Subgroups — #60592

Order 256.

1049 conjugacy classes of subgroups.

The subgroup lattice has 592 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×H(5,𝔽₂)	C₂	1	1	yes	maximal, characteristic, complemented
3	#3125	C₂	1	2	yes	maximal, complemented
4	#3124	C₂	1	2	yes	maximal, complemented
5	#3118	C₂	1	2	yes	maximal, complemented
6	#3118	C₂	1	2	yes	maximal, complemented
7	#3114	C₂	1	2	yes	maximal, complemented
8	#3111	C₂	1	2	yes	maximal, complemented
9	#3105	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	#3077	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×#463	C₂	1	1	yes	maximal, characteristic, complemented
17	#3009	C₂	1	1	yes	maximal, characteristic, complemented
18	#3008	C₂	1	1	yes	maximal, characteristic
19	#2949	C₂	1	1	yes	maximal, characteristic, complemented
20	#2948	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×H(5,𝔽₂)	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×SD₁₆	C₂²	1	1	yes	characteristic
28	C₂²×D₈	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	complemented
36	#542	C₂²	1	2	yes	complemented
37	#536	C₂²	1	1	yes	characteristic
38	#535	C₂²	1	1	yes	characteristic
39	#533	C₂²	1	1	yes	characteristic, complemented
40	#529	C₂²	1	2	yes	complemented
41	#529	C₂²	1	2	yes	complemented
42	C₂×#124	C₂²	1	1	yes	characteristic, complemented
43	#520	—	2	1	no	—
44	#520	C₂²	1	1	yes	characteristic
45	#520	C₂²	1	1	yes	characteristic
46	#520	C₂²	1	2	yes	complemented
47	#519	C₂²	1	1	yes	characteristic, complemented
48	#518	—	2	2	no	—
49	#518	—	2	1	no	—
50	#518	C₂²	1	1	yes	characteristic
51	#518	C₂²	1	2	yes	complemented
52	#518	C₂²	1	1	yes	characteristic, complemented
53	C₄×#41	—	2	1	no	—
54	C₄×#41	C₂²	1	1	yes	characteristic
55	C₄×#41	C₂²	1	1	yes	characteristic
56	C₄×#41	C₂²	1	2	yes	complemented
57	C₂×C₄×D₄	—	2	1	no	—
58	C₂×C₄×D₄	—	2	2	no	—
59	C₂×C₄×D₄	C₂²	1	1	yes	characteristic
60	C₂×C₄×D₄	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	complemented
66	#482	C₂²	1	2	yes	complemented
67	#481	C₂²	1	2	yes	complemented
68	#480	C₂²	1	2	yes	complemented
69	#479	C₂²	1	1	yes	characteristic, complemented
70	#479	C₂²	1	1	yes	characteristic, complemented
71	#478	C₂²	1	1	yes	characteristic, complemented
72	#478	C₂²	1	1	yes	characteristic, complemented
73	#478	C₂²	1	2	yes	complemented
74	#478	C₂²	1	2	yes	complemented
75	#477	C₂²	1	1	yes	characteristic, complemented
76	#476	C₂²	1	1	yes	characteristic, complemented
77	#476	C₂²	1	2	yes	complemented
