Subgroups — #62137

Order 256.

995 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	#3515	C₂	1	1	yes	maximal, characteristic, complemented
2	D₄×#41	C₂	1	1	yes	maximal, characteristic, complemented
3	#3386	C₂	1	1	yes	maximal, characteristic, complemented
4	#3384	C₂	1	1	yes	maximal, characteristic, complemented
5	#3368	C₂	1	1	yes	maximal, characteristic, complemented
6	#3366	C₂	1	1	yes	maximal, characteristic, complemented
7	#3345	C₂	1	2	yes	maximal, complemented
8	#3343	C₂	1	2	yes	maximal, complemented
9	#3335	C₂	1	1	yes	maximal, characteristic, complemented
10	#3334	C₂	1	1	yes	maximal, characteristic, complemented
11	#3318	C₂	1	2	yes	maximal, complemented
12	#3310	C₂	1	2	yes	maximal, complemented
13	#3295	C₂	1	1	yes	maximal, characteristic, complemented
14	#3294	C₂	1	1	yes	maximal, characteristic, complemented
15	#3251	C₂	1	1	yes	maximal, characteristic, complemented
16	#3247	C₂	1	2	yes	maximal, complemented
17	#3234	C₂	1	2	yes	maximal, complemented
18	#3228	C₂	1	1	yes	maximal, characteristic, complemented
19	#3114	C₂	1	2	yes	maximal, complemented
20	#3105	C₂	1	1	yes	maximal, characteristic, complemented
21	#3077	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×#478	C₂	1	2	yes	maximal, complemented
23	#2990	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×#41	—	2	1	no	—
25	#557	C₂²	1	1	yes	characteristic, complemented
26	#554	C₂²	1	1	yes	characteristic, complemented
27	#554	C₂²	1	1	yes	characteristic, complemented
28	#553	C₂²	1	2	yes	complemented
29	#552	—	2	2	no	—
30	#552	—	2	1	no	—
31	#552	C₂²	1	2	yes	complemented
32	#550	C₂²	1	1	yes	characteristic
33	D₄×Q₈	C₂²	1	1	yes	characteristic
34	#548	—	2	1	no	—
35	#547	—	2	1	no	—
36	#547	C₂²	1	1	yes	characteristic
37	#547	C₂²	1	2	yes	—
38	#547	C₂²	1	1	yes	characteristic, complemented
39	#546	—	2	1	no	—
40	#546	—	2	2	no	—
41	D₄²	C₂²	1	1	yes	characteristic
42	D₄²	C₂²	1	2	yes	—
43	#541	—	2	1	no	—
44	#539	—	2	2	no	—
45	#533	C₂²	1	1	yes	characteristic, complemented
46	#532	C₂²	1	1	yes	characteristic
47	#532	C₂²	1	2	yes	—
48	#529	C₂²	1	1	yes	characteristic, complemented
49	#529	C₂²	1	2	yes	complemented
50	C₂×#125	C₂²	1	2	yes	complemented
51	#525	—	2	1	no	—
52	#525	—	2	2	no	—
53	#520	—	2	1	no	—
54	C₄×#41	C₂²	1	1	yes	characteristic
