Subgroups — #60595

Order 256.

1007 conjugacy classes of subgroups.

The subgroup lattice has 577 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	C₄×2₋¹⁺⁴	C₂	1	1	yes	maximal, characteristic, complemented
3	#3125	C₂	1	2	yes	maximal, complemented
4	#3124	C₂	1	2	yes	maximal, complemented
5	#3121	C₂	1	2	yes	maximal, complemented
6	#3121	C₂	1	2	yes	maximal, complemented
7	#3117	C₂	1	2	yes	maximal, complemented
8	#3111	C₂	1	2	yes	maximal, complemented
9	#3108	C₂	1	2	yes	maximal, complemented
10	#3102	C₂	1	2	yes	maximal, complemented
11	#3097	C₂	1	1	yes	maximal, characteristic, complemented
12	#3096	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	#3040	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#464	C₂	1	1	yes	maximal, characteristic, complemented
17	#3011	C₂	1	1	yes	maximal, characteristic, complemented
18	#3010	C₂	1	1	yes	maximal, characteristic
19	#2950	C₂	1	1	yes	maximal, characteristic, complemented
20	#2949	C₂	1	1	yes	maximal, characteristic, complemented
21	#2947	C₂	1	1	yes	maximal, characteristic, complemented
22	#2946	C₂	1	1	yes	maximal, characteristic, complemented
23	#2925	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×2₋¹⁺⁴	C₂²	1	1	yes	characteristic
25	C₂×#137	C₂²	1	1	yes	characteristic
26	C₂×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
27	C₂²×Q₁₆	C₂²	1	1	yes	characteristic
28	C₂²×SD₁₆	C₂²	1	1	yes	characteristic
29	#559	—	2	1	no	—
30	#559	—	2	1	no	—
31	#556	—	2	1	no	—
32	#556	—	2	1	no	—
33	#551	—	2	2	no	—
34	#551	—	2	2	no	—
35	#542	C₂²	1	2	yes	—
36	#542	C₂²	1	2	yes	—
37	#536	C₂²	1	1	yes	characteristic
38	#535	C₂²	1	1	yes	characteristic
39	#533	C₂²	1	1	yes	characteristic
40	#529	C₂²	1	2	yes	—
41	#529	C₂²	1	2	yes	—
42	C₂×#124	C₂²	1	1	yes	characteristic
43	#520	—	2	2	no	—
44	#520	—	2	1	no	—
45	#520	C₂²	1	1	yes	characteristic
46	#520	C₂²	1	1	yes	characteristic
47	#520	C₂²	1	2	yes	complemented
48	#519	—	2	1	no	—
49	#519	C₂²	1	1	yes	characteristic
50	#519	C₂²	1	1	yes	characteristic
51	#519	C₂²	1	2	yes	complemented
52	#518	C₂²	1	1	yes	characteristic
53	C₄×#41	—	2	2	no	—
54	C₄×#41	—	2	1	no	—
55	C₄×#41	C₂²	1	1	yes	characteristic
56	C₄×#41	C₂²	1	1	yes	characteristic
57	C₄×#41	C₂²	1	2	yes	complemented
58	C₂×C₄×Q₈	—	2	1	no	—
59	C₂×C₄×Q₈	C₂²	1	1	yes	characteristic
60	C₂×C₄×Q₈	C₂²	1	2	yes	complemented
61	#485	C₂²	1	2	yes	complemented
