Subgroups — #60575

Order 256.

1040 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	#3461	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×H(5,𝔽₂)	C₂	1	1	yes	maximal, characteristic, complemented
3	#3124	C₂	1	2	yes	maximal, complemented
4	#3123	C₂	1	2	yes	maximal, complemented
5	#3120	C₂	1	2	yes	maximal, complemented
6	#3118	C₂	1	2	yes	maximal, complemented
7	#3116	C₂	1	2	yes	maximal, complemented
8	#3114	C₂	1	2	yes	maximal, complemented
9	#3111	C₂	1	2	yes	maximal, complemented
10	#3110	C₂	1	2	yes	maximal, complemented
11	#3098	C₂	1	1	yes	maximal, characteristic, complemented
12	#3097	C₂	1	1	yes	maximal, characteristic, complemented
13	#3083	C₂	1	1	yes	maximal, characteristic, complemented
14	#3081	C₂	1	1	yes	maximal, characteristic, complemented
15	#3046	C₂	1	1	yes	maximal, characteristic, complemented
16	#3042	C₂	1	1	yes	maximal, characteristic, complemented
17	#3012	C₂	1	1	yes	maximal, characteristic
18	#3009	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄×#137	C₂	1	1	yes	maximal, characteristic, complemented
20	C₄×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic, complemented
21	#2943	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×#440	C₂	1	1	yes	maximal, characteristic, complemented
23	#2923	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	C₂×#135	C₂²	1	1	yes	characteristic
28	C₂²×SD₁₆	C₂²	1	1	yes	characteristic
29	#544	C₂²	1	1	yes	characteristic, complemented
30	#542	—	2	1	no	—
31	#542	C₂²	1	2	yes	complemented
32	#541	—	2	1	no	—
33	#541	C₂²	1	2	yes	complemented
34	#539	—	2	2	no	—
35	#537	C₂²	1	1	yes	characteristic
36	#536	C₂²	1	1	yes	characteristic
37	#536	C₂²	1	1	yes	characteristic, complemented
38	#533	—	2	1	no	—
39	#533	C₂²	1	2	yes	complemented
40	#529	—	2	2	no	—
41	#529	—	2	1	no	—
42	#529	C₂²	1	2	yes	complemented
43	#520	—	2	1	no	—
44	#520	C₂²	1	1	yes	characteristic
45	#520	C₂²	1	2	yes	—
46	#520	C₂²	1	1	yes	characteristic
47	#518	—	2	2	no	—
48	#518	—	2	1	no	—
49	#518	C₂²	1	1	yes	characteristic
50	#518	C₂²	1	2	yes	—
51	C₄×#41	—	2	1	no	—
52	C₄×#41	C₂²	1	2	yes	—
53	C₄×#41	C₂²	1	1	yes	characteristic
54	C₄×#41	C₂²	1	1	yes	characteristic
55	C₄×#41	C₂²	1	1	yes	characteristic, complemented
56	C₂×C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
57	C₂×C₄×D₄	—	2	2	no	—
58	C₂×C₄×D₄	—	2	1	no	—
59	C₂×C₄×D₄	C₂²	1	2	yes	—
60	C₂×C₄×D₄	C₂²	1	1	yes	characteristic