55	C₂×C₄×D₄	C₂²	1	2	yes	—
56	C₂×C₄×D₄	C₂²	1	1	yes	characteristic
57	#501	C₂²	1	2	yes	complemented
58	#501	C₂²	1	2	yes	complemented
59	#500	C₂²	1	1	yes	characteristic, complemented
60	#498	C₂²	1	1	yes	characteristic, complemented
61	#490	C₂²	1	2	yes	complemented
62	#490	C₂²	1	2	yes	complemented
63	#486	C₂²	1	1	yes	characteristic, complemented
64	#486	C₂²	1	1	yes	characteristic, complemented
65	#484	C₂²	1	1	yes	characteristic, complemented
66	#483	C₂²	1	2	yes	complemented
67	#482	C₂²	1	2	yes	complemented
68	#482	C₂²	1	2	yes	complemented
69	#481	C₂²	1	2	yes	complemented
70	#481	C₂²	1	1	yes	characteristic, complemented
71	#481	C₂²	1	2	yes	complemented
72	#480	C₂²	1	2	yes	complemented
73	#480	C₂²	1	2	yes	complemented
74	#480	C₂²	1	2	yes	complemented
75	#478	C₂²	1	1	yes	characteristic
76	#478	C₂²	1	2	yes	—
77	#478	C₂²	1	2	yes	—
78	#478	C₂²	1	2	yes	—
79	#478	C₂²	1	2	yes	complemented
80	#478	C₂²	1	2	yes	complemented
81	#478	C₂²	1	2	yes	complemented
82	#478	C₂²	1	2	yes	complemented
83	#478	C₂²	1	2	yes	complemented
84	#478	C₂²	1	1	yes	characteristic, complemented
85	#478	C₂²	1	2	yes	complemented
86	#477	C₂²	1	2	yes	complemented
87	#476	C₂²	1	1	yes	characteristic
88	#476	C₂²	1	1	yes	characteristic, complemented
89	#476	C₂²	1	2	yes	complemented
90	#475	C₂²	1	1	yes	characteristic, complemented
91	#474	C₂²	1	1	yes	characteristic
92	#474	C₂²	1	1	yes	characteristic, complemented
93	#474	C₂²	1	1	yes	characteristic, complemented
94	#469	C₂²	1	2	yes	complemented
95	#468	C₂²	1	2	yes	complemented
96	#466	C₂²	1	2	yes	complemented
97	#466	C₂²	1	2	yes	complemented
98	#465	C₂²	1	2	yes	complemented
99	#465	C₂²	1	2	yes	complemented
100	#463	C₂²	1	1	yes	characteristic
101	#463	C₂²	1	1	yes	characteristic, complemented
102	#463	C₂²	1	2	yes	complemented
103	#460	C₂²	1	2	yes	complemented
104	#460	C₂²	1	1	yes	characteristic, complemented
105	#459	C₂²	1	2	yes	complemented
106	#459	C₂²	1	1	yes	characteristic, complemented
107	#450	C₂²	1	1	yes	characteristic
108	#450	C₂²	1	2	yes	—
109	#447	C₂²	1	1	yes	characteristic
110	#447	C₂²	1	2	yes	—
111	#446	C₂²	1	1	yes	characteristic, complemented
112	#446	C₂²	1	1	yes	characteristic, complemented
113	#442	C₂²	1	2	yes	—
114	#442	C₂²	1	2	yes	complemented
