Subgroups — #61208

Order 256.

1055 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3506	C₂	1	1	yes	maximal, characteristic, complemented
2	#3500	C₂	1	1	yes	maximal, characteristic, complemented
3	#3326	C₂	1	2	yes	maximal, complemented
4	#3322	C₂	1	2	yes	maximal, complemented
5	#3321	C₂	1	2	yes	maximal, complemented
6	#3319	C₂	1	2	yes	maximal, complemented
7	#3308	C₂	1	2	yes	maximal, complemented
8	#3306	C₂	1	2	yes	maximal, complemented
9	#3301	C₂	1	2	yes	maximal, complemented
10	#3297	C₂	1	2	yes	maximal, complemented
11	#3140	C₂	1	1	yes	maximal, characteristic, complemented
12	#3097	C₂	1	1	yes	maximal, characteristic, complemented
13	#3096	C₂	1	1	yes	maximal, characteristic, complemented
14	#3076	C₂	1	1	yes	maximal, characteristic, complemented
15	#3058	C₂	1	1	yes	maximal, characteristic, complemented
16	#3057	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×#463	C₂	1	1	yes	maximal, characteristic, complemented
18	#3010	C₂	1	1	yes	maximal, characteristic, complemented
19	#3008	C₂	1	1	yes	maximal, characteristic, complemented
20	C₄×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic, complemented
21	#2935	C₂	1	1	yes	maximal, characteristic, complemented
22	#2898	C₂	1	1	yes	maximal, characteristic, complemented
23	#2897	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×2₋¹⁺⁴	C₂²	1	1	yes	characteristic
25	C₂×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
26	C₂×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
27	C₂²×SD₁₆	C₂²	1	1	yes	characteristic, complemented
28	C₂²×D₈	C₂²	1	1	yes	characteristic
29	C₂×#131	C₂²	1	1	yes	characteristic
30	C₂×#131	C₂²	1	1	yes	characteristic, complemented
31	#559	—	2	1	no	—
32	#559	—	2	1	no	—
33	#556	—	2	1	no	—
34	#555	C₂²	1	2	yes	complemented
35	#553	C₂²	1	2	yes	complemented
36	#553	C₂²	1	2	yes	complemented
37	#550	—	2	1	no	—
38	#548	C₂²	1	2	yes	complemented
39	#548	C₂²	1	2	yes	complemented
40	#547	C₂²	1	2	yes	complemented
41	#546	—	2	2	no	—
42	#546	—	2	2	no	—
43	#546	C₂²	1	2	yes	complemented
44	#546	C₂²	1	2	yes	complemented
45	#538	—	2	2	no	—
46	#536	—	2	1	no	—
47	#536	C₂²	1	1	yes	characteristic
48	#535	—	2	1	no	—
49	#535	C₂²	1	1	yes	characteristic
50	#535	C₂²	1	1	yes	characteristic
51	#535	C₂²	1	1	yes	characteristic, complemented
52	#533	C₂²	1	1	yes	characteristic, complemented
53	#532	—	2	1	no	—
54	#532	C₂²	1	1	yes	characteristic
55	C₂×#124	—	2	1	no	—
56	C₂×#124	C₂²	1	1	yes	characteristic
57	#525	—	2	2	no	—
58	#520	C₂²	1	1	yes	characteristic