78	#475	C₂²	1	1	yes	characteristic, complemented
79	#474	C₂²	1	1	yes	characteristic, complemented
80	#474	C₂²	1	2	yes	complemented
81	#464	C₂²	1	2	yes	complemented
82	#464	C₂²	1	2	yes	complemented
83	#463	C₂²	1	2	yes	complemented
84	#463	C₂²	1	2	yes	complemented
85	#463	C₂²	1	2	yes	complemented
86	#463	C₂²	1	2	yes	complemented
87	#463	C₂²	1	2	yes	complemented
88	#463	C₂²	1	2	yes	complemented
89	#452	C₂²	1	2	yes	complemented
90	#452	C₂²	1	2	yes	complemented
91	#450	C₂²	1	2	yes	complemented
92	#450	C₂²	1	2	yes	complemented
93	#449	C₂²	1	2	yes	—
94	#449	C₂²	1	2	yes	—
95	#447	C₂²	1	2	yes	—
96	#447	C₂²	1	2	yes	—
97	#442	C₂²	1	2	yes	complemented
98	#442	C₂²	1	2	yes	complemented
99	#442	C₂²	1	2	yes	complemented
100	#441	C₂²	1	2	yes	complemented
101	#440	C₂²	1	2	yes	complemented
102	#440	C₂²	1	2	yes	complemented
103	#440	C₂²	1	2	yes	complemented
104	#440	C₂²	1	2	yes	complemented
105	C₄×Q₁₆	C₂²	1	2	yes	complemented
106	C₄×SD₁₆	C₂²	1	2	yes	complemented
107	C₄×SD₁₆	C₂²	1	2	yes	complemented
108	C₄×SD₁₆	C₂²	1	2	yes	complemented
109	C₄×SD₁₆	C₂²	1	2	yes	complemented
110	C₄×D₈	C₂²	1	2	yes	complemented
111	C₄×D₈	C₂²	1	2	yes	complemented
112	C₄×D₈	C₂²	1	2	yes	complemented
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, complemented
118	#428	C₂²	1	1	yes	characteristic, complemented
119	#427	C₂²	1	1	yes	characteristic, complemented
120	#427	C₂²	1	1	yes	characteristic, complemented
121	#423	C₂²	1	1	yes	characteristic, complemented
122	C₂×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
123	#419	C₂²	1	1	yes	characteristic, complemented
124	#418	C₂²	1	1	yes	characteristic
125	#418	C₂²	1	1	yes	characteristic
126	#418	C₂²	1	1	yes	characteristic, complemented
127	#416	C₂²	1	1	yes	characteristic
128	#416	C₂²	1	1	yes	characteristic
129	C₂×#103	C₂²	1	1	yes	characteristic, complemented
130	C₂×#102	C₂²	1	1	yes	characteristic, complemented
131	#408	C₂²	1	1	yes	characteristic
132	#408	C₂²	1	1	yes	characteristic
133	#405	C₂²	1	1	yes	characteristic, complemented
134	#405	C₂²	1	1	yes	characteristic, complemented
135	H(5,𝔽₂)	—	2	4	no	—
136	H(5,𝔽₂)	—	2	4	no	—
137	C₂×#41	—	2	1	no	—
138	C₂×#41	C₂³	1	2	yes	—
139	C₂×#41	C₂³	1	1	yes	characteristic
140	C₂×#41	C₂³	1	1	yes	characteristic
141	C₂²×Q₈	C₂³	1	1	yes	characteristic
142	C₂²×D₄	—	2	2	no	—
143	C₂²×D₄	—	2	1	no	—
144	C₂²×D₄	C₂³	1	2	yes	—
145	C₂²×D₄	C₂³	1	1	yes	characteristic
146	C₂²×D₄	C₂³	1	1	yes	characteristic
147	C₂³×C₄	—	2	1	no	—
148	C₂³×C₄	—	2	2	no	—
