Subgroups — #60927

Order 256.

886 conjugacy classes of subgroups.

The subgroup lattice has 570 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	#3461	C₂	1	1	yes	maximal, characteristic, complemented
3	#3263	C₂	1	2	yes	maximal, complemented
4	#3262	C₂	1	2	yes	maximal, complemented
5	#3258	C₂	1	2	yes	maximal, complemented
6	#3258	C₂	1	2	yes	maximal, complemented
7	#3256	C₂	1	2	yes	maximal, complemented
8	#3252	C₂	1	2	yes	maximal, complemented
9	#3250	C₂	1	2	yes	maximal, complemented
10	#3248	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	#3078	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
17	#3059	C₂	1	1	yes	maximal, characteristic, complemented
18	#3057	C₂	1	1	yes	maximal, characteristic, complemented
19	#3044	C₂	1	1	yes	maximal, characteristic, complemented
20	#3042	C₂	1	1	yes	maximal, characteristic, complemented
21	#3040	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×#464	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×Q₁₆	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	#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	—
39	#542	C₂²	1	2	yes	—
40	#542	C₂²	1	2	yes	complemented
41	#541	—	2	1	no	—
42	#541	C₂²	1	2	yes	complemented
43	#539	—	2	2	no	—
44	#537	C₂²	1	1	yes	characteristic
45	#536	C₂²	1	1	yes	characteristic
46	#536	C₂²	1	1	yes	characteristic
47	#536	C₂²	1	1	yes	characteristic
48	#535	C₂²	1	1	yes	characteristic
49	#533	—	2	1	no	—
50	#533	C₂²	1	1	yes	characteristic
51	#533	C₂²	1	2	yes	complemented
52	#529	—	2	2	no	—
53	#529	—	2	1	no	—
54	#529	C₂²	1	2	yes	—
55	#529	C₂²	1	2	yes	—
56	#529	C₂²	1	2	yes	complemented
57	C₂×#124	C₂²	1	1	yes	characteristic
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×Q₈	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	#479	C₂²	1	2	yes	complemented
68	#479	C₂²	1	2	yes	complemented
69	#478	C₂²	1	2	yes	—
70	#478	C₂²	1	2	yes	—
71	#478	C₂²	1	1	yes	characteristic, complemented
72	#478	C₂²	1	1	yes	characteristic, complemented
73	#477	C₂²	1	1	yes	characteristic, complemented
74	#477	C₂²	1	2	yes	complemented
75	#477	C₂²	1	2	yes	complemented
76	#476	C₂²	1	2	yes	—
77	#476	C₂²	1	1	yes	characteristic, complemented
78	#475	C₂²	1	1	yes	characteristic, complemented
79	#475	C₂²	1	2	yes	complemented
80	#475	C₂²	1	2	yes	complemented
81	#474	C₂²	1	2	yes	—
82	#474	C₂²	1	1	yes	characteristic, complemented
83	#470	C₂²	1	2	yes	complemented
84	#470	C₂²	1	2	yes	complemented
85	#470	C₂²	1	2	yes	complemented
86	#469	C₂²	1	2	yes	—
87	#468	C₂²	1	2	yes	—
88	#468	C₂²	1	2	yes	—
89	#468	C₂²	1	2	yes	—
90	#468	C₂²	1	2	yes	complemented
91	#467	C₂²	1	2	yes	complemented
92	#467	C₂²	1	2	yes	complemented
93	#467	C₂²	1	2	yes	complemented
94	#466	C₂²	1	2	yes	—
95	#465	C₂²	1	2	yes	—