59	#520	C₂²	1	1	yes	characteristic, complemented
60	C₄×#41	C₂²	1	1	yes	characteristic
61	C₂×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
62	#489	C₂²	1	2	yes	complemented
63	#489	C₂²	1	2	yes	complemented
64	#488	C₂²	1	2	yes	complemented
65	#488	C₂²	1	2	yes	complemented
66	#485	C₂²	1	2	yes	complemented
67	#485	C₂²	1	2	yes	complemented
68	#484	C₂²	1	2	yes	complemented
69	#483	C₂²	1	2	yes	complemented
70	#482	C₂²	1	2	yes	complemented
71	#482	C₂²	1	2	yes	complemented
72	#481	C₂²	1	2	yes	complemented
73	#480	C₂²	1	2	yes	complemented
74	#479	C₂²	1	1	yes	characteristic, complemented
75	#479	C₂²	1	1	yes	characteristic, complemented
76	#478	C₂²	1	1	yes	characteristic, complemented
77	#478	C₂²	1	1	yes	characteristic, complemented
78	#477	C₂²	1	1	yes	characteristic, complemented
79	#476	C₂²	1	1	yes	characteristic, complemented
80	#475	C₂²	1	1	yes	characteristic, complemented
81	#474	C₂²	1	1	yes	characteristic, complemented
82	#469	C₂²	1	2	yes	complemented
83	#469	C₂²	1	2	yes	complemented
84	#468	C₂²	1	2	yes	complemented
85	#468	C₂²	1	2	yes	complemented
86	#466	C₂²	1	2	yes	complemented
87	#466	C₂²	1	2	yes	complemented
88	#465	C₂²	1	2	yes	complemented
89	#465	C₂²	1	2	yes	complemented
90	#463	C₂²	1	2	yes	complemented
91	#463	C₂²	1	2	yes	complemented
92	#463	C₂²	1	2	yes	complemented
93	#463	C₂²	1	2	yes	complemented
94	#449	C₂²	1	2	yes	—
95	#449	C₂²	1	2	yes	—
96	#449	C₂²	1	2	yes	complemented
97	#449	C₂²	1	2	yes	complemented
98	#448	C₂²	1	2	yes	complemented
99	#448	C₂²	1	2	yes	complemented
100	#447	C₂²	1	2	yes	—
101	#447	C₂²	1	2	yes	—
102	#442	C₂²	1	2	yes	complemented
103	#440	C₂²	1	2	yes	complemented
104	C₄×SD₁₆	C₂²	1	2	yes	complemented
105	C₄×D₈	C₂²	1	2	yes	complemented
106	#436	C₂²	1	2	yes	complemented
107	#435	C₂²	1	2	yes	complemented
108	#435	C₂²	1	2	yes	complemented
109	C₈×D₄	C₂²	1	2	yes	complemented
110	#428	C₂²	1	1	yes	characteristic, complemented
111	#427	C₂²	1	1	yes	characteristic, complemented
112	#427	C₂²	1	1	yes	characteristic, complemented
113	C₂×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
114	#419	C₂²	1	1	yes	characteristic, complemented
115	#419	C₂²	1	1	yes	characteristic, complemented
116	#419	C₂²	1	2	yes	complemented
117	#418	C₂²	1	1	yes	characteristic
118	#418	C₂²	1	1	yes	characteristic
119	#418	C₂²	1	2	yes	complemented
120	#418	C₂²	1	1	yes	characteristic, complemented
121	#417	C₂²	1	1	yes	characteristic
122	#417	C₂²	1	2	yes	complemented
123	#417	C₂²	1	2	yes	complemented