61	#485	C₂²	1	2	yes	complemented
62	#485	C₂²	1	2	yes	complemented
63	#485	C₂²	1	2	yes	complemented
64	#484	C₂²	1	2	yes	complemented
65	#484	C₂²	1	2	yes	complemented
66	#483	C₂²	1	2	yes	complemented
67	#482	C₂²	1	2	yes	complemented
68	#480	C₂²	1	2	yes	complemented
69	#479	C₂²	1	2	yes	complemented
70	#478	C₂²	1	2	yes	complemented
71	#478	C₂²	1	2	yes	complemented
72	#478	C₂²	1	2	yes	complemented
73	#477	C₂²	1	2	yes	complemented
74	#476	C₂²	1	2	yes	complemented
75	#474	C₂²	1	2	yes	complemented
76	#474	C₂²	1	2	yes	complemented
77	#464	C₂²	1	2	yes	complemented
78	#463	C₂²	1	2	yes	complemented
79	#463	C₂²	1	2	yes	complemented
80	#463	C₂²	1	2	yes	complemented
81	#462	C₂²	1	2	yes	complemented
82	#461	C₂²	1	2	yes	complemented
83	#461	C₂²	1	2	yes	complemented
84	#461	C₂²	1	2	yes	complemented
85	#452	C₂²	1	2	yes	—
86	#452	C₂²	1	2	yes	—
87	#452	C₂²	1	2	yes	—
88	#450	C₂²	1	2	yes	—
89	#450	C₂²	1	2	yes	—
90	#450	C₂²	1	2	yes	—
91	#449	C₂²	1	2	yes	—
92	#447	C₂²	1	2	yes	—
93	#442	C₂²	1	2	yes	complemented
94	#442	C₂²	1	1	yes	characteristic, complemented
95	#442	C₂²	1	1	yes	characteristic, complemented
96	#441	C₂²	1	2	yes	complemented
97	#441	C₂²	1	1	yes	characteristic, complemented
98	#441	C₂²	1	1	yes	characteristic, complemented
99	#440	C₂²	1	1	yes	characteristic, complemented
100	#440	C₂²	1	2	yes	complemented
101	#440	C₂²	1	2	yes	complemented
102	#440	C₂²	1	2	yes	complemented
103	#440	C₂²	1	1	yes	characteristic, complemented
104	#440	C₂²	1	2	yes	complemented
105	#440	C₂²	1	2	yes	complemented
106	#440	C₂²	1	1	yes	characteristic, complemented
107	#440	C₂²	1	2	yes	complemented
108	#440	C₂²	1	1	yes	characteristic, complemented
109	C₄×Q₁₆	C₂²	1	2	yes	complemented
110	C₄×SD₁₆	C₂²	1	2	yes	complemented
111	C₄×SD₁₆	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	#432	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	C₂×#107	C₂²	1	1	yes	characteristic, complemented
121	#424	C₂²	1	1	yes	characteristic, complemented
122	#424	C₂²	1	1	yes	characteristic, complemented
123	#419	C₂²	1	1	yes	characteristic, complemented
124	#418	C₂²	1	1	yes	characteristic
125	#417	C₂²	1	1	yes	characteristic
126	#417	C₂²	1	1	yes	characteristic, complemented
127	#416	C₂²	1	1	yes	characteristic
128	#416	C₂²	1	1	yes	characteristic, complemented
129	C₂×#103	C₂²	1	1	yes	characteristic, complemented
130	C₂×#102	C₂²	1	1	yes	characteristic