62	#485	C₂²	1	2	yes	complemented
63	#484	C₂²	1	2	yes	complemented
64	#483	C₂²	1	2	yes	complemented
65	#482	C₂²	1	2	yes	—
66	#482	C₂²	1	2	yes	—
67	#481	C₂²	1	2	yes	—
68	#480	C₂²	1	2	yes	—
69	#479	C₂²	1	1	yes	characteristic, complemented
70	#479	C₂²	1	1	yes	characteristic, complemented
71	#479	C₂²	1	2	yes	complemented
72	#479	C₂²	1	2	yes	complemented
73	#478	C₂²	1	1	yes	characteristic, complemented
74	#478	C₂²	1	1	yes	characteristic, complemented
75	#477	C₂²	1	1	yes	characteristic, complemented
76	#477	C₂²	1	2	yes	complemented
77	#476	C₂²	1	1	yes	characteristic, 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	#464	C₂²	1	2	yes	—
82	#464	C₂²	1	2	yes	—
83	#464	C₂²	1	2	yes	—
84	#464	C₂²	1	2	yes	—
85	#464	C₂²	1	2	yes	—
86	#464	C₂²	1	2	yes	—
87	#463	C₂²	1	2	yes	—
88	#463	C₂²	1	2	yes	—
89	#452	C₂²	1	2	yes	complemented
90	#452	C₂²	1	2	yes	complemented
91	#451	C₂²	1	2	yes	complemented
92	#451	C₂²	1	2	yes	complemented
93	#449	C₂²	1	2	yes	—
94	#449	C₂²	1	2	yes	—
95	#448	C₂²	1	2	yes	—
96	#448	C₂²	1	2	yes	—
97	#442	C₂²	1	2	yes	—
98	#441	C₂²	1	2	yes	complemented
99	#441	C₂²	1	2	yes	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	complemented
105	C₄×Q₁₆	C₂²	1	2	yes	complemented
106	C₄×Q₁₆	C₂²	1	2	yes	complemented
107	C₄×Q₁₆	C₂²	1	2	yes	complemented
108	C₄×SD₁₆	C₂²	1	2	yes	—
109	C₄×SD₁₆	C₂²	1	2	yes	—
110	C₄×SD₁₆	C₂²	1	2	yes	—
111	C₄×SD₁₆	C₂²	1	2	yes	complemented
112	C₄×D₈	C₂²	1	2	yes	—
113	#433	C₂²	1	2	yes	complemented
114	#433	C₂²	1	2	yes	complemented
115	#432	C₂²	1	2	yes	complemented
116	#431	C₂²	1	2	yes	complemented
117	#428	C₂²	1	1	yes	characteristic
118	#428	C₂²	1	1	yes	characteristic
119	#427	C₂²	1	1	yes	characteristic
120	#427	C₂²	1	1	yes	characteristic
121	#423	C₂²	1	1	yes	characteristic
122	C₂×C₄⋊C₈	C₂²	1	1	yes	characteristic
123	#419	C₂²	1	1	yes	characteristic
124	#419	C₂²	1	1	yes	characteristic
125	#419	C₂²	1	1	yes	characteristic
126	#418	C₂²	1	1	yes	characteristic
127	#416	C₂²	1	1	yes	characteristic
128	#416	C₂²	1	1	yes	characteristic
129	C₂×#103	C₂²	1	1	yes	characteristic
130	C₂×#102	C₂²	1	1	yes	characteristic
131	#408	C₂²	1	1	yes	characteristic
132	#408	C₂²	1	1	yes	characteristic
133	#405	C₂²	1	1	yes	characteristic
134	#405	C₂²	1	1	yes	characteristic
135	2₋¹⁺⁴	—	2	4	no	—
136	2₋¹⁺⁴	—	2	4	no	—
137	C₂×#41	—	2	2	no	—
138	C₂×#41	—	2	1	no	—
139	C₂×#41	C₂³	1	2	yes	—
140	C₂×#41	C₂³	1	1	yes	characteristic