124	#416	C₂²	1	1	yes	characteristic
125	#416	C₂²	1	1	yes	characteristic
126	#416	C₂²	1	2	yes	complemented
127	#416	C₂²	1	2	yes	complemented
128	C₂×#103	C₂²	1	1	yes	characteristic, complemented
129	C₂×#103	C₂²	1	2	yes	complemented
130	C₂×#102	C₂²	1	1	yes	characteristic
131	C₂×#102	C₂²	1	2	yes	complemented
132	#408	C₂²	1	1	yes	characteristic
133	#408	C₂²	1	1	yes	characteristic, complemented
134	C₄×M₁₆	C₂²	1	1	yes	characteristic, complemented
135	2₋¹⁺⁴	—	2	4	no	—
136	2₋¹⁺⁴	—	4	2	no	—
137	H(5,𝔽₂)	—	2	4	no	—
138	H(5,𝔽₂)	—	4	2	no	—
139	C₂×#41	—	2	1	no	—
140	C₂×#41	—	2	1	no	—
141	C₂×#41	—	2	2	no	—
142	C₂×#41	—	2	2	no	—
143	C₂×#41	C₂³	1	2	yes	—
144	C₂×#41	C₂³	1	2	yes	—
145	C₂×#41	C₂³	1	1	yes	characteristic
146	C₂×#41	C₂³	1	1	yes	characteristic
147	C₂×#41	C₂³	1	1	yes	characteristic
148	C₂²×Q₈	—	2	1	no	—
149	C₂²×Q₈	C₂³	1	1	yes	characteristic
150	C₂²×Q₈	C₂³	1	2	yes	—
151	C₂²×D₄	—	2	1	no	—
152	C₂²×D₄	—	2	2	no	—
153	C₂²×D₄	C₂³	1	1	yes	characteristic
154	C₂²×D₄	C₂³	1	1	yes	characteristic
155	C₂²×D₄	C₂³	1	2	yes	—
156	C₂³×C₄	—	2	1	no	—
157	AGL(1,ℤ/8)	—	2	4	no	—
158	C₂×SD₁₆	—	4	2	no	—
159	C₂×SD₁₆	C₂³	1	2	yes	—
160	C₂×SD₁₆	C₂³	1	2	yes	—
161	C₂×SD₁₆	C₂³	1	2	yes	—
162	C₂×D₈	—	4	2	no	—
163	C₂×D₈	C₂³	1	2	yes	—
164	C₂×D₈	C₂³	1	2	yes	—
165	C₂×D₈	C₂³	1	2	yes	—
166	#131	—	4	2	no	—
167	#131	—	4	2	no	—
168	C₂×M₁₆	C₂³	1	1	yes	characteristic
169	C₂×M₁₆	C₂³	1	1	yes	characteristic
170	C₂×M₁₆	C₂³	1	2	yes	—
171	C₂×M₁₆	C₂³	1	2	yes	—
172	C₂²×C₈	C₂³	1	1	yes	characteristic
173	C₂²×C₈	C₂³	1	1	yes	characteristic
174	C₂²×C₈	C₂³	1	2	yes	—
175	C₂²×C₈	C₂³	1	2	yes	—
176	C₄⋊Q₈	—	2	1	no	—
177	C₄⋊Q₈	D₄	1	1	yes	characteristic
178	C₄⋊Q₈	C₂³	1	1	yes	characteristic
179	C₄⋊Q₈	C₂³	1	1	yes	characteristic
180	#127	—	2	1	no	—
181	#127	—	2	1	no	—
182	#127	—	2	1	no	—
183	#127	D₄	1	1	yes	characteristic
184	#126	—	2	2	no	—
185	#126	—	2	2	no	—
186	#125	C₂³	1	1	yes	characteristic
187	#125	C₂³	1	1	yes	characteristic
188	#124	—	2	1	no	—
189	#124	—	2	1	no	—
190	#124	—	2	1	no	—
191	#124	—	2	1	no	—
192	#124	—	2	2	no	—
193	#124	—	2	2	no	—
194	#124	—	2	2	no	—
195	#124	—	2	2	no	—
196	#124	—	2	1	no	—
197	#124	—	2	1	no	—
198	#124	D₄	1	1	yes	characteristic
199	#124	D₄	1	1	yes	characteristic
200	#124	C₂³	1	2	yes	—
201	#124	C₂³	1	2	yes	—
202	#123	—	2	2	no	—
203	#123	—	2	2	no	—
204	#123	—	2	2	no	—
205	#123	—	2	2	no	—
206	#123	—	2	2	no	—
207	#123	—	2	2	no	—
208	#123	—	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	C₂³	1	2	yes	—
215	C₂²⋊Q₈	C₂³	1	2	yes	—