115	#440	C₂²	1	2	yes	—
116	#440	C₂²	1	2	yes	complemented
117	C₄×SD₁₆	C₂²	1	1	yes	characteristic
118	C₄×SD₁₆	C₂²	1	1	yes	characteristic, complemented
119	C₄×D₈	C₂²	1	1	yes	characteristic
120	C₄×D₈	C₂²	1	1	yes	characteristic, complemented
121	#435	C₂²	1	2	yes	complemented
122	#435	C₂²	1	2	yes	complemented
123	C₈×D₄	C₂²	1	1	yes	characteristic, complemented
124	C₈×D₄	C₂²	1	1	yes	characteristic, complemented
125	#432	C₂²	1	2	yes	complemented
126	#431	C₂²	1	1	yes	characteristic, complemented
127	#428	C₂²	1	2	yes	complemented
128	C₂×#107	C₂²	1	2	yes	complemented
129	C₂×#106	C₂²	1	2	yes	complemented
130	#423	C₂²	1	1	yes	characteristic, complemented
131	C₂×C₄⋊C₈	C₂²	1	2	yes	complemented
132	#418	C₂²	1	2	yes	—
133	C₂×#102	C₂²	1	2	yes	—
134	C₂×#102	C₂²	1	2	yes	—
135	C₂×#41	—	2	1	no	—
136	C₂×#41	—	2	1	no	—
137	C₂×#41	—	2	2	no	—
138	C₂×#41	—	2	1	no	—
139	C₂×#41	—	2	2	no	—
140	C₂×#41	—	2	1	no	—
141	C₂×#41	—	4	8	no	—
142	C₂×#41	D₄	1	1	yes	characteristic
143	C₂²×Q₈	—	2	1	no	—
144	C₂²×D₄	—	2	2	no	—
145	C₂²×D₄	—	2	1	no	—
146	C₂²×D₄	C₂³	1	2	yes	—
147	C₂²×D₄	C₂³	1	1	yes	characteristic
148	C₂³×C₄	—	2	2	no	—
149	C₂³×C₄	—	2	1	no	—
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×D₈	C₂³	1	1	yes	characteristic
154	C₂×D₈	C₂³	1	1	yes	characteristic
155	C₂×D₈	C₂³	1	2	yes	—
156	C₂×M₁₆	C₂³	1	2	yes	—
157	C₂²×C₈	C₂³	1	2	yes	—
158	C₂²×C₈	C₂³	1	2	yes	—
159	C₄⋊Q₈	—	2	1	no	—
160	C₄⋊Q₈	C₂³	1	1	yes	characteristic
161	C₄⋊Q₈	C₂³	1	2	yes	—
162	C₄⋊Q₈	C₂³	1	1	yes	characteristic
163	C₄⋊Q₈	C₂³	1	1	yes	characteristic
164	#127	C₂³	1	1	yes	characteristic
165	#127	C₂³	1	2	yes	—
166	#126	—	2	2	no	—
167	#126	—	2	2	no	—
168	#126	—	2	2	no	—
169	#126	—	2	1	no	—
170	#125	—	2	2	no	—
171	#125	—	2	2	no	—
172	#125	—	2	1	no	—
173	#125	—	2	2	no	—
174	#125	—	2	2	no	—
175	#125	C₂³	1	1	yes	characteristic
176	#125	C₂³	1	2	yes	—
177	#125	C₂³	1	2	yes	—
178	#125	C₂³	1	2	yes	—
179	#124	—	2	1	no	—
180	#124	—	2	2	no	—
181	#124	C₂³	1	1	yes	characteristic
182	#123	—	2	2	no	—
183	#123	—	2	1	no	—
184	#123	—	2	2	no	—
185	#123	—	2	2	no	—
186	#123	—	2	2	no	—
187	#123	—	2	2	no	—
188	#123	—	2	2	no	—
189	#123	—	2	2	no	—
190	C₂²⋊Q₈	—	2	1	no	—
191	C₂²⋊Q₈	—	2	1	no	—
192	C₂²⋊Q₈	—	2	1	no	—
193	C₂²⋊Q₈	—	2	1	no	—
194	C₂²⋊Q₈	—	2	2	no	—