131	#408	C₂²	1	1	yes	characteristic
132	#408	C₂²	1	1	yes	characteristic
133	C₄×M₁₆	C₂²	1	1	yes	characteristic, complemented
134	C₂×#97	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	C₂×#41	C₂³	1	1	yes	characteristic
142	C₂²×Q₈	C₂³	1	1	yes	characteristic
143	C₂²×D₄	—	2	2	no	—
144	C₂²×D₄	—	2	1	no	—
145	C₂²×D₄	C₂³	1	2	yes	—
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	#135	—	2	4	no	—
152	C₂×Q₁₆	C₂³	1	1	yes	characteristic
153	C₂×Q₁₆	C₂³	1	2	yes	—
154	C₂×SD₁₆	—	2	4	no	—
155	C₂×SD₁₆	C₂³	1	2	yes	—
156	C₂×SD₁₆	C₂³	1	2	yes	—
157	C₂×SD₁₆	C₂³	1	1	yes	characteristic
158	C₂×SD₁₆	C₂³	1	1	yes	characteristic
159	C₂×SD₁₆	C₂³	1	2	yes	—
160	C₂×SD₁₆	C₂³	1	2	yes	—
161	C₂×D₈	C₂³	1	1	yes	characteristic
162	C₂×D₈	C₂³	1	2	yes	—
163	C₂×M₁₆	C₂³	1	1	yes	characteristic
164	C₂×M₁₆	C₂³	1	1	yes	characteristic
165	C₂²×C₈	C₂³	1	1	yes	characteristic
166	C₂²×C₈	C₂³	1	1	yes	characteristic
167	C₄⋊Q₈	—	2	1	no	—
168	C₄⋊Q₈	—	2	1	no	—
169	C₄⋊Q₈	C₂³	1	2	yes	—
170	C₄⋊Q₈	C₂³	1	2	yes	—
171	#126	—	2	2	no	—
172	#126	—	2	2	no	—
173	#126	—	2	2	no	—
174	#126	—	2	2	no	—
175	#125	—	2	2	no	—
176	#125	—	2	1	no	—
177	#125	—	2	2	no	—
178	#125	—	2	2	no	—
179	#125	C₂³	1	2	yes	—
180	#124	—	2	1	no	—
181	#124	—	2	2	no	—
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	C₂²⋊Q₈	—	2	1	no	—
188	C₂²⋊Q₈	—	2	2	no	—
189	C₂²⋊Q₈	—	2	1	no	—
190	C₂²⋊Q₈	—	2	1	no	—
191	C₂²⋊Q₈	—	2	2	no	—
192	C₂²⋊Q₈	—	2	2	no	—
193	C₂²⋊Q₈	C₂³	1	2	yes	—
194	C₂²⋊Q₈	C₂³	1	2	yes	—
195	C₂²⋊Q₈	C₂³	1	2	yes	—
196	#121	—	2	2	no	—
197	#121	—	2	1	no	—
198	#121	C₂³	1	2	yes	—
199	C₄×Q₈	—	2	1	no	—
200	C₄×Q₈	—	2	1	no	—
201	C₄×Q₈	—	2	1	no	—
202	C₄×Q₈	—	2	2	no	—
203	C₄×Q₈	D₄	1	1	yes	characteristic
204	C₄×Q₈	D₄	1	1	yes	characteristic
205	C₄×Q₈	C₂³	1	2	yes	—
206	C₄×Q₈	C₂³	1	2	yes	—
207	C₄×Q₈	C₂³	1	1	yes	characteristic
208	C₄×Q₈	C₂³	1	1	yes	characteristic
209	C₄×Q₈	C₂³	1	2	yes	—
210	C₄×Q₈	C₂³	1	1	yes	characteristic
211	C₄×Q₈	C₂³	1	1	yes	characteristic
212	C₄×D₄	—	2	2	no	—
213	C₄×D₄	—	2	1	no	—
214	C₄×D₄	—	2	1	no	—
215	C₄×D₄	—	2	2	no	—
216	C₄×D₄	—	2	1	no	—
217	C₄×D₄	—	2	2	no	—
218	C₄×D₄	—	2	1	no	—
219	C₄×D₄	—	2	1	no	—
220	C₄×D₄	—	2	2	no	—
221	C₄×D₄	—	2	2	no	—
222	C₄×D₄	—	2	1	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	2	no	—
228	C₄×D₄	—	2	1	no	—
229	C₄×D₄	—	2	2	no	—
230	C₄×D₄	—	2	1	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	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	2	yes	—