216	#121	—	2	2	no	—
217	#121	—	2	2	no	—
218	#121	—	2	2	no	—
219	#121	—	2	2	no	—
220	#121	—	2	2	no	—
221	#121	—	2	2	no	—
222	#121	—	2	2	no	—
223	#121	D₄	1	2	yes	—
224	#121	D₄	1	2	yes	—
225	#121	C₂³	1	2	yes	—
226	#121	C₂³	1	2	yes	—
227	#121	C₂³	1	2	yes	—
228	#121	C₂³	1	2	yes	—
229	#121	C₂³	1	2	yes	—
230	#121	C₂³	1	2	yes	—
231	#120	—	2	2	no	—
232	#120	—	2	2	no	—
233	#120	—	2	2	no	—
234	#120	—	2	2	no	—
235	#120	—	2	2	no	—
236	C₄×Q₈	—	2	1	no	—
237	C₄×Q₈	—	2	1	no	—
238	C₄×Q₈	—	2	1	no	—
239	C₄×Q₈	—	2	1	no	—
240	C₄×Q₈	C₂³	1	1	yes	characteristic
241	C₄×Q₈	C₂³	1	1	yes	characteristic
242	C₄×D₄	—	2	2	no	—
243	C₄×D₄	—	2	1	no	—
244	C₄×D₄	—	2	2	no	—
245	C₄×D₄	—	2	1	no	—
246	C₄×D₄	—	2	1	no	—
247	C₄×D₄	—	2	1	no	—
248	C₄×D₄	—	2	2	no	—
249	C₄×D₄	—	2	2	no	—
250	C₄×D₄	—	2	2	no	—
251	C₄×D₄	—	2	2	no	—
252	C₄×D₄	—	2	1	no	—
253	C₄×D₄	—	2	1	no	—
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	C₄×D₄	C₂³	1	2	yes	—
260	#117	—	2	2	no	—
261	#117	—	2	1	no	—
262	#117	C₂³	1	1	yes	characteristic
263	#117	C₂³	1	1	yes	characteristic
264	#117	C₂³	1	2	yes	—
265	#117	C₂³	1	1	yes	characteristic
266	#117	C₂³	1	2	yes	—
267	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
268	C₂×C₄⋊C₄	C₂³	1	2	yes	—
269	C₂×C₄⋊C₄	C₂³	1	2	yes	—
270	C₂×C₂²⋊C₄	—	2	1	no	—
271	C₂×C₂²⋊C₄	—	2	1	no	—
272	C₂×C₂²⋊C₄	—	2	1	no	—
273	C₂×C₂²⋊C₄	—	2	2	no	—
274	C₂×C₂²⋊C₄	—	2	2	no	—
275	C₂×C₄²	—	2	1	no	—
276	C₂×C₄²	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	1	yes	characteristic
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	C₄⋊C₈	C₂³	1	1	yes	characteristic
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	#103	C₂³	1	1	yes	characteristic
292	#103	C₂³	1	2	yes	—
293	#103	C₂³	1	2	yes	—
294	#103	C₂³	1	2	yes	—
295	#103	C₂³	1	2	yes	—
296	#103	C₂³	1	1	yes	characteristic
297	#103	C₂³	1	1	yes	characteristic
298	#103	C₂³	1	1	yes	characteristic
299	#103	C₂³	1	2	yes	—
300	#103	C₂³	1	2	yes	—
301	#103	C₂³	1	2	yes	—
302	#102	C₂³	1	2	yes	—
303	#102	C₂³	1	2	yes	—
304	#102	C₂³	1	1	yes	characteristic
305	#102	C₂³	1	2	yes	—
306	#102	C₂³	1	2	yes	—
307	#102	C₂³	1	1	yes	characteristic
308	#102	C₂³	1	1	yes	characteristic
309	#102	C₂³	1	1	yes	characteristic
310	#102	C₂³	1	2	yes	—
311	#102	C₂³	1	2	yes	—
312	#102	C₂³	1	2	yes	—
313	#102	C₂³	1	2	yes	—
314	#102	C₂³	1	2	yes	—
315	C₂²⋊C₈	C₂³	1	2	yes	—
316	C₂²⋊C₈	C₂³	1	2	yes	—
317	C₂²⋊C₈	C₂³	1	2	yes	—
318	C₂²⋊C₈	C₂³	1	2	yes	—
319	#97	C₂³	1	2	yes	—
320	C₄×C₈	C₂³	1	2	yes	—
321	C₂⁴	—	2	2	no	—
322	C₂⁴	—	2	1	no	—
323	C₂⁴	—	2	1	no	—