141	C₂×#41	C₂³	1	1	yes	characteristic
142	C₂²×Q₈	—	2	1	no	—
143	C₂²×Q₈	C₂³	1	2	yes	—
144	C₂²×Q₈	C₂³	1	1	yes	characteristic
145	C₂²×Q₈	C₂³	1	1	yes	characteristic
146	C₂²×D₄	C₂³	1	1	yes	characteristic
147	#137	—	2	4	no	—
148	AGL(1,ℤ/8)	—	2	4	no	—
149	C₂×Q₁₆	—	2	4	no	—
150	C₂×Q₁₆	C₂³	1	2	yes	—
151	C₂×Q₁₆	C₂³	1	2	yes	—
152	C₂×Q₁₆	C₂³	1	2	yes	—
153	C₂×SD₁₆	—	2	4	no	—
154	C₂×SD₁₆	C₂³	1	2	yes	—
155	C₂×SD₁₆	C₂³	1	2	yes	—
156	C₂×SD₁₆	C₂³	1	2	yes	—
157	C₂×SD₁₆	C₂³	1	2	yes	—
158	C₂×D₈	C₂³	1	2	yes	—
159	C₂×M₁₆	C₂³	1	1	yes	characteristic
160	C₂×M₁₆	C₂³	1	1	yes	characteristic
161	C₂²×C₈	C₂³	1	1	yes	characteristic
162	C₂²×C₈	C₂³	1	1	yes	characteristic
163	C₄⋊Q₈	—	2	1	no	—
164	C₄⋊Q₈	C₂³	1	1	yes	characteristic
165	C₄⋊Q₈	C₂³	1	1	yes	characteristic
166	#127	—	2	1	no	—
167	#126	—	2	2	no	—
168	#126	—	2	2	no	—
169	#126	—	2	2	no	—
170	#126	—	2	2	no	—
171	#125	C₂³	1	1	yes	characteristic
172	#125	C₂³	1	1	yes	characteristic
173	#124	—	2	1	no	—
174	#124	—	2	1	no	—
175	#124	—	2	2	no	—
176	#124	—	2	2	no	—
177	#124	—	2	1	no	—
178	#124	—	2	1	no	—
179	#124	C₂³	1	2	yes	—
180	#124	C₂³	1	2	yes	—
181	#123	—	2	2	no	—
182	#123	—	2	2	no	—
183	#123	—	2	2	no	—
184	#123	—	2	2	no	—
185	#123	—	2	2	no	—
186	C₂²⋊Q₈	—	2	1	no	—
187	C₂²⋊Q₈	—	2	1	no	—
188	C₂²⋊Q₈	—	2	2	no	—
189	C₂²⋊Q₈	—	2	2	no	—
190	C₂²⋊Q₈	C₂³	1	2	yes	—
191	C₂²⋊Q₈	C₂³	1	2	yes	—
192	#121	C₂³	1	2	yes	—
193	#121	C₂³	1	2	yes	—
194	#120	—	2	2	no	—
195	C₄×Q₈	—	2	1	no	—
196	C₄×Q₈	—	2	1	no	—
197	C₄×Q₈	—	2	2	no	—
198	C₄×Q₈	—	2	1	no	—
199	C₄×Q₈	—	2	2	no	—
200	C₄×Q₈	—	2	1	no	—
201	C₄×Q₈	—	2	1	no	—
202	C₄×Q₈	—	2	1	no	—
203	C₄×Q₈	—	2	2	no	—
204	C₄×Q₈	—	2	1	no	—
205	C₄×Q₈	—	2	2	no	—
206	C₄×Q₈	—	2	1	no	—
207	C₄×Q₈	—	2	1	no	—
208	C₄×Q₈	D₄	1	1	yes	characteristic
209	C₄×Q₈	D₄	1	1	yes	characteristic
210	C₄×Q₈	C₂³	1	2	yes	—
211	C₄×Q₈	C₂³	1	2	yes	—
212	C₄×Q₈	C₂³	1	1	yes	characteristic
213	C₄×Q₈	C₂³	1	2	yes	—
214	C₄×Q₈	C₂³	1	2	yes	—
215	C₄×Q₈	C₂³	1	1	yes	characteristic
216	C₄×Q₈	C₂³	1	2	yes	—
217	C₄×Q₈	C₂³	1	2	yes	—
218	C₄×Q₈	C₂³	1	2	yes	—
219	C₄×D₄	—	2	2	no	—
220	C₄×D₄	—	2	1	no	—
221	C₄×D₄	—	2	1	no	—
222	C₄×D₄	—	2	2	no	—
223	C₄×D₄	—	2	1	no	—
224	C₄×D₄	—	2	2	no	—
225	C₄×D₄	—	2	2	no	—
226	C₄×D₄	—	2	2	no	—
227	C₄×D₄	—	2	1	no	—
228	C₄×D₄	—	2	1	no	—
229	C₄×D₄	—	2	2	no	—
230	C₄×D₄	—	2	2	no	—
231	C₄×D₄	—	2	2	no	—
232	C₄×D₄	D₄	1	2	yes	—
233	C₄×D₄	D₄	1	1	yes	characteristic