239	C₄×D₄	C₂³	1	2	yes	—
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	1	yes	characteristic
245	#117	—	2	2	no	—
246	#117	—	2	1	no	—
247	#117	—	2	2	no	—
248	#117	—	2	1	no	—
249	#117	—	2	2	no	—
250	#117	—	2	1	no	—
251	#117	—	2	2	no	—
252	#117	C₂³	1	1	yes	characteristic
253	#117	C₂³	1	2	yes	—
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	C₂³	1	1	yes	characteristic
261	C₂×C₄⋊C₄	C₂³	1	2	yes	—
262	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	1	no	—
270	C₂×C₄²	—	2	2	no	—
271	C₂×C₄²	—	2	1	no	—
272	C₂×C₄²	C₂³	1	1	yes	characteristic
273	C₂×C₄²	C₂³	1	2	yes	—
274	#107	C₂³	1	2	yes	—
275	#107	C₂³	1	2	yes	—
276	#107	C₂³	1	1	yes	characteristic
277	#107	C₂³	1	1	yes	characteristic
278	#107	C₂³	1	2	yes	—
279	#107	C₂³	1	2	yes	—
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	2	yes	—
285	C₄⋊C₈	C₂³	1	2	yes	—
286	C₄⋊C₈	C₂³	1	2	yes	—
287	C₄⋊C₈	C₂³	1	2	yes	—
288	#103	C₂³	1	2	yes	—
289	#103	C₂³	1	2	yes	—
290	#103	C₂³	1	1	yes	characteristic
291	#103	C₂³	1	1	yes	characteristic
292	#103	C₂³	1	1	yes	characteristic
293	#103	C₂³	1	1	yes	characteristic
294	#103	C₂³	1	2	yes	—
295	#103	C₂³	1	2	yes	—
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	C₂²⋊C₈	C₂³	1	2	yes	—
309	C₂²⋊C₈	C₂³	1	2	yes	—
310	C₂²⋊C₈	C₂³	1	2	yes	—
311	C₂²⋊C₈	C₂³	1	2	yes	—
312	#97	C₂³	1	1	yes	characteristic
313	#97	C₂³	1	1	yes	characteristic
314	#97	C₂³	1	1	yes	characteristic
315	#97	C₂³	1	1	yes	characteristic
316	#97	C₂³	1	2	yes	—
317	C₄×C₈	C₂³	1	2	yes	—
318	C₂⁴	—	2	2	no	—
319	C₂⁴	—	2	1	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	—	2	2	no	—
327	#41	—	2	2	no	—
328	#41	#41	1	4	yes	—
329	C₂×Q₈	—	2	1	no	—
330	C₂×Q₈	—	2	2	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×Q₈	C₂⁴	1	1	yes	characteristic
337	C₂×D₄	—	2	16	no	—
338	C₂×D₄	—	2	8	no	—
339	C₂×D₄	—	2	2	no	—
340	C₂×D₄	—	2	1	no	—
341	C₂×D₄	—	2	4	no	—
342	C₂×D₄	—	2	4	no	—
343	C₂×D₄	—	2	1	no	—
344	C₂×D₄	—	2	2	no	—
345	C₂×D₄	—	2	2	no	—
346	C₂×D₄	—	2	1	no	—
347	C₂×D₄	—	2	2	no	—
348	C₂×D₄	C₂×D₄	1	2	yes	—
349	C₂×D₄	C₂×D₄	1	1	yes	characteristic
350	C₂×D₄	#41	1	4	yes	—
351	C₂×D₄	C₂⁴	1	1	yes	characteristic
352	C₂×D₄	C₂⁴	1	1	yes	characteristic
353	C₂×D₄	C₂⁴	1	2	yes	—
354	C₂²×C₄	—	2	2	no	—
355	C₂²×C₄	—	2	1	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	1	no	—
361	C₂²×C₄	—	2	1	no	—
362	C₂²×C₄	—	2	1	no	—
363	C₂²×C₄	—	2	2	no	—
364	C₂²×C₄	—	2	1	no	—