324	#41	—	2	2	no	—
325	#41	—	2	2	no	—
326	#41	—	2	2	no	—
327	#41	—	2	2	no	—
328	#41	—	2	2	no	—
329	#41	—	2	4	no	—
330	#41	—	2	4	no	—
331	#41	—	4	2	no	—
332	#41	—	4	2	no	—
333	#41	—	4	4	no	—
334	#41	—	4	4	no	—
335	#41	—	4	8	no	—
336	#41	—	8	4	no	—
337	#41	#41	1	4	yes	complemented
338	C₂×Q₈	—	2	1	no	—
339	C₂×Q₈	—	2	2	no	—
340	C₂×Q₈	—	2	1	no	—
341	C₂×Q₈	—	2	1	no	—
342	C₂×Q₈	—	2	4	no	—
343	C₂×Q₈	—	2	2	no	—
344	C₂×Q₈	—	2	2	no	—
345	C₂×Q₈	—	4	2	no	—
346	C₂×Q₈	—	4	4	no	—
347	C₂×Q₈	C₂×D₄	1	1	yes	characteristic
348	C₂×Q₈	C₂×D₄	1	1	yes	characteristic
349	C₂×Q₈	C₂⁴	1	2	yes	—
350	C₂×Q₈	C₂⁴	1	1	yes	characteristic
351	C₂×D₄	—	2	1	no	—
352	C₂×D₄	—	2	4	no	—
353	C₂×D₄	—	2	2	no	—
354	C₂×D₄	—	2	2	no	—
355	C₂×D₄	—	2	2	no	—
356	C₂×D₄	—	2	2	no	—
357	C₂×D₄	—	2	2	no	—
358	C₂×D₄	—	2	2	no	—
359	C₂×D₄	—	2	2	no	—
360	C₂×D₄	—	2	2	no	—
361	C₂×D₄	—	2	1	no	—
362	C₂×D₄	—	2	2	no	—
363	C₂×D₄	—	2	1	no	—
364	C₂×D₄	—	2	2	no	—
365	C₂×D₄	—	2	2	no	—
366	C₂×D₄	—	2	2	no	—
367	C₂×D₄	—	2	2	no	—
368	C₂×D₄	—	4	2	no	—
369	C₂×D₄	—	4	4	no	—
370	C₂×D₄	—	4	8	no	—
371	C₂×D₄	C₂×D₄	1	2	yes	—
372	C₂×D₄	C₂×D₄	1	2	yes	—
373	C₂×D₄	C₂×D₄	1	1	yes	characteristic
374	C₂×D₄	C₂×D₄	1	1	yes	characteristic
375	C₂×D₄	C₂×D₄	1	2	yes	—
376	C₂×D₄	C₂×D₄	1	2	yes	—
377	C₂×D₄	C₂⁴	1	2	yes	—
378	C₂×D₄	C₂⁴	1	2	yes	—
379	C₂×D₄	C₂⁴	1	1	yes	characteristic
380	C₂²×C₄	—	2	1	no	—
381	C₂²×C₄	—	2	1	no	—
382	C₂²×C₄	—	2	2	no	—
383	C₂²×C₄	—	2	1	no	—
384	C₂²×C₄	—	2	2	no	—
385	C₂²×C₄	—	2	2	no	—
386	C₂²×C₄	—	2	2	no	—
387	C₂²×C₄	—	2	2	no	—
388	C₂²×C₄	—	2	2	no	—
389	C₂²×C₄	—	2	1	no	—
390	C₂²×C₄	—	2	1	no	—
391	C₂²×C₄	—	2	2	no	—
392	C₂²×C₄	—	8	2	no	—
393	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
394	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
395	C₂²×C₄	C₂⁴	1	2	yes	—
396	C₂²×C₄	C₂⁴	1	2	yes	—
397	C₂²×C₄	C₂⁴	1	1	yes	characteristic
398	SD₁₆	—	2	4	no	—
399	SD₁₆	—	4	2	no	—
400	SD₁₆	—	4	2	no	—
401	D₈	—	2	4	no	—
402	D₈	—	4	2	no	—
403	D₈	—	4	2	no	—
404	M₁₆	—	2	2	no	—
405	M₁₆	—	2	2	no	—
406	M₁₆	—	4	2	no	—
407	M₁₆	—	4	2	no	—
408	C₂×C₈	—	2	2	no	—
409	C₂×C₈	—	2	2	no	—
410	C₂×C₈	—	4	2	no	—
411	C₂×C₈	—	4	2	no	—
412	C₂×C₈	C₂⁴	1	2	yes	—
413	C₂×C₈	C₂⁴	1	2	yes	—
414	C₂×C₈	C₂⁴	1	1	yes	characteristic
415	C₂×C₈	C₂⁴	1	1	yes	characteristic
416	C₂×C₈	C₂⁴	1	1	yes	characteristic
417	C₂×C₈	C₂⁴	1	1	yes	characteristic
418	C₄⋊C₄	—	2	1	no	—
419	C₄⋊C₄	—	2	2	no	—
420	C₄⋊C₄	—	2	2	no	—
421	C₄⋊C₄	—	2	1	no	—
422	C₄⋊C₄	—	2	1	no	—
423	C₄⋊C₄	—	2	1	no	—
424	C₄⋊C₄	—	2	1	no	—
425	C₄⋊C₄	—	2	1	no	—