149	#137	—	2	4	no	—
150	AGL(1,ℤ/8)	—	2	4	no	—
151	C₂×Q₁₆	C₂³	1	2	yes	—
152	C₂×SD₁₆	—	2	4	no	—
153	C₂×SD₁₆	C₂³	1	2	yes	—
154	C₂×SD₁₆	C₂³	1	2	yes	—
155	C₂×SD₁₆	C₂³	1	2	yes	—
156	C₂×SD₁₆	C₂³	1	2	yes	—
157	C₂×D₈	—	2	4	no	—
158	C₂×D₈	C₂³	1	2	yes	—
159	C₂×D₈	C₂³	1	2	yes	—
160	C₂×D₈	C₂³	1	2	yes	—
161	C₂×M₁₆	C₂³	1	1	yes	characteristic
162	C₂×M₁₆	C₂³	1	1	yes	characteristic
163	C₂²×C₈	C₂³	1	1	yes	characteristic
164	C₂²×C₈	C₂³	1	1	yes	characteristic
165	C₄⋊Q₈	—	2	1	no	—
166	C₄⋊Q₈	C₂³	1	1	yes	characteristic
167	C₄⋊Q₈	C₂³	1	1	yes	characteristic
168	#127	—	2	1	no	—
169	#126	—	2	2	no	—
170	#126	—	2	2	no	—
171	#126	—	2	2	no	—
172	#126	—	2	2	no	—
173	#125	C₂³	1	1	yes	characteristic
174	#125	C₂³	1	1	yes	characteristic
175	#124	—	2	1	no	—
176	#124	—	2	1	no	—
177	#124	—	2	2	no	—
178	#124	—	2	2	no	—
179	#124	—	2	1	no	—
180	#124	—	2	1	no	—
181	#124	C₂³	1	2	yes	—
182	#124	C₂³	1	2	yes	—
183	#123	—	2	2	no	—
184	#123	—	2	2	no	—
185	#123	—	2	2	no	—
186	#123	—	2	2	no	—
187	#123	—	2	2	no	—
188	C₂²⋊Q₈	—	2	1	no	—
189	C₂²⋊Q₈	—	2	1	no	—
190	C₂²⋊Q₈	—	2	2	no	—
191	C₂²⋊Q₈	—	2	2	no	—
192	C₂²⋊Q₈	C₂³	1	2	yes	—
193	C₂²⋊Q₈	C₂³	1	2	yes	—
194	#121	C₂³	1	2	yes	—
195	#121	C₂³	1	2	yes	—
196	#120	—	2	2	no	—
197	C₄×Q₈	—	2	1	no	—
198	C₄×Q₈	—	2	1	no	—
199	C₄×Q₈	—	2	1	no	—
200	C₄×Q₈	—	2	1	no	—
201	C₄×Q₈	—	2	1	no	—
202	C₄×Q₈	D₄	1	1	yes	characteristic
203	C₄×Q₈	D₄	1	1	yes	characteristic
204	C₄×Q₈	C₂³	1	1	yes	characteristic
205	C₄×Q₈	C₂³	1	1	yes	characteristic
206	C₄×Q₈	C₂³	1	2	yes	—
207	C₄×Q₈	C₂³	1	2	yes	—
208	C₄×Q₈	C₂³	1	2	yes	—
209	C₄×D₄	—	2	2	no	—
210	C₄×D₄	—	2	1	no	—
211	C₄×D₄	—	2	1	no	—
212	C₄×D₄	—	2	2	no	—
213	C₄×D₄	—	2	1	no	—
214	C₄×D₄	—	2	2	no	—
215	C₄×D₄	—	2	2	no	—
216	C₄×D₄	—	2	2	no	—
217	C₄×D₄	—	2	1	no	—
218	C₄×D₄	—	2	2	no	—
219	C₄×D₄	—	2	1	no	—
220	C₄×D₄	—	2	2	no	—
221	C₄×D₄	—	2	1	no	—
222	C₄×D₄	—	2	1	no	—
223	C₄×D₄	—	2	2	no	—
224	C₄×D₄	—	2	2	no	—
225	C₄×D₄	—	2	2	no	—
226	C₄×D₄	—	2	1	no	—
227	C₄×D₄	—	2	2	no	—
228	C₄×D₄	—	2	1	no	—
229	C₄×D₄	—	2	2	no	—
230	C₄×D₄	D₄	1	2	yes	—
231	C₄×D₄	D₄	1	1	yes	characteristic
232	C₄×D₄	D₄	1	2	yes	—
233	C₄×D₄	D₄	1	1	yes	characteristic
234	C₄×D₄	C₂³	1	2	yes	—
235	C₄×D₄	C₂³	1	2	yes	—
236	C₄×D₄	C₂³	1	1	yes	characteristic
237	C₄×D₄	C₂³	1	2	yes	—
238	C₄×D₄	C₂³	1	2	yes	—
239	C₄×D₄	C₂³	1	1	yes	characteristic
240	C₄×D₄	C₂³	1	2	yes	—
241	C₄×D₄	C₂³	1	2	yes	—
242	C₄×D₄	C₂³	1	2	yes	—
243	#117	—	2	1	no	—
244	#117	—	2	2	no	—
245	#117	—	2	2	no	—
246	#117	—	2	1	no	—
247	#117	—	2	2	no	—