195	C₂²⋊Q₈	—	2	1	no	—
196	C₂²⋊Q₈	—	2	2	no	—
197	C₂²⋊Q₈	—	2	2	no	—
198	C₂²⋊Q₈	—	2	1	no	—
199	C₂²⋊Q₈	—	2	2	no	—
200	C₂²⋊Q₈	C₂³	1	1	yes	characteristic
201	C₂²⋊Q₈	C₂³	1	2	yes	—
202	#121	—	2	2	no	—
203	#121	—	2	2	no	—
204	#121	—	2	1	no	—
205	#121	—	2	1	no	—
206	#121	—	2	2	no	—
207	#121	—	2	1	no	—
208	#121	—	2	2	no	—
209	#121	C₂³	1	2	yes	—
210	#121	C₂³	1	1	yes	characteristic
211	#121	C₂³	1	2	yes	—
212	#121	C₂³	1	2	yes	—
213	#121	C₂³	1	2	yes	—
214	#120	—	2	2	no	—
215	#120	—	2	2	no	—
216	#120	—	2	2	no	—
217	C₄×Q₈	—	2	1	no	—
218	C₄×Q₈	—	2	1	no	—
219	C₄×Q₈	—	2	1	no	—
220	C₄×Q₈	D₄	1	1	yes	characteristic
221	C₄×Q₈	C₂³	1	2	yes	—
222	C₄×Q₈	C₂³	1	1	yes	characteristic
223	C₄×Q₈	C₂³	1	1	yes	characteristic
224	C₄×D₄	—	2	1	no	—
225	C₄×D₄	—	2	2	no	—
226	C₄×D₄	—	2	1	no	—
227	C₄×D₄	—	2	2	no	—
228	C₄×D₄	—	2	2	no	—
229	C₄×D₄	—	2	1	no	—
230	C₄×D₄	—	2	1	no	—
231	C₄×D₄	—	2	2	no	—
232	C₄×D₄	—	2	2	no	—
233	C₄×D₄	—	2	1	no	—
234	C₄×D₄	D₄	1	1	yes	characteristic
235	C₄×D₄	D₄	1	2	yes	—
236	C₄×D₄	C₂³	1	1	yes	characteristic
237	C₄×D₄	C₂³	1	2	yes	—
238	C₄×D₄	C₂³	1	1	yes	characteristic
239	C₄×D₄	C₂³	1	1	yes	characteristic
240	C₄×D₄	C₂³	1	2	yes	—
241	C₄×D₄	C₂³	1	1	yes	characteristic
242	C₄×D₄	C₂³	1	2	yes	—
243	C₄×D₄	C₂³	1	1	yes	characteristic
244	C₄×D₄	C₂³	1	2	yes	—
245	C₄×D₄	C₂³	1	1	yes	characteristic
246	C₄×D₄	C₂³	1	2	yes	—
247	#117	—	2	2	no	—
248	#117	—	2	1	no	—
249	#117	—	2	2	no	—
250	#117	D₄	1	1	yes	characteristic
251	#117	D₄	1	2	yes	—
252	#117	C₂³	1	2	yes	—
253	C₂×C₄⋊C₄	—	2	2	no	—
254	C₂×C₄⋊C₄	—	2	2	no	—
255	C₂×C₄⋊C₄	—	2	1	no	—
256	C₂×C₄⋊C₄	C₂³	1	2	yes	—
257	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
258	C₂×C₄⋊C₄	C₂³	1	2	yes	—
259	C₂×C₄⋊C₄	C₂³	1	2	yes	—
260	C₂×C₂²⋊C₄	—	2	2	no	—
261	C₂×C₂²⋊C₄	—	2	1	no	—
262	C₂×C₄²	C₂³	1	2	yes	—
263	C₂×C₄²	C₂³	1	1	yes	characteristic
264	#107	C₂³	1	1	yes	characteristic
265	#107	C₂³	1	2	yes	—
266	#107	C₂³	1	2	yes	—
267	#107	C₂³	1	2	yes	—
268	#107	C₂³	1	2	yes	—
269	#107	C₂³	1	1	yes	characteristic
270	#107	C₂³	1	2	yes	—
271	#106	C₂³	1	1	yes	characteristic
272	#106	C₂³	1	2	yes	—
273	#106	C₂³	1	2	yes	—
274	#106	C₂³	1	2	yes	—
275	#106	C₂³	1	2	yes	—
276	#106	C₂³	1	1	yes	characteristic
277	#106	C₂³	1	2	yes	—
278	C₄⋊C₈	C₂³	1	1	yes	characteristic
279	C₄⋊C₈	C₂³	1	2	yes	—
