#117	C₂³	1	2	yes	—
268	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
269	C₂×C₂²⋊C₄	—	2	1	no	—
270	C₂×C₂²⋊C₄	—	2	1	no	—
271	C₂×C₂²⋊C₄	—	2	1	no	—
272	C₂×C₂²⋊C₄	—	2	2	no	—
273	C₂×C₄²	—	2	1	no	—
274	C₂×C₄²	C₂³	1	1	yes	characteristic
275	C₂×C₄²	C₂³	1	2	yes	—
276	#107	C₂³	1	1	yes	characteristic
277	#107	C₂³	1	1	yes	characteristic
278	#107	C₂³	1	1	yes	characteristic
279	#107	C₂³	1	1	yes	characteristic
280	#107	C₂³	1	2	yes	—
281	#107	C₂³	1	2	yes	—
282	#106	C₂³	1	1	yes	characteristic
283	#106	C₂³	1	1	yes	characteristic
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	C₄⋊C₈	C₂³	1	1	yes	characteristic
289	C₄⋊C₈	C₂³	1	1	yes	characteristic
290	C₄⋊C₈	C₂³	1	1	yes	characteristic
291	C₄⋊C₈	C₂³	1	1	yes	characteristic
292	C₄⋊C₈	C₂³	1	2	yes	—
293	C₄⋊C₈	C₂³	1	2	yes	—
294	C₄⋊C₈	C₂³	1	2	yes	—
295	C₄⋊C₈	C₂³	1	2	yes	—
296	C₄⋊C₈	C₂³	1	2	yes	—
297	C₄⋊C₈	C₂³	1	2	yes	—
298	#103	C₂³	1	2	yes	—
299	#103	C₂³	1	2	yes	—
300	#103	C₂³	1	1	yes	characteristic
301	#103	C₂³	1	1	yes	characteristic
302	#103	C₂³	1	1	yes	characteristic
303	#103	C₂³	1	1	yes	characteristic
304	#103	C₂³	1	2	yes	—
305	#103	C₂³	1	2	yes	—
306	#102	C₂³	1	2	yes	—
307	#102	C₂³	1	2	yes	—
308	#102	C₂³	1	1	yes	characteristic
309	#102	C₂³	1	1	yes	characteristic
310	#102	C₂³	1	1	yes	characteristic
311	#102	C₂³	1	1	yes	characteristic
312	#102	C₂³	1	2	yes	—
313	#102	C₂³	1	2	yes	—
314	#102	C₂³	1	2	yes	—
315	#102	C₂³	1	2	yes	—
316	#102	C₂³	1	2	yes	—
317	#102	C₂³	1	2	yes	—
318	C₂⁴	—	2	1	no	—
319	C₂⁴	—	2	1	no	—
320	#41	—	2	2	no	—
321	#41	—	2	2	no	—
322	#41	—	2	2	no	—
323	#41	—	2	2	no	—
324	#41	—	8	4	no	—
325	C₂×Q₈	—	2	1	no	—
326	C₂×Q₈	—	2	1	no	—
327	C₂×Q₈	—	2	1	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	2	yes	—
333	C₂×Q₈	C₂⁴	1	1	yes	characteristic
334	C₂×D₄	—	2	1	no	—
335	C₂×D₄	—	2	2	no	—
336	C₂×D₄	—	2	2	no	—
337	C₂×D₄	—	2	2	no	—
338	C₂×D₄	—	2	2	no	—
339	C₂×D₄	—	2	2	no	—
340	C₂×D₄	—	2	1	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	—	2	2	no	—
347	C₂×D₄	—	2	2	no	—
348	C₂×D₄	C₂×D₄	1	2	yes	—
349	C₂×D₄	C₂×D₄	1	1	yes	characteristic
350	C₂×D₄	C₂⁴	1	2	yes	—
351	C₂×D₄	C₂⁴	1	2	yes	—
352	C₂×D₄	C₂⁴	1	1	yes	characteristic
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	1	no	—
359	C₂²×C₄	—	2	2	no	—
360	C₂²×C₄	—	2	2	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	—	4	2	no	—
370	SD₁₆	—	4	2	no	—
371	SD₁₆	—	4	2	no	—
372	SD₁₆	—	4	2	no	—
373	SD₁₆	—	4	2	no	—
374	D₈	—	4	2	no	—
375	D₈	—	4	2	no	—
376	D₈	—	4	2	no	—
377	M₁₆	—	2	2	no	—
378	M₁₆	—	2	2	no	—
379	M₁₆	—	4	2	no	—
380	M₁₆	—	4	2	no	—
381	C₂×C₈	—	2	2	no	—
382	C₂×C₈	—	2	2	no	—
383	C₂×C₈	—	4	2	no	—
384	C₂×C₈	—	4	2	no	—
385	C₂×C₈	C₂⁴	1	2	yes	—
386	C₂×C₈	C₂⁴	1	1	yes	characteristic
387	C₂×C₈	C₂⁴	1	1	yes	characteristic
388	C₂×C₈	C₂⁴	1	2	yes	—
389	C₂×C₈	C₂⁴	1	1	yes	characteristic
390	C₂×C₈	C₂⁴	1	1	yes	characteristic
391	C₄⋊C₄	—	2	1	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	2	no	—
399	C₄⋊C₄	—	2	2	no	—