96	#465	C₂²	1	2	yes	—
97	#465	C₂²	1	2	yes	—
98	#465	C₂²	1	2	yes	complemented
99	#464	C₂²	1	2	yes	—
100	#464	C₂²	1	2	yes	—
101	#464	C₂²	1	2	yes	—
102	#464	C₂²	1	2	yes	—
103	#464	C₂²	1	2	yes	—
104	#464	C₂²	1	2	yes	—
105	#464	C₂²	1	2	yes	complemented
106	#464	C₂²	1	2	yes	complemented
107	#463	C₂²	1	2	yes	—
108	#463	C₂²	1	2	yes	—
109	#463	C₂²	1	2	yes	—
110	#463	C₂²	1	2	yes	—
111	#462	C₂²	1	2	yes	complemented
112	#462	C₂²	1	2	yes	complemented
113	#461	C₂²	1	2	yes	—
114	#461	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	#419	C₂²	1	1	yes	characteristic
129	#419	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	C₂³	1	1	yes	characteristic
136	C₂×#41	C₂³	1	1	yes	characteristic
137	C₂²×Q₈	C₂³	1	1	yes	characteristic
138	C₂²×Q₈	C₂³	1	1	yes	characteristic
139	C₂²×D₄	C₂³	1	1	yes	characteristic
140	#137	—	4	2	no	—
141	AGL(1,ℤ/8)	—	4	2	no	—
142	C₂×Q₁₆	—	4	2	no	—
143	C₂×Q₁₆	C₂³	1	2	yes	—
144	C₂×Q₁₆	C₂³	1	2	yes	—
145	C₂×Q₁₆	C₂³	1	2	yes	—
146	C₂×SD₁₆	—	4	2	no	—
147	C₂×SD₁₆	C₂³	1	2	yes	—
148	C₂×SD₁₆	C₂³	1	2	yes	—
149	C₂×SD₁₆	C₂³	1	2	yes	—
150	C₂×SD₁₆	C₂³	1	2	yes	—
151	C₂×D₈	C₂³	1	2	yes	—
152	#131	—	4	2	no	—
153	#131	—	4	2	no	—
154	C₂×M₁₆	C₂³	1	1	yes	characteristic
155	C₂×M₁₆	C₂³	1	1	yes	characteristic
156	C₂×M₁₆	C₂³	1	2	yes	—
157	C₂×M₁₆	C₂³	1	2	yes	—
158	C₂²×C₈	C₂³	1	1	yes	characteristic
159	C₂²×C₈	C₂³	1	1	yes	characteristic
160	C₂²×C₈	C₂³	1	2	yes	—
161	C₂²×C₈	C₂³	1	2	yes	—
162	C₄⋊Q₈	—	2	1	no	—
163	C₄⋊Q₈	—	2	1	no	—
164	C₄⋊Q₈	—	2	1	no	—
165	C₄⋊Q₈	C₂³	1	2	yes	—
166	C₄⋊Q₈	C₂³	1	1	yes	characteristic
167	C₄⋊Q₈	C₂³	1	1	yes	characteristic
168	C₄⋊Q₈	C₂³	1	2	yes	—
169	#127	—	2	1	no	—
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	2	no	—
176	#126	—	2	2	no	—
177	#126	—	2	2	no	—
178	#125	—	2	2	no	—
179	#125	—	2	1	no	—
180	#125	—	2	2	no	—
181	#125	—	2	2	no	—
182	#125	C₂³	1	1	yes	characteristic
183	#125	C₂³	1	1	yes	characteristic
184	#125	C₂³	1	2	yes	—
185	#124	—	2	1	no	—
186	#124	—	2	1	no	—
187	#124	—	2	1	no	—
188	#124	—	2	2	no	—
189	#124	—	2	2	no	—
190	#124	—	2	2	no	—
191	#124	—	2	1	no	—
192	#124	—	2	1	no	—
193	#124	C₂³	1	2	yes	—
194	#124	C₂³	1	2	yes	—
195	#124	C₂³	1	2	yes	—
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	#123	—	2	2	no	—
204	#123	—	2	2	no	—
205	C₂²⋊Q₈	—	2	1	no	—
206	C₂²⋊Q₈	—	2	1	no	—
207	C₂²⋊Q₈	—	2	1	no	—
208	C₂²⋊Q₈	—	2	2	no	—
209	C₂²⋊Q₈	—	2	1	no	—
210	C₂²⋊Q₈	—	2	1	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	C₂³	1	2	yes	—
216	C₂²⋊Q₈	C₂³	1	2	yes	—
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	1	no	—
222	#121	C₂³	1	2	yes	—
223	#121	C₂³	1	2	yes	—
224	#121	C₂³	1	2	yes	—
225	#120	—	2	2	no	—
226	C₄×Q₈	—	2	1	no	—
227	C₄×Q₈	—	2	1	no	—
228	C₄×Q₈	—	2	1	no	—
229	C₄×Q₈	—	2	1	no	—
230	C₄×Q₈	—	2	2	no	—
231	C₄×Q₈	—	2	1	no	—