280	C₄⋊C₈	C₂³	1	2	yes	—
281	C₄⋊C₈	C₂³	1	2	yes	—
282	C₄⋊C₈	C₂³	1	1	yes	characteristic
283	C₄⋊C₈	C₂³	1	1	yes	characteristic
284	C₄⋊C₈	C₂³	1	1	yes	characteristic
285	#103	C₂³	1	1	yes	characteristic
286	#103	C₂³	1	1	yes	characteristic
287	#103	C₂³	1	2	yes	—
288	#102	C₂³	1	1	yes	characteristic
289	#102	C₂³	1	1	yes	characteristic
290	#102	C₂³	1	2	yes	—
291	#102	C₂³	1	2	yes	—
292	#102	C₂³	1	2	yes	—
293	#102	C₂³	1	2	yes	—
294	#102	C₂³	1	2	yes	—
295	#102	C₂³	1	2	yes	—
296	#102	C₂³	1	2	yes	—
297	#102	C₂³	1	2	yes	—
298	#102	C₂³	1	1	yes	characteristic
299	#102	C₂³	1	1	yes	characteristic
300	#102	C₂³	1	1	yes	characteristic
301	#102	C₂³	1	1	yes	characteristic
302	#102	C₂³	1	2	yes	—
303	#102	C₂³	1	2	yes	—
304	#102	C₂³	1	2	yes	—
305	C₂²⋊C₈	C₂³	1	1	yes	characteristic
306	C₂²⋊C₈	C₂³	1	1	yes	characteristic
307	C₂²⋊C₈	C₂³	1	2	yes	—
308	C₂²⋊C₈	C₂³	1	2	yes	—
309	#97	C₂³	1	2	yes	—
310	#97	C₂³	1	2	yes	—
311	C₄×C₈	C₂³	1	1	yes	characteristic
312	C₄×C₈	C₂³	1	1	yes	characteristic
313	C₂⁴	—	2	1	no	—
314	C₂⁴	—	2	2	no	—
315	#41	—	2	4	no	—
316	#41	—	4	8	no	—
317	#41	—	4	4	no	—
318	#41	—	4	8	no	—
319	#41	—	4	4	no	—
320	#41	—	4	4	no	—
321	#41	—	4	4	no	—
322	C₂×Q₈	—	2	1	no	—
323	C₂×Q₈	—	2	2	no	—
324	C₂×Q₈	—	2	1	no	—
325	C₂×Q₈	—	2	1	no	—
326	C₂×Q₈	—	4	4	no	—
327	C₂×Q₈	C₂×D₄	1	1	yes	characteristic
328	C₂×Q₈	C₂⁴	1	1	yes	characteristic
329	C₂×D₄	—	2	4	no	—
330	C₂×D₄	—	2	2	no	—
331	C₂×D₄	—	2	2	no	—
332	C₂×D₄	—	2	2	no	—
333	C₂×D₄	—	2	2	no	—
334	C₂×D₄	—	2	2	no	—
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	1	no	—
340	C₂×D₄	—	2	2	no	—
341	C₂×D₄	—	2	1	no	—
342	C₂×D₄	—	4	2	no	—
343	C₂×D₄	—	4	1	no	—
344	C₂×D₄	—	4	8	no	—
345	C₂×D₄	—	4	4	no	—
346	C₂×D₄	C₂×D₄	1	2	yes	—
347	C₂×D₄	C₂×D₄	1	1	yes	characteristic
348	C₂×D₄	C₂⁴	1	2	yes	—
349	C₂×D₄	C₂⁴	1	1	yes	characteristic
350	C₂×D₄	C₂⁴	1	1	yes	characteristic
351	C₂×D₄	C₂⁴	1	1	yes	characteristic
352	C₂²×C₄	—	2	1	no	—
353	C₂²×C₄	—	2	2	no	—
354	C₂²×C₄	—	2	2	no	—
355	C₂²×C₄	—	2	2	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	2	no	—
361	C₂²×C₄	—	2	1	no	—
362	C₂²×C₄	—	2	2	no	—
363	C₂²×C₄	—	2	1	no	—
364	C₂²×C₄	—	2	2	no	—
365	C₂²×C₄	—	4	8	no	—
366	C₂²×C₄	—	4	4	no	—
367	C₂²×C₄	C₂×D₄	1	2	yes	—
368	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