365	C₂²×C₄	—	2	2	no	—
366	C₂²×C₄	—	2	1	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	2	no	—
379	Q₁₆	—	2	4	no	—
380	SD₁₆	—	2	2	no	—
381	SD₁₆	—	2	4	no	—
382	SD₁₆	—	2	4	no	—
383	SD₁₆	—	2	2	no	—
384	SD₁₆	—	2	4	no	—
385	SD₁₆	—	2	4	no	—
386	D₈	—	2	2	no	—
387	D₈	—	2	4	no	—
388	M₁₆	—	2	2	no	—
389	M₁₆	—	2	2	no	—
390	C₂×C₈	—	2	2	no	—
391	C₂×C₈	—	2	2	no	—
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	C₂×C₈	C₂⁴	1	1	yes	characteristic
397	C₂×C₈	C₂⁴	1	1	yes	characteristic
398	C₄⋊C₄	—	2	1	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	1	no	—
408	C₄⋊C₄	—	2	2	no	—
409	C₄⋊C₄	—	2	2	no	—
410	C₄⋊C₄	—	2	2	no	—
411	C₄⋊C₄	—	2	2	no	—
412	C₄⋊C₄	—	2	2	no	—
413	C₄⋊C₄	—	2	2	no	—
414	C₄⋊C₄	—	2	2	no	—
415	C₄⋊C₄	—	2	2	no	—
416	C₄⋊C₄	C₂×D₄	1	2	yes	—
417	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
418	C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
419	C₄⋊C₄	C₂×D₄	1	2	yes	—
420	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
421	C₄⋊C₄	C₂⁴	1	2	yes	—
422	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
423	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
424	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
425	C₄⋊C₄	C₂⁴	1	2	yes	—
426	C₂²⋊C₄	—	2	2	no	—
427	C₂²⋊C₄	—	2	1	no	—
428	C₂²⋊C₄	—	2	2	no	—
429	C₂²⋊C₄	—	2	2	no	—
430	C₂²⋊C₄	—	2	1	no	—
431	C₂²⋊C₄	—	2	2	no	—
432	C₂²⋊C₄	—	2	1	no	—
433	C₂²⋊C₄	—	2	2	no	—
434	C₂²⋊C₄	—	2	2	no	—
435	C₂²⋊C₄	—	2	1	no	—
436	C₂²⋊C₄	—	2	2	no	—
437	C₂²⋊C₄	—	2	2	no	—
438	C₂²⋊C₄	—	2	2	no	—
439	C₂²⋊C₄	—	2	1	no	—
440	C₂²⋊C₄	—	2	1	no	—
441	C₂²⋊C₄	—	2	2	no	—
442	C₂²⋊C₄	—	2	2	no	—
443	C₂²⋊C₄	—	2	2	no	—
444	C₂²⋊C₄	C₂×D₄	1	2	yes	—
445	C₂²⋊C₄	C₂×D₄	1	2	yes	—
446	C₂²⋊C₄	C₂×D₄	1	2	yes	—
447	C₄²	—	2	1	no	—
448	C₄²	—	2	1	no	—
449	C₄²	—	2	2	no	—
450	C₄²	—	2	2	no	—
451	C₄²	—	2	1	no	—
452	C₄²	—	2	2	no	—
453	C₄²	—	2	1	no	—
454	C₄²	—	2	1	no	—
455	C₄²	—	2	1	no	—
456	C₄²	—	2	2	no	—
457	C₄²	C₂×D₄	1	1	yes	characteristic
458	C₄²	C₂×D₄	1	1	yes	characteristic
459	C₄²	C₂×D₄	1	2	yes	—
460	C₄²	C₂×D₄	1	2	yes	—
461	C₄²	C₂⁴	1	1	yes	characteristic
462	C₄²	C₂⁴	1	1	yes	characteristic
463	C₄²	C₂⁴	1	2	yes	—
464	C₂³	—	2	8	no	—
465	C₂³	—	2	2	no	—
466	C₂³	—	2	1	no	—
467	C₂³	—	2	4	no	—
468	C₂³	—	2	1	no	—
469	C₂³	—	8	1	no	—
470	C₂³	—	8	2	no	—
471	C₂³	—	8	1	no	—
472	C₂³	—	8	2	no	—
473	C₂³	C₂²×D₄	1	2	yes	—
474	C₂³	C₂²×D₄	1	1	yes	characteristic
475	Q₈	—	2	2	no	—
476	Q₈	—	2	1	no	—