426	C₄⋊C₄	—	2	2	no	—
427	C₄⋊C₄	—	2	2	no	—
428	C₄⋊C₄	—	2	1	no	—
429	C₄⋊C₄	—	2	1	no	—
430	C₄⋊C₄	—	2	1	no	—
431	C₄⋊C₄	C₂×D₄	1	2	yes	—
432	C₄⋊C₄	C₂×D₄	1	2	yes	—
433	C₄⋊C₄	C₂⁴	1	2	yes	—
434	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
435	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
436	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
437	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
438	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
439	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
440	C₂²⋊C₄	—	2	2	no	—
441	C₂²⋊C₄	—	2	2	no	—
442	C₂²⋊C₄	—	2	1	no	—
443	C₂²⋊C₄	—	2	1	no	—
444	C₂²⋊C₄	—	2	1	no	—
445	C₂²⋊C₄	—	2	2	no	—
446	C₂²⋊C₄	—	2	2	no	—
447	C₂²⋊C₄	—	2	2	no	—
448	C₂²⋊C₄	—	2	2	no	—
449	C₂²⋊C₄	—	2	2	no	—
450	C₂²⋊C₄	—	2	2	no	—
451	C₂²⋊C₄	—	2	2	no	—
452	C₂²⋊C₄	—	2	2	no	—
453	C₂²⋊C₄	—	2	2	no	—
454	C₂²⋊C₄	—	2	2	no	—
455	C₂²⋊C₄	—	2	1	no	—
456	C₂²⋊C₄	—	2	1	no	—
457	C₂²⋊C₄	—	2	2	no	—
458	C₂²⋊C₄	—	2	2	no	—
459	C₂²⋊C₄	—	2	2	no	—
460	C₂²⋊C₄	—	2	2	no	—
461	C₂²⋊C₄	C₂×D₄	1	2	yes	—
462	C₂²⋊C₄	C₂×D₄	1	2	yes	—
463	C₂²⋊C₄	C₂×D₄	1	2	yes	—
464	C₂²⋊C₄	C₂×D₄	1	2	yes	—
465	C₄²	—	2	1	no	—
466	C₄²	—	2	1	no	—
467	C₄²	—	2	1	no	—
468	C₄²	—	2	2	no	—
469	C₄²	—	2	2	no	—
470	C₄²	—	2	1	no	—
471	C₄²	—	2	1	no	—
472	C₄²	C₂×D₄	1	1	yes	characteristic
473	C₄²	C₂×D₄	1	1	yes	characteristic
474	C₄²	C₂⁴	1	1	yes	characteristic
475	C₄²	C₂⁴	1	1	yes	characteristic
476	C₂³	—	2	1	no	—
477	C₂³	—	2	2	no	—
478	C₂³	—	2	2	no	—
479	C₂³	—	4	4	no	—
480	C₂³	—	4	2	no	—
481	C₂³	—	4	2	no	—
482	C₂³	—	8	1	no	—
483	C₂³	—	8	1	no	—
484	C₂³	—	8	1	no	—
485	C₂³	—	8	1	no	—
486	C₂³	—	8	2	no	—
487	C₂³	—	8	2	no	—
488	C₂³	C₂²×D₄	1	2	yes	—
489	C₂³	C₂²×D₄	1	2	yes	—
490	C₂³	C₂²×D₄	1	1	yes	characteristic
491	Q₈	—	2	2	no	—
492	Q₈	—	2	2	no	—
493	Q₈	—	2	1	no	—
494	Q₈	—	2	2	no	—
495	Q₈	—	2	2	no	—
496	Q₈	—	4	4	no	—
497	Q₈	—	4	2	no	—
498	Q₈	—	4	2	no	—
499	Q₈	—	8	1	no	—
500	Q₈	C₂×#41	1	2	yes	—
501	D₄	—	2	4	no	—
502	D₄	—	2	4	no	—
503	D₄	—	2	4	no	—
504	D₄	—	2	2	no	—
505	D₄	—	2	2	no	—
506	D₄	—	2	2	no	—
507	D₄	—	2	2	no	—
508	D₄	—	2	1	no	—
509	D₄	—	2	2	no	—
510	D₄	—	2	2	no	—
511	D₄	—	4	2	no	—
512	D₄	—	4	2	no	—
513	D₄	—	4	4	no	—
514	D₄	—	4	4	no	—
515	D₄	—	4	4	no	—
516	D₄	—	4	2	no	—
517	D₄	—	4	2	no	—
518	D₄	—	8	2	no	—
519	D₄	—	8	2	no	—
520	D₄	—	8	2	no	—
521	D₄	—	8	2	no	—
522	D₄	—	8	2	no	—
523	D₄	—	8	2	no	—
524	D₄	C₂×#41	1	2	yes	—
525	C₂×C₄	—	2	1	no	—
526	C₂×C₄	—	2	4	no	—
527	C₂×C₄	—	2	2	no	—
528	C₂×C₄	—	2	2	no	—
529	C₂×C₄	—	2	2	no	—
530	C₂×C₄	—	2	2	no	—