369	C₂²×C₄	C₂×D₄	1	2	yes	—
370	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
371	C₂²×C₄	C₂⁴	1	2	yes	—
372	C₂²×C₄	C₂⁴	1	1	yes	characteristic
373	SD₁₆	—	2	2	no	—
374	SD₁₆	—	4	1	no	—
375	SD₁₆	—	4	2	no	—
376	D₈	—	2	2	no	—
377	D₈	—	4	1	no	—
378	D₈	—	4	2	no	—
379	M₁₆	—	4	2	no	—
380	C₂×C₈	—	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	1	no	—
391	C₄⋊C₄	—	2	2	no	—
392	C₄⋊C₄	—	2	1	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	1	no	—
398	C₄⋊C₄	—	2	2	no	—
399	C₄⋊C₄	—	2	2	no	—
400	C₄⋊C₄	—	2	2	no	—
401	C₄⋊C₄	—	2	1	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	—	2	1	no	—
407	C₄⋊C₄	—	2	2	no	—
408	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
409	C₄⋊C₄	C₂×D₄	1	2	yes	—
410	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
411	C₄⋊C₄	C₂×D₄	1	2	yes	—
412	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
413	C₄⋊C₄	C₂⁴	1	2	yes	—
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	C₄⋊C₄	C₂⁴	1	2	yes	—
419	C₂²⋊C₄	—	2	2	no	—
420	C₂²⋊C₄	—	2	2	no	—
421	C₂²⋊C₄	—	2	1	no	—
422	C₂²⋊C₄	—	2	1	no	—
423	C₂²⋊C₄	—	2	2	no	—
424	C₂²⋊C₄	—	2	1	no	—
425	C₂²⋊C₄	—	2	2	no	—
426	C₂²⋊C₄	—	2	1	no	—
427	C₂²⋊C₄	—	2	2	no	—
428	C₂²⋊C₄	—	2	1	no	—
429	C₂²⋊C₄	—	2	1	no	—
430	C₂²⋊C₄	—	2	1	no	—
431	C₂²⋊C₄	—	2	1	no	—
432	C₂²⋊C₄	—	2	2	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	1	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	2	no	—
443	C₄²	—	2	1	no	—
444	C₄²	C₂×D₄	1	2	yes	—
445	C₄²	C₂×D₄	1	1	yes	characteristic
446	C₄²	C₂×D₄	1	1	yes	characteristic
447	C₄²	C₂×D₄	1	2	yes	—
448	C₄²	C₂⁴	1	1	yes	characteristic
449	C₄²	C₂⁴	1	2	yes	—
450	C₄²	C₂⁴	1	1	yes	characteristic
451	C₂³	—	2	1	no	—
452	C₂³	—	2	1	no	—
453	C₂³	—	2	2	no	—
454	C₂³	—	2	1	no	—
455	C₂³	—	4	4	no	—
456	C₂³	—	4	2	no	—
457	C₂³	—	4	2	no	—
458	C₂³	—	4	4	no	—
459	C₂³	—	8	2	no	—
460	C₂³	—	8	1	no	—
461	C₂³	C₂²×D₄	1	1	yes	characteristic
462	C₂³	C₂²×D₄	1	2	yes	—
463	Q₈	—	2	2	no	—
464	Q₈	—	2	1	no	—
465	Q₈	—	2	1	no	—
466	Q₈	—	4	4	no	—
467	Q₈	—	4	2	no	—
468	Q₈	—	4	2	no	—
469	Q₈	—	8	1	no	—
470	D₄	—	2	4	no	—
471	D₄	—	2	1	no	—
472	D₄	—	2	2	no	—
473	D₄	—	2	1	no	—
474	D₄	—	2	1	no	—
475	D₄	—	2	1	no	—
476	D₄	—	2	1	no	—
477	D₄	—	2	2	no	—
478	D₄	—	4	4	no	—
479	D₄	—	4	2	no	—
480	D₄	—	4	4	no	—
481	D₄	—	4	4	no	—
482	D₄	—	4	4	no	—