232	C₄×Q₈	—	2	1	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	2	yes	—
240	C₄×Q₈	C₂³	1	2	yes	—
241	C₄×D₄	—	2	1	no	—
242	C₄×D₄	—	2	1	no	—
243	C₄×D₄	—	2	2	no	—
244	C₄×D₄	—	2	2	no	—
245	C₄×D₄	—	2	2	no	—
246	C₄×D₄	—	2	1	no	—
247	C₄×D₄	—	2	1	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	1	yes	characteristic
253	C₄×D₄	C₂³	1	1	yes	characteristic
254	C₄×D₄	C₂³	1	2	yes	—
255	C₄×D₄	C₂³	1	2	yes	—
256	#117	—	2	2	no	—
257	#117	—	2	2	no	—
258	#117	—	2	1	no	—
259	#117	—	2	2	no	—
260	#117	—	2	2	no	—
261	#117	—	2	2	no	—
262	#117	C₂³	1	1	yes	characteristic
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	2	yes	—
267	C₂×C₄⋊C₄	—	2	1	no	—
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	2	no	—
272	C₂×C₄²	—	2	1	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	#103	C₂³	1	2	yes	—
307	#103	C₂³	1	2	yes	—
308	#103	C₂³	1	2	yes	—
309	#103	C₂³	1	2	yes	—
310	#102	C₂³	1	2	yes	—
311	#102	C₂³	1	2	yes	—
312	#102	C₂³	1	1	yes	characteristic
313	#102	C₂³	1	1	yes	characteristic
314	#102	C₂³	1	1	yes	characteristic
315	#102	C₂³	1	1	yes	characteristic
316	#102	C₂³	1	2	yes	—
317	#102	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	C₂×Q₈	—	2	1	no	—
324	C₂×Q₈	—	2	1	no	—
325	C₂×Q₈	—	2	1	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	—	2	2	no	—
332	C₂×Q₈	C₂×D₄	1	1	yes	characteristic
333	C₂×Q₈	C₂⁴	1	2	yes	—
334	C₂×Q₈	C₂⁴	1	2	yes	—
335	C₂×Q₈	C₂⁴	1	1	yes	characteristic
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	1	no	—
341	C₂×D₄	—	2	2	no	—
342	C₂×D₄	—	2	2	no	—
343	C₂×D₄	C₂×D₄	1	2	yes	—
344	C₂×D₄	C₂×D₄	1	1	yes	characteristic
345	C₂×D₄	C₂⁴	1	1	yes	characteristic
346	C₂×D₄	C₂⁴	1	2	yes	—
347	C₂²×C₄	—	2	1	no	—
348	C₂²×C₄	—	2	1	no	—
349	C₂²×C₄	—	2	1	no	—
350	C₂²×C₄	—	2	1	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	C₂×D₄	1	1	yes	characteristic
356	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
357	C₂²×C₄	C₂×D₄	1	2	yes	—
358	C₂²×C₄	C₂×D₄	1	2	yes	—
359	C₂²×C₄	C₂⁴	1	2	yes	—
360	C₂²×C₄	C₂⁴	1	1	yes	characteristic
361	Q₁₆	—	4	2	no	—
362	Q₁₆	—	4	2	no	—
363	Q₁₆	—	4	2	no	—
364	SD₁₆	—	4	2	no	—
365	SD₁₆	—	4	2	no	—
366	SD₁₆	—	4	2	no	—
367	SD₁₆	—	4	2	no	—
368	D₈	—	4	2	no	—
369	M₁₆	—	2	2	no	—
370	M₁₆	—	2	2	no	—
371	M₁₆	—	4	2	no	—
372	M₁₆	—	4	2	no	—
373	C₂×C₈	—	2	2	no	—
374	C₂×C₈	—	2	2	no	—
375	C₂×C₈	—	4	2	no	—
376	C₂×C₈	—	4	2	no	—
377	C₂×C₈	C₂⁴	1	1	yes	characteristic
378	C₂×C₈	C₂⁴	1	1	yes	characteristic
379	C₂×C₈	C₂⁴	1	2	yes	—
380	C₂×C₈	C₂⁴	1	1	yes	characteristic
381	C₂×C₈	C₂⁴	1	1	yes	characteristic
382	C₂×C₈	C₂⁴	1	2	yes	—
383	C₄⋊C₄	—	2	2	no	—
384	C₄⋊C₄	—	2	2	no	—
385	C₄⋊C₄	—	2	1	no	—
386	C₄⋊C₄	—	2	1	no	—
387	C₄⋊C₄	—	2	1	no	—
388	C₄⋊C₄	—	2	1	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	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	1	no	—