248	#117	—	2	2	no	—
249	#117	—	2	2	no	—
250	#117	C₂³	1	1	yes	characteristic
251	#117	C₂³	1	2	yes	—
252	#117	C₂³	1	1	yes	characteristic
253	#117	C₂³	1	1	yes	characteristic
254	#117	C₂³	1	1	yes	characteristic
255	#117	C₂³	1	2	yes	—
256	C₂×C₄⋊C₄	—	2	1	no	—
257	C₂×C₄⋊C₄	—	2	2	no	—
258	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
259	C₂×C₄⋊C₄	C₂³	1	2	yes	—
260	C₂×C₂²⋊C₄	—	2	1	no	—
261	C₂×C₂²⋊C₄	—	2	2	no	—
262	C₂×C₂²⋊C₄	—	2	1	no	—
263	C₂×C₂²⋊C₄	—	2	1	no	—
264	C₂×C₂²⋊C₄	—	2	2	no	—
265	C₂×C₂²⋊C₄	—	2	2	no	—
266	C₂×C₂²⋊C₄	—	2	2	no	—
267	C₂×C₂²⋊C₄	—	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	#102	C₂³	1	2	yes	—
299	#102	C₂³	1	2	yes	—
300	#102	C₂³	1	1	yes	characteristic
301	#102	C₂³	1	1	yes	characteristic
302	#102	C₂³	1	1	yes	characteristic
303	#102	C₂³	1	1	yes	characteristic
304	#102	C₂³	1	2	yes	—
305	#102	C₂³	1	2	yes	—
306	#102	C₂³	1	2	yes	—
307	#102	C₂³	1	2	yes	—
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	2	no	—
319	C₂⁴	—	2	1	no	—
320	C₂⁴	—	2	1	no	—
321	#41	—	2	8	no	—
322	#41	—	2	4	no	—
323	#41	—	2	4	no	—
324	#41	—	2	2	no	—
325	#41	—	2	2	no	—
326	#41	—	2	2	no	—
327	#41	#41	1	4	yes	—
328	C₂×Q₈	—	2	1	no	—
329	C₂×Q₈	—	2	1	no	—
330	C₂×Q₈	—	2	1	no	—
331	C₂×Q₈	—	2	2	no	—
332	C₂×Q₈	—	2	2	no	—
333	C₂×Q₈	C₂×D₄	1	1	yes	characteristic
334	C₂×Q₈	C₂⁴	1	2	yes	—
335	C₂×Q₈	C₂⁴	1	1	yes	characteristic
336	C₂×D₄	—	2	16	no	—
337	C₂×D₄	—	2	8	no	—
338	C₂×D₄	—	2	2	no	—
339	C₂×D₄	—	2	1	no	—
340	C₂×D₄	—	2	4	no	—
341	C₂×D₄	—	2	4	no	—
342	C₂×D₄	—	2	2	no	—
343	C₂×D₄	—	2	2	no	—
344	C₂×D₄	—	2	2	no	—
345	C₂×D₄	—	2	1	no	—
346	C₂×D₄	—	2	1	no	—
347	C₂×D₄	—	2	2	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	#41	1	4	yes	—
353	C₂×D₄	C₂⁴	1	2	yes	—
354	C₂×D₄	C₂⁴	1	1	yes	characteristic
355	C₂×D₄	C₂⁴	1	2	yes	—
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	2	no	—
364	C₂²×C₄	—	2	1	no	—
365	C₂²×C₄	—	2	2	no	—
366	C₂²×C₄	—	2	2	no	—
367	C₂²×C₄	—	2	2	no	—
368	C₂²×C₄	—	2	2	no	—
369	C₂²×C₄	—	2	2	no	—
370	C₂²×C₄	—	8	2	no	—
371	C₂²×C₄	—	8	4	no	—
372	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
373	C₂²×C₄	C₂×D₄	1	2	yes	—
374	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
375	C₂²×C₄	C₂×D₄	1	2	yes	—
376	C₂²×C₄	C₂⁴	1	2	yes	—
377	C₂²×C₄	C₂⁴	1	1	yes	characteristic
378	Q₁₆	—	2	4	no	—
379	SD₁₆	—	2	4	no	—
380	SD₁₆	—	2	4	no	—
381	SD₁₆	—	2	4	no	—
382	SD₁₆	—	2	4	no	—
383	D₈	—	2	4	no	—
384	D₈	—	2	4	no	—
385	D₈	—	2	4	no	—
386	M₁₆	—	2	2	no	—
387	M₁₆	—	2	2	no	—
388	C₂×C₈	—	2	2	no	—