234	C₄×D₄	D₄	1	2	yes	—
235	C₄×D₄	D₄	1	1	yes	characteristic
236	C₄×D₄	C₂³	1	1	yes	characteristic
237	C₄×D₄	C₂³	1	1	yes	characteristic
238	C₄×D₄	C₂³	1	2	yes	—
239	C₄×D₄	C₂³	1	2	yes	—
240	C₄×D₄	C₂³	1	2	yes	—
241	#117	—	2	1	no	—
242	#117	—	2	2	no	—
243	#117	—	2	2	no	—
244	#117	—	2	2	no	—
245	#117	—	2	2	no	—
246	#117	—	2	2	no	—
247	#117	—	2	1	no	—
248	#117	—	2	2	no	—
249	#117	—	2	2	no	—
250	#117	—	2	2	no	—
251	#117	C₂³	1	1	yes	characteristic
252	#117	C₂³	1	2	yes	—
253	#117	C₂³	1	1	yes	characteristic
254	#117	C₂³	1	1	yes	characteristic
255	#117	C₂³	1	1	yes	characteristic
256	#117	C₂³	1	2	yes	—
257	C₂×C₄⋊C₄	—	2	1	no	—
258	C₂×C₄⋊C₄	—	2	2	no	—
259	C₂×C₄⋊C₄	—	2	1	no	—
260	C₂×C₄⋊C₄	—	2	2	no	—
261	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
262	C₂×C₄⋊C₄	C₂³	1	2	yes	—
263	C₂×C₂²⋊C₄	—	2	1	no	—
264	C₂×C₂²⋊C₄	—	2	1	no	—
265	C₂×C₂²⋊C₄	—	2	2	no	—
266	C₂×C₄²	—	2	1	no	—
267	C₂×C₄²	—	2	2	no	—
268	C₂×C₄²	—	2	1	no	—
269	C₂×C₄²	—	2	2	no	—
270	C₂×C₄²	C₂³	1	1	yes	characteristic
271	C₂×C₄²	C₂³	1	2	yes	—
272	#107	C₂³	1	1	yes	characteristic
273	#107	C₂³	1	1	yes	characteristic
274	#107	C₂³	1	1	yes	characteristic
275	#107	C₂³	1	1	yes	characteristic
276	#107	C₂³	1	2	yes	—
277	#107	C₂³	1	2	yes	—
278	#106	C₂³	1	1	yes	characteristic
279	#106	C₂³	1	1	yes	characteristic
280	#106	C₂³	1	1	yes	characteristic
281	#106	C₂³	1	1	yes	characteristic
282	#106	C₂³	1	2	yes	—
283	#106	C₂³	1	2	yes	—
284	C₄⋊C₈	C₂³	1	1	yes	characteristic
285	C₄⋊C₈	C₂³	1	1	yes	characteristic
286	C₄⋊C₈	C₂³	1	1	yes	characteristic
287	C₄⋊C₈	C₂³	1	1	yes	characteristic
288	C₄⋊C₈	C₂³	1	2	yes	—
289	C₄⋊C₈	C₂³	1	2	yes	—
290	#103	C₂³	1	2	yes	—
291	#103	C₂³	1	2	yes	—
292	#103	C₂³	1	1	yes	characteristic
293	#103	C₂³	1	1	yes	characteristic
294	#103	C₂³	1	1	yes	characteristic
295	#103	C₂³	1	1	yes	characteristic
296	#103	C₂³	1	2	yes	—
297	#103	C₂³	1	2	yes	—
298	#103	C₂³	1	2	yes	—
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	1	yes	characteristic
306	#102	C₂³	1	1	yes	characteristic
307	#102	C₂³	1	1	yes	characteristic
308	#102	C₂³	1	2	yes	—
309	#102	C₂³	1	2	yes	—
310	C₂²⋊C₈	C₂³	1	2	yes	—
311	C₂²⋊C₈	C₂³	1	2	yes	—
312	C₂²⋊C₈	C₂³	1	2	yes	—
313	C₂²⋊C₈	C₂³	1	2	yes	—
314	#97	C₂³	1	2	yes	—
315	#97	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	16	no	—
320	#41	—	2	8	no	—
321	#41	—	2	4	no	—
322	#41	—	2	4	no	—
323	#41	—	2	2	no	—
324	#41	—	2	2	no	—