400	C₄⋊C₄	—	2	2	no	—
401	C₄⋊C₄	—	2	2	no	—
402	C₄⋊C₄	—	2	1	no	—
403	C₄⋊C₄	—	2	1	no	—
404	C₄⋊C₄	—	2	2	no	—
405	C₄⋊C₄	—	2	2	no	—
406	C₄⋊C₄	—	2	1	no	—
407	C₄⋊C₄	—	2	1	no	—
408	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
409	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
410	C₄⋊C₄	C₂×D₄	1	2	yes	—
411	C₄⋊C₄	C₂×D₄	1	2	yes	—
412	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
413	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
414	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
415	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
416	C₄⋊C₄	C₂⁴	1	2	yes	—
417	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
418	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
419	C₂²⋊C₄	—	2	1	no	—
420	C₂²⋊C₄	—	2	1	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	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	2	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	C₂×D₄	1	2	yes	—
443	C₂²⋊C₄	C₂×D₄	1	2	yes	—
444	C₂²⋊C₄	C₂×D₄	1	2	yes	—
445	C₄²	—	2	1	no	—
446	C₄²	—	2	1	no	—
447	C₄²	—	2	1	no	—
448	C₄²	—	2	2	no	—
449	C₄²	—	2	2	no	—
450	C₄²	—	2	1	no	—
451	C₄²	—	2	1	no	—
452	C₄²	C₂×D₄	1	1	yes	characteristic
453	C₄²	C₂×D₄	1	2	yes	—
454	C₄²	C₂×D₄	1	1	yes	characteristic
455	C₄²	C₂×D₄	1	2	yes	—
456	C₄²	C₂⁴	1	1	yes	characteristic
457	C₄²	C₂⁴	1	1	yes	characteristic
458	C₄²	C₂⁴	1	2	yes	—
459	C₂³	—	2	2	no	—
460	C₂³	—	2	2	no	—
461	C₂³	—	2	1	no	—
462	C₂³	—	4	2	no	—
463	C₂³	—	4	2	no	—
464	C₂³	—	8	1	no	—
465	C₂³	—	8	1	no	—
466	C₂³	—	8	1	no	—
467	C₂³	—	8	1	no	—
468	C₂³	C₂²×D₄	1	2	yes	—
469	C₂³	C₂²×D₄	1	1	yes	characteristic
470	Q₈	—	2	2	no	—
471	Q₈	—	2	2	no	—
472	Q₈	—	2	1	no	—
473	Q₈	—	2	2	no	—
474	Q₈	—	2	1	no	—
475	Q₈	—	4	2	no	—
476	Q₈	—	8	1	no	—
477	Q₈	—	8	1	no	—
478	Q₈	—	8	2	no	—
479	D₄	—	2	4	no	—
480	D₄	—	2	2	no	—
481	D₄	—	2	2	no	—
482	D₄	—	2	2	no	—
483	D₄	—	2	1	no	—
484	D₄	—	2	2	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	D₄	—	8	2	no	—
497	C₂×C₄	—	2	2	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	2	no	—
503	C₂×C₄	—	2	1	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	1	no	—
509	C₂×C₄	—	4	2	no	—
510	C₂×C₄	—	4	1	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	—	8	2	no	—
517	C₂×C₄	—	8	1	no	—
518	C₂×C₄	—	8	2	no	—
519	C₂×C₄	—	8	2	no	—
520	C₂×C₄	—	8	1	no	—
521	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
522	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
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	2	yes	—
527	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
528	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
529	C₂×C₄	H(5,𝔽₂)	1	2	yes	—
530	C₂×C₄	2₋¹⁺⁴	1	2	yes	—
531	C₂×C₄	C₂⁵	1	1	yes	characteristic
532	C₈	—	2	1	no	—
533	C₈	—	2	1	no	—
534	C₈	—	2	1	no	—
535	C₈	—	2	1	no	—
536	C₈	—	2	2	no	—
537	C₈	—	2	2	no	—
538	C₂²	—	2	1	no	—
539	C₂²	—	2	1	no	—
540	C₂²	—	2	2	no	—
541	C₂²	—	2	2	no	—
542	C₂²	—	2	2	no	—
543	C₂²	—	4	1	no	—