531	C₂×C₄	—	2	1	no	—
532	C₂×C₄	—	2	1	no	—
533	C₂×C₄	—	2	1	no	—
534	C₂×C₄	—	2	1	no	—
535	C₂×C₄	—	2	2	no	—
536	C₂×C₄	—	2	1	no	—
537	C₂×C₄	—	2	1	no	—
538	C₂×C₄	—	2	2	no	—
539	C₂×C₄	—	4	1	no	—
540	C₂×C₄	—	4	1	no	—
541	C₂×C₄	—	4	4	no	—
542	C₂×C₄	—	4	4	no	—
543	C₂×C₄	—	4	4	no	—
544	C₂×C₄	—	4	4	no	—
545	C₂×C₄	—	4	2	no	—
546	C₂×C₄	—	8	1	no	—
547	C₂×C₄	—	8	1	no	—
548	C₂×C₄	—	8	2	no	—
549	C₂×C₄	—	8	1	no	—
550	C₂×C₄	—	8	2	no	—
551	C₂×C₄	—	8	2	no	—
552	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
553	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
554	C₂×C₄	C₂²×D₄	1	2	yes	—
555	C₂×C₄	C₂²×D₄	1	2	yes	—
556	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
557	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
558	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
559	C₂×C₄	C₂×#41	1	2	yes	—
560	C₂×C₄	H(5,𝔽₂)	1	2	yes	—
561	C₂×C₄	C₂⁵	1	1	yes	characteristic
562	C₈	—	2	2	no	—
563	C₈	—	2	1	no	—
564	C₈	—	2	1	no	—
565	C₈	—	2	1	no	—
566	C₈	—	2	1	no	—
567	C₈	—	2	2	no	—
568	C₂²	—	2	1	no	—
569	C₂²	—	2	1	no	—
570	C₂²	—	2	2	no	—
571	C₂²	—	2	2	no	—
572	C₂²	—	2	2	no	—
573	C₂²	—	2	2	no	—
574	C₂²	—	2	2	no	—
575	C₂²	—	2	2	no	—
576	C₂²	—	2	2	no	—
577	C₂²	—	4	1	no	—
578	C₂²	—	4	1	no	—
579	C₂²	—	4	2	no	—
580	C₂²	—	4	2	no	—
581	C₂²	—	4	2	no	—
582	C₂²	—	4	2	no	—
583	C₂²	—	4	2	no	—
584	C₂²	—	4	2	no	—
585	C₂²	—	8	4	no	—
586	C₂²	—	16	2	no	—
587	C₂²	—	16	4	no	—
588	C₂²	#546	1	2	yes	—
589	C₂²	C₂³×D₄	1	1	yes	characteristic
590	C₄	—	2	1	no	—
591	C₄	—	2	1	no	—
592	C₄	—	2	1	no	—
593	C₄	—	2	1	no	—
594	C₄	—	2	2	no	—
595	C₄	—	2	2	no	—
596	C₄	—	2	2	no	—
597	C₄	—	4	1	no	—
598	C₄	—	4	1	no	—
599	C₄	—	4	1	no	—
600	C₄	—	4	2	no	—
601	C₄	—	4	1	no	—
602	C₄	—	4	1	no	—
603	C₄	—	4	1	no	—
604	C₄	—	4	2	no	—
605	C₄	#546	1	2	yes	—
606	C₄	C₂²×#41	1	1	yes	characteristic
607	C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
608	C₂	—	2	2	no	—
609	C₂	—	4	2	no	—
610	C₂	—	4	2	no	—
611	C₂	—	4	2	no	—
612	C₂	—	8	2	no	—
613	C₂	—	8	2	no	—
614	C₂	C₂×#546	1	1	yes	characteristic
615	C₂	#3584	1	1	yes	characteristic
616	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 ◁ #532 ◁ G
LECS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. #3506	C₂	semidirect
2. #3500	C₂	semidirect
3. #3326	C₂	semidirect
4. #3322	C₂	semidirect
5. #3321	C₂	semidirect
6. #3319	C₂	semidirect
7. #3308	C₂	semidirect
8. #3306	C₂	semidirect
9. #3301	C₂	semidirect
10. #3297	C₂	semidirect
11. #3140	C₂	semidirect
12. #3097	C₂	semidirect
13. #3096	C₂	semidirect