325	#41	—	2	2	no	—
326	#41	#41	1	4	yes	—
327	C₂×Q₈	—	2	8	no	—
328	C₂×Q₈	—	2	4	no	—
329	C₂×Q₈	—	2	4	no	—
330	C₂×Q₈	—	2	2	no	—
331	C₂×Q₈	—	2	1	no	—
332	C₂×Q₈	—	2	1	no	—
333	C₂×Q₈	—	2	1	no	—
334	C₂×Q₈	—	2	1	no	—
335	C₂×Q₈	—	2	2	no	—
336	C₂×Q₈	—	2	2	no	—
337	C₂×Q₈	—	2	2	no	—
338	C₂×Q₈	C₂×D₄	1	1	yes	characteristic
339	C₂×Q₈	#41	1	4	yes	—
340	C₂×Q₈	C₂⁴	1	2	yes	—
341	C₂×Q₈	C₂⁴	1	1	yes	characteristic
342	C₂×Q₈	C₂⁴	1	2	yes	—
343	C₂×D₄	—	2	2	no	—
344	C₂×D₄	—	2	1	no	—
345	C₂×D₄	—	2	2	no	—
346	C₂×D₄	—	2	2	no	—
347	C₂×D₄	—	2	1	no	—
348	C₂×D₄	—	2	2	no	—
349	C₂×D₄	—	2	2	no	—
350	C₂×D₄	C₂×D₄	1	2	yes	—
351	C₂×D₄	C₂×D₄	1	1	yes	characteristic
352	C₂×D₄	C₂⁴	1	2	yes	—
353	C₂×D₄	C₂⁴	1	1	yes	characteristic
354	C₂²×C₄	—	2	2	no	—
355	C₂²×C₄	—	2	1	no	—
356	C₂²×C₄	—	2	2	no	—
357	C₂²×C₄	—	2	1	no	—
358	C₂²×C₄	—	2	1	no	—
359	C₂²×C₄	—	2	2	no	—
360	C₂²×C₄	—	2	1	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	—	2	2	no	—
366	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
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	C₂⁴	1	2	yes	—
371	C₂²×C₄	C₂⁴	1	1	yes	characteristic
372	Q₁₆	—	2	4	no	—
373	Q₁₆	—	2	4	no	—
374	Q₁₆	—	2	4	no	—
375	SD₁₆	—	2	4	no	—
376	SD₁₆	—	2	4	no	—
377	SD₁₆	—	2	4	no	—
378	SD₁₆	—	2	4	no	—
379	D₈	—	2	4	no	—
380	M₁₆	—	2	2	no	—
381	M₁₆	—	2	2	no	—
382	C₂×C₈	—	2	2	no	—
383	C₂×C₈	—	2	2	no	—
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	C₂×C₈	C₂⁴	1	1	yes	characteristic
389	C₂×C₈	C₂⁴	1	1	yes	characteristic
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	1	no	—
395	C₄⋊C₄	—	2	2	no	—
396	C₄⋊C₄	—	2	1	no	—
397	C₄⋊C₄	—	2	2	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	1	no	—
406	C₄⋊C₄	—	2	1	no	—
407	C₄⋊C₄	—	2	1	no	—
408	C₄⋊C₄	—	2	1	no	—
409	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
410	C₄⋊C₄	C₂×D₄	1	2	yes	—
411	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
412	C₄⋊C₄	C₂×D₄	1	2	yes	—
413	C₄⋊C₄	C₂⁴	1	2	yes	—
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	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
418	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
419	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
420	C₂²⋊C₄	—	2	1	no	—
421	C₂²⋊C₄	—	2	2	no	—
422	C₂²⋊C₄	—	2	1	no	—
423	C₂²⋊C₄	—	2	1	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	1	no	—
433	C₂²⋊C₄	—	2	2	no	—
434	C₂²⋊C₄	—	2	1	no	—
435	C₂²⋊C₄	—	2	2	no	—
436	C₂²⋊C₄	—	2	2	no	—