483	D₄	—	4	4	no	—
484	D₄	—	4	4	no	—
485	D₄	—	4	2	no	—
486	D₄	—	8	2	no	—
487	D₄	—	8	1	no	—
488	D₄	—	8	1	no	—
489	D₄	AGL(1,ℤ/8)	1	4	yes	—
490	D₄	2₋¹⁺⁴	1	2	yes	—
491	C₂×C₄	—	2	4	no	—
492	C₂×C₄	—	2	2	no	—
493	C₂×C₄	—	2	2	no	—
494	C₂×C₄	—	2	1	no	—
495	C₂×C₄	—	2	2	no	—
496	C₂×C₄	—	2	1	no	—
497	C₂×C₄	—	2	1	no	—
498	C₂×C₄	—	2	2	no	—
499	C₂×C₄	—	2	2	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	—	4	2	no	—
506	C₂×C₄	—	4	1	no	—
507	C₂×C₄	—	4	2	no	—
508	C₂×C₄	—	4	4	no	—
509	C₂×C₄	—	4	4	no	—
510	C₂×C₄	—	4	2	no	—
511	C₂×C₄	—	4	4	no	—
512	C₂×C₄	—	4	2	no	—
513	C₂×C₄	—	4	4	no	—
514	C₂×C₄	—	4	4	no	—
515	C₂×C₄	—	4	2	no	—
516	C₂×C₄	—	4	2	no	—
517	C₂×C₄	—	4	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	2	yes	—
522	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
523	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
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	C₂⁵	1	1	yes	characteristic
529	C₈	—	2	1	no	—
530	C₈	—	2	1	no	—
531	C₈	—	2	1	no	—
532	C₈	—	2	1	no	—
533	C₈	—	2	2	no	—
534	C₈	—	2	2	no	—
535	C₂²	—	2	2	no	—
536	C₂²	—	2	2	no	—
537	C₂²	—	2	1	no	—
538	C₂²	—	2	1	no	—
539	C₂²	—	2	2	no	—
540	C₂²	—	2	1	no	—
541	C₂²	—	4	1	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	—	4	1	no	—
551	C₂²	—	4	1	no	—
552	C₂²	—	8	8	no	—
553	C₂²	—	8	4	no	—
554	C₂²	C₂×AGL(1,ℤ/8)	1	4	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	2	no	—
560	C₄	—	2	1	no	—
561	C₄	—	2	1	no	—
562	C₄	—	2	2	no	—
563	C₄	—	4	1	no	—
564	C₄	—	4	2	no	—
565	C₄	—	4	1	no	—
566	C₄	—	4	1	no	—
567	C₄	—	4	1	no	—
568	C₄	—	4	2	no	—
569	C₄	—	4	1	no	—
570	C₄	—	4	2	no	—
571	C₄	C₂×AGL(1,ℤ/8)	1	2	yes	—
572	C₄	C₂×2₋¹⁺⁴	1	1	yes	characteristic
573	C₄	#585	1	1	yes	characteristic
574	C₂	—	2	4	no	—
575	C₂	—	4	1	no	—
576	C₂	—	4	2	no	—
577	C₂	—	8	1	no	—
578	C₂	—	8	2	no	—
579	C₂	—	8	1	no	—
580	C₂	#3489	1	1	yes	characteristic
581	C₂	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
582	C₂	#3584	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. #3515	C₂	semidirect
2. D₄×#41	C₂	semidirect
3. #3386	C₂	semidirect
4. #3384	C₂	semidirect
5. #3368	C₂	semidirect
6. #3366	C₂	semidirect
7. #3345	C₂	semidirect
8. #3343	C₂	semidirect
9. #3335	C₂	semidirect
10. #3334	C₂	semidirect
11. #3318	C₂	semidirect
12. #3310	C₂	semidirect