14. #3076	C₂	semidirect
15. #3058	C₂	semidirect
16. #3057	C₂	semidirect
17. C₂×#463	C₂	semidirect
18. #3010	C₂	semidirect
19. #3008	C₂	semidirect
20. C₄×AGL(1,ℤ/8)	C₂	semidirect
21. #2935	C₂	semidirect
22. #2898	C₂	semidirect
23. #2897	C₂	semidirect
27. C₂²×SD₁₆	C₂²	semidirect
30. C₂×#131	C₂²	semidirect
34. #555	C₂²	semidirect
35. #553	C₂²	semidirect
36. #553	C₂²	semidirect
38. #548	C₂²	semidirect
39. #548	C₂²	semidirect
40. #547	C₂²	semidirect
43. #546	C₂²	semidirect
44. #546	C₂²	semidirect
51. #535	C₂²	semidirect
52. #533	C₂²	semidirect
59. #520	C₂²	semidirect
61. C₂×C₄×D₄	C₂²	semidirect
62. #489	C₂²	semidirect
63. #489	C₂²	semidirect
64. #488	C₂²	semidirect
65. #488	C₂²	semidirect
66. #485	C₂²	semidirect
67. #485	C₂²	semidirect
68. #484	C₂²	semidirect
69. #483	C₂²	semidirect
70. #482	C₂²	semidirect
71. #482	C₂²	semidirect
72. #481	C₂²	semidirect
73. #480	C₂²	semidirect
74. #479	C₂²	semidirect
75. #479	C₂²	semidirect
76. #478	C₂²	semidirect
77. #478	C₂²	semidirect
78. #477	C₂²	semidirect
79. #476	C₂²	semidirect
80. #475	C₂²	semidirect
81. #474	C₂²	semidirect
82. #469	C₂²	semidirect
83. #469	C₂²	semidirect
84. #468	C₂²	semidirect
85. #468	C₂²	semidirect
86. #466	C₂²	semidirect
87. #466	C₂²	semidirect
88. #465	C₂²	semidirect
89. #465	C₂²	semidirect
90. #463	C₂²	semidirect
91. #463	C₂²	semidirect
92. #463	C₂²	semidirect
93. #463	C₂²	semidirect
96. #449	C₂²	semidirect
97. #449	C₂²	semidirect
98. #448	C₂²	semidirect
99. #448	C₂²	semidirect
102. #442	C₂²	semidirect
103. #440	C₂²	semidirect
104. C₄×SD₁₆	C₂²	semidirect
105. C₄×D₈	C₂²	semidirect
106. #436	C₂²	semidirect
107. #435	C₂²	semidirect
108. #435	C₂²	semidirect
109. C₈×D₄	C₂²	semidirect
110. #428	C₂²	semidirect
111. #427	C₂²	semidirect
112. #427	C₂²	semidirect
113. C₂×C₄⋊C₈	C₂²	semidirect
114. #419	C₂²	semidirect
115. #419	C₂²	semidirect
116. #419	C₂²	semidirect
119. #418	C₂²	semidirect
120. #418	C₂²	semidirect
122. #417	C₂²	semidirect
123. #417	C₂²	semidirect
126. #416	C₂²	semidirect
127. #416	C₂²	semidirect
128. C₂×#103	C₂²	semidirect
129. C₂×#103	C₂²	semidirect
131. C₂×#102	C₂²	semidirect
133. #408	C₂²	semidirect
134. C₄×M₁₆	C₂²	semidirect
337. #41	#41	semidirect

Maximal subgroups

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

subgroup	index
#3506	2
#3500	2
#3326	2
#3322	2
#3321	2
#3319	2
#3308	2
#3306	2
#3301	2
#3297	2
#3140	2
#3097	2
#3096	2
#3076	2
#3058	2
#3057	2
C₂×#463	2
#3010	2
#3008	2
C₄×AGL(1,ℤ/8)	2
#2935	2
#2898	2
#2897	2