389	C₂×C₈	—	2	2	no	—
390	C₂×C₈	C₂⁴	1	1	yes	characteristic
391	C₂×C₈	C₂⁴	1	1	yes	characteristic
392	C₂×C₈	C₂⁴	1	2	yes	—
393	C₂×C₈	C₂⁴	1	2	yes	—
394	C₂×C₈	C₂⁴	1	1	yes	characteristic
395	C₂×C₈	C₂⁴	1	1	yes	characteristic
396	C₄⋊C₄	—	2	2	no	—
397	C₄⋊C₄	—	2	1	no	—
398	C₄⋊C₄	—	2	2	no	—
399	C₄⋊C₄	—	2	1	no	—
400	C₄⋊C₄	—	2	1	no	—
401	C₄⋊C₄	—	2	1	no	—
402	C₄⋊C₄	—	2	1	no	—
403	C₄⋊C₄	—	2	2	no	—
404	C₄⋊C₄	—	2	2	no	—
405	C₄⋊C₄	—	2	2	no	—
406	C₄⋊C₄	—	2	2	no	—
407	C₄⋊C₄	—	2	1	no	—
408	C₄⋊C₄	—	2	1	no	—
409	C₄⋊C₄	—	2	1	no	—
410	C₄⋊C₄	—	2	1	no	—
411	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
412	C₄⋊C₄	C₂×D₄	1	2	yes	—
413	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
414	C₄⋊C₄	C₂×D₄	1	2	yes	—
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	2	yes	—
420	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
421	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
422	C₂²⋊C₄	—	2	2	no	—
423	C₂²⋊C₄	—	2	1	no	—
424	C₂²⋊C₄	—	2	1	no	—
425	C₂²⋊C₄	—	2	1	no	—
426	C₂²⋊C₄	—	2	2	no	—
427	C₂²⋊C₄	—	2	2	no	—
428	C₂²⋊C₄	—	2	2	no	—
429	C₂²⋊C₄	—	2	1	no	—
430	C₂²⋊C₄	—	2	2	no	—
431	C₂²⋊C₄	—	2	2	no	—
432	C₂²⋊C₄	—	2	2	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	—	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	—	2	2	no	—
443	C₂²⋊C₄	C₂×D₄	1	2	yes	—
444	C₂²⋊C₄	C₂×D₄	1	2	yes	—
445	C₂²⋊C₄	C₂×D₄	1	2	yes	—
446	C₄²	—	2	1	no	—
447	C₄²	—	2	2	no	—
448	C₄²	—	2	1	no	—
449	C₄²	—	2	2	no	—
450	C₄²	—	2	1	no	—
451	C₄²	—	2	2	no	—
452	C₄²	—	2	2	no	—
453	C₄²	—	2	1	no	—
454	C₄²	—	2	1	no	—
455	C₄²	C₂×D₄	1	2	yes	—
456	C₄²	C₂×D₄	1	1	yes	characteristic
457	C₄²	C₂×D₄	1	2	yes	—
458	C₄²	C₂×D₄	1	1	yes	characteristic
459	C₄²	C₂⁴	1	2	yes	—
460	C₄²	C₂⁴	1	1	yes	characteristic
461	C₄²	C₂⁴	1	1	yes	characteristic
462	C₂³	—	2	8	no	—
463	C₂³	—	2	2	no	—
464	C₂³	—	2	1	no	—
465	C₂³	—	2	4	no	—
466	C₂³	—	2	2	no	—
467	C₂³	—	4	2	no	—
468	C₂³	—	8	1	no	—
469	C₂³	—	8	2	no	—
470	C₂³	—	8	1	no	—
471	C₂³	—	8	2	no	—
472	C₂³	—	8	1	no	—
473	C₂³	—	8	1	no	—
474	C₂³	C₂²×D₄	1	2	yes	—
475	C₂³	C₂²×D₄	1	1	yes	characteristic
476	Q₈	—	2	2	no	—
477	Q₈	—	2	1	no	—
478	Q₈	—	2	2	no	—
479	Q₈	—	2	2	no	—
480	Q₈	—	4	2	no	—
481	Q₈	—	8	1	no	—
482	Q₈	—	8	1	no	—
483	Q₈	C₂×#41	1	2	yes	—
484	D₄	—	2	8	no	—
485	D₄	—	2	8	no	—
486	D₄	—	2	4	no	—
487	D₄	—	2	4	no	—
488	D₄	—	2	2	no	—
489	D₄	—	2	4	no	—
490	D₄	—	2	2	no	—
491	D₄	—	2	1	no	—
492	D₄	—	2	2	no	—
493	D₄	—	2	2	no	—
494	D₄	—	4	2	no	—
495	D₄	—	8	2	no	—
496	D₄	—	8	2	no	—
497	D₄	C₂×#41	1	2	yes	—