544	C₂²	—	4	2	no	—
545	C₂²	—	4	2	no	—
546	C₂²	—	4	2	no	—
547	C₂²	—	4	1	no	—
548	C₂²	—	4	2	no	—
549	C₂²	—	4	1	no	—
550	C₂²	—	4	2	no	—
551	C₂²	—	4	2	no	—
552	C₂²	—	8	4	no	—
553	C₂²	—	16	2	no	—
554	C₂²	#537	1	2	yes	—
555	C₂²	C₂³×D₄	1	1	yes	characteristic
556	C₄	—	2	1	no	—
557	C₄	—	2	2	no	—
558	C₄	—	2	1	no	—
559	C₄	—	2	1	no	—
560	C₄	—	2	1	no	—
561	C₄	—	2	2	no	—
562	C₄	—	2	2	no	—
563	C₄	—	4	1	no	—
564	C₄	—	4	1	no	—
565	C₄	—	4	1	no	—
566	C₄	—	4	2	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	#537	1	2	yes	—
573	C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
574	C₄	C₂×2₋¹⁺⁴	1	1	yes	characteristic
575	C₂	—	2	2	no	—
576	C₂	—	4	2	no	—
577	C₂	—	8	1	no	—
578	C₂	—	8	2	no	—
579	C₂	—	8	2	no	—
580	C₂	C₂×#537	1	1	yes	characteristic
581	C₂	#3584	1	1	yes	characteristic
582	C₂	#3585	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. #3510	C₂	semidirect
2. #3460	C₂	semidirect
3. #3263	C₂	semidirect
4. #3262	C₂	semidirect
5. #3257	C₂	semidirect
6. #3257	C₂	semidirect
7. #3256	C₂	semidirect
8. #3251	C₂	semidirect
9. #3250	C₂	semidirect
10. #3247	C₂	semidirect
11. #3082	C₂	semidirect
12. #3081	C₂	semidirect
13. #3077	C₂	semidirect
14. #3076	C₂	semidirect
15. #3063	C₂	semidirect
16. #3062	C₂	semidirect
17. #3058	C₂	semidirect
18. #3057	C₂	semidirect
19. #3043	C₂	semidirect
20. #3041	C₂	semidirect
21. #3040	C₂	semidirect
22. C₂×#463	C₂	semidirect
23. #2906	C₂	semidirect
38. #542	C₂²	semidirect
39. #542	C₂²	semidirect
40. #542	C₂²	semidirect
42. #540	C₂²	semidirect
51. #532	C₂²	semidirect
53. #529	C₂²	semidirect
54. #529	C₂²	semidirect
55. #529	C₂²	semidirect
63. #479	C₂²	semidirect
64. #479	C₂²	semidirect
65. #479	C₂²	semidirect
66. #479	C₂²	semidirect
67. #478	C₂²	semidirect
68. #478	C₂²	semidirect
69. #478	C₂²	semidirect
70. #478	C₂²	semidirect
71. #478	C₂²	semidirect
72. #478	C₂²	semidirect
73. #477	C₂²	semidirect
74. #477	C₂²	semidirect
75. #476	C₂²	semidirect
76. #476	C₂²	semidirect
77. #476	C₂²	semidirect
78. #475	C₂²	semidirect
79. #475	C₂²	semidirect
80. #474	C₂²	semidirect
81. #474	C₂²	semidirect
82. #474	C₂²	semidirect
83. #470	C₂²	semidirect
86. #469	C₂²	semidirect
87. #468	C₂²	semidirect
88. #468	C₂²	semidirect
89. #468	C₂²	semidirect
90. #468	C₂²	semidirect
91. #467	C₂²	semidirect
94. #466	C₂²	semidirect
95. #465	C₂²	semidirect
96. #465	C₂²	semidirect
97. #465	C₂²	semidirect
98. #465	C₂²	semidirect
99. #464	C₂²	semidirect
100. #464	C₂²	semidirect
101. #464	C₂²	semidirect
102. #464	C₂²	semidirect
109. #463	C₂²	semidirect
110. #463	C₂²	semidirect
111. #460	C₂²	semidirect
112. #460	C₂²	semidirect
121. #424	C₂²	semidirect
122. #424	C₂²	semidirect
124. #423	C₂²	semidirect
126. 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
#3510	2
#3460	2
#3263	2
#3262	2
#3257	2
#3256	2
#3251	2
#3250	2
#3247	2
#3082	2
#3081	2
#3077	2
#3076	2
#3063	2
#3062	2
#3058	2
#3057	2
#3043	2
#3041	2
#3040	2
C₂×#463	2
#2906	2