399	C₄⋊C₄	—	2	1	no	—
400	C₄⋊C₄	—	2	2	no	—
401	C₄⋊C₄	—	2	2	no	—
402	C₄⋊C₄	—	2	2	no	—
403	C₄⋊C₄	—	2	2	no	—
404	C₄⋊C₄	—	2	1	no	—
405	C₄⋊C₄	—	2	1	no	—
406	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
407	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
408	C₄⋊C₄	C₂×D₄	1	2	yes	—
409	C₄⋊C₄	C₂×D₄	1	2	yes	—
410	C₄⋊C₄	C₂⁴	1	2	yes	—
411	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
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	1	yes	characteristic
417	C₂²⋊C₄	—	2	1	no	—
418	C₂²⋊C₄	—	2	1	no	—
419	C₂²⋊C₄	—	2	2	no	—
420	C₂²⋊C₄	—	2	2	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	1	no	—
432	C₂²⋊C₄	—	2	1	no	—
433	C₂²⋊C₄	—	2	2	no	—
434	C₂²⋊C₄	—	2	2	no	—
435	C₂²⋊C₄	—	2	2	no	—
436	C₂²⋊C₄	—	2	2	no	—
437	C₂²⋊C₄	—	2	2	no	—
438	C₂²⋊C₄	C₂×D₄	1	2	yes	—
439	C₂²⋊C₄	C₂×D₄	1	2	yes	—
440	C₂²⋊C₄	C₂×D₄	1	2	yes	—
441	C₄²	—	2	2	no	—
442	C₄²	—	2	1	no	—
443	C₄²	—	2	1	no	—
444	C₄²	—	2	1	no	—
445	C₄²	—	2	2	no	—
446	C₄²	—	2	2	no	—
447	C₄²	—	2	2	no	—
448	C₄²	—	2	1	no	—
449	C₄²	—	2	1	no	—
450	C₄²	C₂×D₄	1	1	yes	characteristic
451	C₄²	C₂×D₄	1	2	yes	—
452	C₄²	C₂×D₄	1	1	yes	characteristic
453	C₄²	C₂×D₄	1	2	yes	—
454	C₄²	C₂⁴	1	1	yes	characteristic
455	C₄²	C₂⁴	1	2	yes	—
456	C₄²	C₂⁴	1	1	yes	characteristic
457	C₂³	—	2	1	no	—
458	C₂³	—	2	2	no	—
459	C₂³	—	4	2	no	—
460	C₂³	—	8	1	no	—
461	C₂³	—	8	1	no	—
462	C₂³	C₂²×D₄	1	2	yes	—
463	C₂³	C₂²×D₄	1	1	yes	characteristic
464	Q₈	—	2	2	no	—
465	Q₈	—	2	2	no	—
466	Q₈	—	2	1	no	—
467	Q₈	—	2	2	no	—
468	Q₈	—	2	2	no	—
469	Q₈	—	2	2	no	—
470	Q₈	—	2	1	no	—
471	Q₈	—	4	2	no	—
472	Q₈	—	4	2	no	—
473	Q₈	—	8	1	no	—
474	Q₈	—	8	2	no	—
475	Q₈	—	8	1	no	—
476	D₄	—	2	4	no	—
477	D₄	—	2	2	no	—
478	D₄	—	2	1	no	—
479	D₄	—	2	2	no	—
480	D₄	—	2	2	no	—
481	D₄	—	2	1	no	—
482	D₄	—	4	2	no	—
483	D₄	—	4	2	no	—
484	D₄	—	8	2	no	—
485	D₄	—	8	2	no	—
486	D₄	—	8	2	no	—
487	C₂×C₄	—	2	2	no	—
488	C₂×C₄	—	2	2	no	—
489	C₂×C₄	—	2	1	no	—
490	C₂×C₄	—	2	1	no	—
491	C₂×C₄	—	2	2	no	—
492	C₂×C₄	—	2	1	no	—
493	C₂×C₄	—	2	2	no	—
494	C₂×C₄	—	2	1	no	—
495	C₂×C₄	—	2	1	no	—
496	C₂×C₄	—	2	2	no	—
497	C₂×C₄	—	2	1	no	—
498	C₂×C₄	—	2	1	no	—
499	C₂×C₄	—	4	1	no	—
500	C₂×C₄	—	4	2	no	—
501	C₂×C₄	—	4	2	no	—
502	C₂×C₄	—	4	1	no	—
503	C₂×C₄	—	4	2	no	—
504	C₂×C₄	—	4	2	no	—
505	C₂×C₄	—	4	2	no	—
506	C₂×C₄	—	4	2	no	—
507	C₂×C₄	—	8	2	no	—
508	C₂×C₄	—	8	1	no	—
509	C₂×C₄	—	8	2	no	—
510	C₂×C₄	—	8	1	no	—
511	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
512	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
513	C₂×C₄	C₂²×D₄	1	2	yes	—
514	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
515	C₂×C₄	C₂²×D₄	1	2	yes	—
516	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
517	C₂×C₄	C₂²×D₄	1	2	yes	—
518	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