498	D₄	C₂×#41	1	4	yes	—
499	C₂×C₄	—	2	8	no	—
500	C₂×C₄	—	2	1	no	—
501	C₂×C₄	—	2	4	no	—
502	C₂×C₄	—	2	2	no	—
503	C₂×C₄	—	2	2	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	—	2	2	no	—
509	C₂×C₄	—	2	1	no	—
510	C₂×C₄	—	2	1	no	—
511	C₂×C₄	—	2	1	no	—
512	C₂×C₄	—	4	2	no	—
513	C₂×C₄	—	4	1	no	—
514	C₂×C₄	—	4	2	no	—
515	C₂×C₄	—	4	1	no	—
516	C₂×C₄	—	4	2	no	—
517	C₂×C₄	—	4	4	no	—
518	C₂×C₄	—	4	2	no	—
519	C₂×C₄	—	8	2	no	—
520	C₂×C₄	—	8	2	no	—
521	C₂×C₄	—	8	1	no	—
522	C₂×C₄	—	8	2	no	—
523	C₂×C₄	—	8	2	no	—
524	C₂×C₄	—	8	2	no	—
525	C₂×C₄	—	8	2	no	—
526	C₂×C₄	—	8	1	no	—
527	C₂×C₄	—	8	2	no	—
528	C₂×C₄	C₂²×D₄	1	2	yes	—
529	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
530	C₂×C₄	C₂²×D₄	1	2	yes	—
531	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
532	C₂×C₄	C₂²×D₄	1	2	yes	—
533	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
534	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
535	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
536	C₂×C₄	C₂×#41	1	2	yes	—
537	C₂×C₄	C₂×#41	1	2	yes	—
538	C₂×C₄	C₂⁵	1	1	yes	characteristic
539	C₈	—	2	1	no	—
540	C₈	—	2	1	no	—
541	C₈	—	2	1	no	—
542	C₈	—	2	1	no	—
543	C₈	—	2	2	no	—
544	C₈	—	2	2	no	—
545	C₂²	—	2	1	no	—
546	C₂²	—	2	1	no	—
547	C₂²	—	2	2	no	—
548	C₂²	—	2	2	no	—
549	C₂²	—	2	2	no	—
550	C₂²	—	2	4	no	—
551	C₂²	—	2	2	no	—
552	C₂²	—	4	2	no	—
553	C₂²	—	4	1	no	—
554	C₂²	—	4	2	no	—
555	C₂²	—	4	1	no	—
556	C₂²	—	4	2	no	—
557	C₂²	—	4	2	no	—
558	C₂²	—	4	2	no	—
559	C₂²	—	8	4	no	—
560	C₂²	—	8	8	no	—
561	C₂²	—	16	2	no	—
562	C₂²	#525	1	2	yes	—
563	C₂²	C₂³×D₄	1	1	yes	characteristic
564	C₄	—	2	1	no	—
565	C₄	—	2	2	no	—
566	C₄	—	2	1	no	—
567	C₄	—	2	1	no	—
568	C₄	—	2	2	no	—
569	C₄	—	2	1	no	—
570	C₄	—	2	2	no	—
571	C₄	—	2	2	no	—
572	C₄	—	4	1	no	—
573	C₄	—	4	1	no	—
574	C₄	—	4	1	no	—
575	C₄	—	4	1	no	—
576	C₄	—	4	2	no	—
577	C₄	—	4	1	no	—
578	C₄	—	4	1	no	—
579	C₄	—	4	2	no	—
580	C₄	#525	1	2	yes	—
581	C₄	C₂²×#41	1	1	yes	characteristic
582	C₄	C₂²×#41	1	1	yes	characteristic
583	C₂	—	2	2	no	—
584	C₂	—	4	2	no	—
585	C₂	—	4	4	no	—
586	C₂	—	4	2	no	—
587	C₂	—	8	2	no	—
588	C₂	C₂×#525	1	1	yes	characteristic
589	C₂	#3584	1	1	yes	characteristic
590	C₂	#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵
prime radical	#3008	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×H(5,𝔽₂)	C₂	semidirect
3. #3125	C₂	semidirect
4. #3124	C₂	semidirect
5. #3118	C₂	semidirect
6. #3118	C₂	semidirect
7. #3114	C₂	semidirect
8. #3111	C₂	semidirect
9. #3105	C₂	semidirect