437	C₂²⋊C₄	C₂×D₄	1	2	yes	—
438	C₂²⋊C₄	C₂×D₄	1	2	yes	—
439	C₂²⋊C₄	C₂×D₄	1	2	yes	—
440	C₄²	—	2	2	no	—
441	C₄²	—	2	1	no	—
442	C₄²	—	2	2	no	—
443	C₄²	—	2	1	no	—
444	C₄²	—	2	2	no	—
445	C₄²	—	2	2	no	—
446	C₄²	—	2	2	no	—
447	C₄²	—	2	2	no	—
448	C₄²	—	2	1	no	—
449	C₄²	—	2	2	no	—
450	C₄²	—	2	2	no	—
451	C₄²	—	2	1	no	—
452	C₄²	—	2	1	no	—
453	C₄²	C₂×D₄	1	2	yes	—
454	C₄²	C₂×D₄	1	1	yes	characteristic
455	C₄²	C₂×D₄	1	2	yes	—
456	C₄²	C₂×D₄	1	1	yes	characteristic
457	C₄²	C₂⁴	1	2	yes	—
458	C₄²	C₂⁴	1	1	yes	characteristic
459	C₄²	C₂⁴	1	1	yes	characteristic
460	C₂³	—	2	1	no	—
461	C₂³	—	2	2	no	—
462	C₂³	—	4	2	no	—
463	C₂³	—	8	1	no	—
464	C₂³	—	8	1	no	—
465	C₂³	C₂²×D₄	1	2	yes	—
466	C₂³	C₂²×D₄	1	1	yes	characteristic
467	Q₈	—	2	8	no	—
468	Q₈	—	2	2	no	—
469	Q₈	—	2	4	no	—
470	Q₈	—	2	1	no	—
471	Q₈	—	2	2	no	—
472	Q₈	—	2	2	no	—
473	Q₈	—	2	2	no	—
474	Q₈	—	4	2	no	—
475	Q₈	—	8	1	no	—
476	Q₈	—	8	1	no	—
477	Q₈	C₂×#41	1	2	yes	—
478	Q₈	C₂×#41	1	4	yes	—
479	D₄	—	2	8	no	—
480	D₄	—	2	4	no	—
481	D₄	—	2	4	no	—
482	D₄	—	2	2	no	—
483	D₄	—	2	1	no	—
484	D₄	—	2	2	no	—
485	D₄	—	2	2	no	—
486	D₄	—	4	2	no	—
487	D₄	—	8	2	no	—
488	D₄	—	8	2	no	—
489	D₄	C₂×#41	1	2	yes	—
490	C₂×C₄	—	2	8	no	—
491	C₂×C₄	—	2	8	no	—
492	C₂×C₄	—	2	4	no	—
493	C₂×C₄	—	2	2	no	—
494	C₂×C₄	—	2	1	no	—
495	C₂×C₄	—	2	4	no	—
496	C₂×C₄	—	2	2	no	—
497	C₂×C₄	—	2	2	no	—
498	C₂×C₄	—	2	1	no	—
499	C₂×C₄	—	2	2	no	—
500	C₂×C₄	—	2	1	no	—
501	C₂×C₄	—	2	1	no	—
502	C₂×C₄	—	2	1	no	—
503	C₂×C₄	—	2	2	no	—
504	C₂×C₄	—	2	1	no	—
505	C₂×C₄	—	2	1	no	—
506	C₂×C₄	—	4	2	no	—
507	C₂×C₄	—	4	1	no	—
508	C₂×C₄	—	4	2	no	—
509	C₂×C₄	—	4	1	no	—
510	C₂×C₄	—	4	2	no	—
511	C₂×C₄	—	4	2	no	—
512	C₂×C₄	—	8	2	no	—
513	C₂×C₄	—	8	2	no	—
514	C₂×C₄	—	8	1	no	—
515	C₂×C₄	—	8	2	no	—
516	C₂×C₄	—	8	1	no	—
517	C₂×C₄	—	8	2	no	—
518	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
519	C₂×C₄	C₂²×D₄	1	2	yes	—
520	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
521	C₂×C₄	C₂²×D₄	1	2	yes	—
522	C₂×C₄	C₂²×D₄	1	2	yes	—
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	C₂×#41	1	2	yes	—
527	C₂×C₄	C₂×#41	1	2	yes	—
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	1	no	—
536	C₂²	—	2	1	no	—
537	C₂²	—	2	2	no	—
538	C₂²	—	2	2	no	—
539	C₂²	—	2	2	no	—
540	C₂²	—	2	2	no	—
541	C₂²	—	4	1	no	—
542	C₂²	—	4	1	no	—
543	C₂²	—	4	2	no	—
544	C₂²	—	4	2	no	—
545	C₂²	—	4	2	no	—
546	C₂²	—	16	2	no	—
547	C₂²	#525	1	2	yes	—