13. #3295	C₂	semidirect
14. #3294	C₂	semidirect
15. #3251	C₂	semidirect
16. #3247	C₂	semidirect
17. #3234	C₂	semidirect
18. #3228	C₂	semidirect
19. #3114	C₂	semidirect
20. #3105	C₂	semidirect
21. #3077	C₂	semidirect
22. C₂×#478	C₂	semidirect
23. #2990	C₂	semidirect
25. #557	C₂²	semidirect
26. #554	C₂²	semidirect
27. #554	C₂²	semidirect
28. #553	C₂²	semidirect
31. #552	C₂²	semidirect
38. #547	C₂²	semidirect
45. #533	C₂²	semidirect
48. #529	C₂²	semidirect
49. #529	C₂²	semidirect
50. C₂×#125	C₂²	semidirect
57. #501	C₂²	semidirect
58. #501	C₂²	semidirect
59. #500	C₂²	semidirect
60. #498	C₂²	semidirect
61. #490	C₂²	semidirect
62. #490	C₂²	semidirect
63. #486	C₂²	semidirect
64. #486	C₂²	semidirect
65. #484	C₂²	semidirect
66. #483	C₂²	semidirect
67. #482	C₂²	semidirect
68. #482	C₂²	semidirect
69. #481	C₂²	semidirect
70. #481	C₂²	semidirect
71. #481	C₂²	semidirect
72. #480	C₂²	semidirect
73. #480	C₂²	semidirect
74. #480	C₂²	semidirect
79. #478	C₂²	semidirect
80. #478	C₂²	semidirect
81. #478	C₂²	semidirect
82. #478	C₂²	semidirect
83. #478	C₂²	semidirect
84. #478	C₂²	semidirect
85. #478	C₂²	semidirect
86. #477	C₂²	semidirect
88. #476	C₂²	semidirect
89. #476	C₂²	semidirect
90. #475	C₂²	semidirect
92. #474	C₂²	semidirect
93. #474	C₂²	semidirect
94. #469	C₂²	semidirect
95. #468	C₂²	semidirect
96. #466	C₂²	semidirect
97. #466	C₂²	semidirect
98. #465	C₂²	semidirect
99. #465	C₂²	semidirect
101. #463	C₂²	semidirect
102. #463	C₂²	semidirect
103. #460	C₂²	semidirect
104. #460	C₂²	semidirect
105. #459	C₂²	semidirect
106. #459	C₂²	semidirect
111. #446	C₂²	semidirect
112. #446	C₂²	semidirect
114. #442	C₂²	semidirect
116. #440	C₂²	semidirect
118. C₄×SD₁₆	C₂²	semidirect
120. C₄×D₈	C₂²	semidirect
121. #435	C₂²	semidirect
122. #435	C₂²	semidirect
123. C₈×D₄	C₂²	semidirect
124. C₈×D₄	C₂²	semidirect
125. #432	C₂²	semidirect
126. #431	C₂²	semidirect
127. #428	C₂²	semidirect
128. C₂×#107	C₂²	semidirect
129. C₂×#106	C₂²	semidirect
130. #423	C₂²	semidirect
131. 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
#3515	2
D₄×#41	2
#3386	2
#3384	2
#3368	2
#3366	2
#3345	2
#3343	2
#3335	2
#3334	2
#3318	2
#3310	2
#3295	2
#3294	2
#3251	2
#3247	2
#3234	2
#3228	2
#3114	2
#3105	2
#3077	2
C₂×#478	2
#2990	2