519	C₂×C₄	H(5,𝔽₂)	1	2	yes	—
520	C₂×C₄	2₋¹⁺⁴	1	2	yes	—
521	C₂×C₄	C₂⁵	1	1	yes	characteristic
522	C₈	—	2	1	no	—
523	C₈	—	2	1	no	—
524	C₈	—	2	1	no	—
525	C₈	—	2	1	no	—
526	C₈	—	2	2	no	—
527	C₈	—	2	2	no	—
528	C₂²	—	2	1	no	—
529	C₂²	—	2	1	no	—
530	C₂²	—	2	2	no	—
531	C₂²	—	2	2	no	—
532	C₂²	—	2	2	no	—
533	C₂²	—	4	1	no	—
534	C₂²	—	4	2	no	—
535	C₂²	—	4	1	no	—
536	C₂²	—	4	2	no	—
537	C₂²	—	4	1	no	—
538	C₂²	—	4	2	no	—
539	C₂²	—	16	2	no	—
540	C₂²	#537	1	2	yes	—
541	C₂²	C₂³×D₄	1	1	yes	characteristic
542	C₄	—	2	1	no	—
543	C₄	—	2	1	no	—
544	C₄	—	2	2	no	—
545	C₄	—	2	1	no	—
546	C₄	—	2	2	no	—
547	C₄	—	2	1	no	—
548	C₄	—	2	2	no	—
549	C₄	—	4	1	no	—
550	C₄	—	4	2	no	—
551	C₄	—	4	1	no	—
552	C₄	—	4	1	no	—
553	C₄	—	4	1	no	—
554	C₄	—	4	1	no	—
555	C₄	—	4	1	no	—
556	C₄	—	4	1	no	—
557	C₄	—	4	2	no	—
558	C₄	—	4	2	no	—
559	C₄	#537	1	2	yes	—
560	C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
561	C₄	C₂×2₋¹⁺⁴	1	1	yes	characteristic
562	C₂	—	2	2	no	—
563	C₂	—	4	2	no	—
564	C₂	—	8	1	no	—
565	C₂	—	8	2	no	—
566	C₂	C₂×#537	1	1	yes	characteristic
567	C₂	#3584	1	1	yes	characteristic
568	C₂	#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵
prime radical	#3062	C₂
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. #3461	C₂	semidirect
3. #3263	C₂	semidirect
4. #3262	C₂	semidirect
5. #3258	C₂	semidirect
6. #3258	C₂	semidirect
7. #3256	C₂	semidirect
8. #3252	C₂	semidirect
9. #3250	C₂	semidirect
10. #3248	C₂	semidirect
11. #3082	C₂	semidirect
12. #3081	C₂	semidirect
13. #3078	C₂	semidirect
14. #3076	C₂	semidirect
15. #3063	C₂	semidirect
17. #3059	C₂	semidirect
18. #3057	C₂	semidirect
19. #3044	C₂	semidirect
20. #3042	C₂	semidirect
21. #3040	C₂	semidirect
22. C₂×#464	C₂	semidirect
23. #2906	C₂	semidirect
40. #542	C₂²	semidirect
42. #541	C₂²	semidirect
51. #533	C₂²	semidirect
56. #529	C₂²	semidirect
63. #479	C₂²	semidirect
64. #479	C₂²	semidirect
65. #479	C₂²	semidirect
66. #479	C₂²	semidirect
67. #479	C₂²	semidirect
68. #479	C₂²	semidirect
71. #478	C₂²	semidirect
72. #478	C₂²	semidirect
73. #477	C₂²	semidirect
74. #477	C₂²	semidirect
75. #477	C₂²	semidirect
77. #476	C₂²	semidirect
78. #475	C₂²	semidirect
79. #475	C₂²	semidirect
80. #475	C₂²	semidirect
82. #474	C₂²	semidirect
83. #470	C₂²	semidirect
84. #470	C₂²	semidirect
85. #470	C₂²	semidirect
90. #468	C₂²	semidirect
91. #467	C₂²	semidirect
92. #467	C₂²	semidirect
93. #467	C₂²	semidirect
98. #465	C₂²	semidirect
105. #464	C₂²	semidirect
106. #464	C₂²	semidirect
111. #462	C₂²	semidirect
112. #462	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
#3461	2
#3263	2
#3262	2
#3258	2
#3256	2
#3252	2
#3250	2
#3248	2
#3082	2
#3081	2
#3078	2
#3076	2
#3063	2
#3062	2
#3059	2
#3057	2
#3044	2
#3042	2
#3040	2
C₂×#464	2
#2906	2