548	C₂²	C₂³×D₄	1	1	yes	characteristic
549	C₄	—	2	1	no	—
550	C₄	—	2	2	no	—
551	C₄	—	2	1	no	—
552	C₄	—	2	1	no	—
553	C₄	—	2	2	no	—
554	C₄	—	2	1	no	—
555	C₄	—	2	4	no	—
556	C₄	—	2	2	no	—
557	C₄	—	2	2	no	—
558	C₄	—	4	2	no	—
559	C₄	—	4	1	no	—
560	C₄	—	4	1	no	—
561	C₄	—	4	1	no	—
562	C₄	—	4	1	no	—
563	C₄	—	4	1	no	—
564	C₄	—	4	1	no	—
565	C₄	—	4	2	no	—
566	C₄	#525	1	2	yes	—
567	C₄	C₂²×#41	1	1	yes	characteristic
568	C₄	C₂²×#41	1	1	yes	characteristic
569	C₂	—	2	2	no	—
570	C₂	—	4	2	no	—
571	C₂	—	4	2	no	—
572	C₂	—	8	2	no	—
573	C₂	C₂×#525	1	1	yes	characteristic
574	C₂	#3584	1	1	yes	characteristic
575	C₂	#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵
prime radical	#3010	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. C₄×2₋¹⁺⁴	C₂	semidirect
3. #3125	C₂	semidirect
4. #3124	C₂	semidirect
5. #3121	C₂	semidirect
6. #3121	C₂	semidirect
7. #3117	C₂	semidirect
8. #3111	C₂	semidirect
9. #3108	C₂	semidirect
10. #3102	C₂	semidirect
11. #3097	C₂	semidirect
12. #3096	C₂	semidirect
13. #3078	C₂	semidirect
14. #3076	C₂	semidirect
15. #3040	C₂	semidirect
16. C₂×#464	C₂	semidirect
17. #3011	C₂	semidirect
19. #2950	C₂	semidirect
20. #2949	C₂	semidirect
21. #2947	C₂	semidirect
22. #2946	C₂	semidirect
23. #2925	C₂	semidirect
47. #520	C₂²	semidirect
51. #519	C₂²	semidirect
57. C₄×#41	C₂²	semidirect
60. C₂×C₄×Q₈	C₂²	semidirect
61. #485	C₂²	semidirect
62. #485	C₂²	semidirect
63. #484	C₂²	semidirect
64. #483	C₂²	semidirect
69. #479	C₂²	semidirect
70. #479	C₂²	semidirect
71. #479	C₂²	semidirect
72. #479	C₂²	semidirect
73. #478	C₂²	semidirect
74. #478	C₂²	semidirect
75. #477	C₂²	semidirect
76. #477	C₂²	semidirect
77. #476	C₂²	semidirect
78. #475	C₂²	semidirect
79. #475	C₂²	semidirect
80. #474	C₂²	semidirect
89. #452	C₂²	semidirect
90. #452	C₂²	semidirect
91. #451	C₂²	semidirect
92. #451	C₂²	semidirect
98. #441	C₂²	semidirect
99. #441	C₂²	semidirect
100. #441	C₂²	semidirect
104. #440	C₂²	semidirect
105. C₄×Q₁₆	C₂²	semidirect
106. C₄×Q₁₆	C₂²	semidirect
107. C₄×Q₁₆	C₂²	semidirect
111. C₄×SD₁₆	C₂²	semidirect
113. #433	C₂²	semidirect
114. #433	C₂²	semidirect
115. #432	C₂²	semidirect
116. #431	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
C₄×2₋¹⁺⁴	2
#3125	2
#3124	2
#3121	2
#3117	2
#3111	2
#3108	2
#3102	2
#3097	2
#3096	2
#3078	2
#3076	2
#3040	2
C₂×#464	2
#3011	2
#3010	2
#2950	2
#2949	2
#2947	2
#2946	2
#2925	2