10. #3102	C₂	semidirect
11. #3097	C₂	semidirect
12. #3096	C₂	semidirect
13. #3077	C₂	semidirect
14. #3076	C₂	semidirect
15. #3040	C₂	semidirect
16. C₂×#463	C₂	semidirect
17. #3009	C₂	semidirect
19. #2949	C₂	semidirect
20. #2948	C₂	semidirect
21. #2947	C₂	semidirect
22. #2946	C₂	semidirect
23. #2925	C₂	semidirect
35. #542	C₂²	semidirect
36. #542	C₂²	semidirect
39. #533	C₂²	semidirect
40. #529	C₂²	semidirect
41. #529	C₂²	semidirect
42. C₂×#124	C₂²	semidirect
46. #520	C₂²	semidirect
47. #519	C₂²	semidirect
51. #518	C₂²	semidirect
52. #518	C₂²	semidirect
56. C₄×#41	C₂²	semidirect
60. C₂×C₄×D₄	C₂²	semidirect
61. #485	C₂²	semidirect
62. #485	C₂²	semidirect
63. #484	C₂²	semidirect
64. #483	C₂²	semidirect
65. #482	C₂²	semidirect
66. #482	C₂²	semidirect
67. #481	C₂²	semidirect
68. #480	C₂²	semidirect
69. #479	C₂²	semidirect
70. #479	C₂²	semidirect
71. #478	C₂²	semidirect
72. #478	C₂²	semidirect
73. #478	C₂²	semidirect
74. #478	C₂²	semidirect
75. #477	C₂²	semidirect
76. #476	C₂²	semidirect
77. #476	C₂²	semidirect
78. #475	C₂²	semidirect
79. #474	C₂²	semidirect
80. #474	C₂²	semidirect
81. #464	C₂²	semidirect
82. #464	C₂²	semidirect
83. #463	C₂²	semidirect
84. #463	C₂²	semidirect
85. #463	C₂²	semidirect
86. #463	C₂²	semidirect
87. #463	C₂²	semidirect
88. #463	C₂²	semidirect
89. #452	C₂²	semidirect
90. #452	C₂²	semidirect
91. #450	C₂²	semidirect
92. #450	C₂²	semidirect
97. #442	C₂²	semidirect
98. #442	C₂²	semidirect
99. #442	C₂²	semidirect
100. #441	C₂²	semidirect
101. #440	C₂²	semidirect
102. #440	C₂²	semidirect
103. #440	C₂²	semidirect
104. #440	C₂²	semidirect
105. C₄×Q₁₆	C₂²	semidirect
106. C₄×SD₁₆	C₂²	semidirect
107. C₄×SD₁₆	C₂²	semidirect
108. C₄×SD₁₆	C₂²	semidirect
109. C₄×SD₁₆	C₂²	semidirect
110. C₄×D₈	C₂²	semidirect
111. C₄×D₈	C₂²	semidirect
112. C₄×D₈	C₂²	semidirect
113. #433	C₂²	semidirect
114. #433	C₂²	semidirect
115. #432	C₂²	semidirect
116. #431	C₂²	semidirect
117. #428	C₂²	semidirect
118. #428	C₂²	semidirect
119. #427	C₂²	semidirect
120. #427	C₂²	semidirect
121. #423	C₂²	semidirect
122. C₂×C₄⋊C₈	C₂²	semidirect
123. #419	C₂²	semidirect
126. #418	C₂²	semidirect
129. C₂×#103	C₂²	semidirect
130. C₂×#102	C₂²	semidirect
133. #405	C₂²	semidirect
134. #405	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×H(5,𝔽₂)	2
#3125	2
#3124	2
#3118	2
#3114	2
#3111	2
#3105	2
#3102	2
#3097	2
#3096	2
#3077	2
#3076	2
#3040	2
C₂×#463	2
#3009	2
#3008	2
#2949	2
#2948	2
#2947	2
#2946	2
#2925	2