477	Q₈	—	2	2	no	—
478	Q₈	—	2	1	no	—
479	Q₈	—	2	2	no	—
480	Q₈	—	2	1	no	—
481	Q₈	—	4	2	no	—
482	Q₈	—	8	2	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	1	no	—
493	D₄	—	2	1	no	—
494	D₄	—	4	2	no	—
495	D₄	—	8	2	no	—
496	D₄	C₂×#41	1	2	yes	—
497	D₄	C₂×#41	1	4	yes	—
498	C₂×C₄	—	2	8	no	—
499	C₂×C₄	—	2	1	no	—
500	C₂×C₄	—	2	4	no	—
501	C₂×C₄	—	2	2	no	—
502	C₂×C₄	—	2	2	no	—
503	C₂×C₄	—	2	1	no	—
504	C₂×C₄	—	2	1	no	—
505	C₂×C₄	—	2	2	no	—
506	C₂×C₄	—	2	1	no	—
507	C₂×C₄	—	2	1	no	—
508	C₂×C₄	—	2	2	no	—
509	C₂×C₄	—	2	1	no	—
510	C₂×C₄	—	2	2	no	—
511	C₂×C₄	—	4	1	no	—
512	C₂×C₄	—	4	2	no	—
513	C₂×C₄	—	4	1	no	—
514	C₂×C₄	—	4	2	no	—
515	C₂×C₄	—	4	2	no	—
516	C₂×C₄	—	4	4	no	—
517	C₂×C₄	—	4	2	no	—
518	C₂×C₄	—	4	2	no	—
519	C₂×C₄	—	4	2	no	—
520	C₂×C₄	—	8	1	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	1	no	—
528	C₂×C₄	—	8	2	no	—
529	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
530	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
531	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
532	C₂×C₄	C₂²×D₄	1	2	yes	—
533	C₂×C₄	C₂²×D₄	1	2	yes	—
534	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
535	C₂×C₄	C₂²×D₄	1	2	yes	—
536	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
537	C₂×C₄	C₂×#41	1	2	yes	—
538	C₂×C₄	C₂×#41	1	2	yes	—
539	C₂×C₄	C₂⁵	1	1	yes	characteristic
540	C₈	—	2	1	no	—
541	C₈	—	2	1	no	—
542	C₈	—	2	1	no	—
543	C₈	—	2	1	no	—
544	C₈	—	2	2	no	—
545	C₈	—	2	2	no	—
546	C₂²	—	2	1	no	—
547	C₂²	—	2	1	no	—
548	C₂²	—	2	2	no	—
549	C₂²	—	2	2	no	—
550	C₂²	—	2	2	no	—
551	C₂²	—	2	4	no	—
552	C₂²	—	2	2	no	—
553	C₂²	—	4	2	no	—
554	C₂²	—	4	1	no	—
555	C₂²	—	4	2	no	—
556	C₂²	—	4	1	no	—
557	C₂²	—	4	1	no	—
558	C₂²	—	4	1	no	—
559	C₂²	—	4	1	no	—
560	C₂²	—	8	4	no	—
561	C₂²	—	8	8	no	—
562	C₂²	#525	1	2	yes	—
563	C₂²	C₂³×D₄	1	1	yes	characteristic
564	C₄	—	2	1	no	—
565	C₄	—	2	1	no	—
566	C₄	—	2	2	no	—
567	C₄	—	2	1	no	—
568	C₄	—	2	1	no	—
569	C₄	—	2	2	no	—
570	C₄	—	2	2	no	—
571	C₄	—	2	2	no	—
572	C₄	—	4	2	no	—
573	C₄	—	4	1	no	—
574	C₄	—	4	2	no	—
575	C₄	—	4	1	no	—
576	C₄	—	4	1	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	1	no	—
588	C₂	C₂×#525	1	1	yes	characteristic
589	C₂	#3585	1	1	yes	characteristic
590	C₂	#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵
prime radical	#3012	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. #3461	C₂	semidirect
2. C₄×H(5,𝔽₂)	C₂	semidirect
3. #3124	C₂	semidirect
4. #3123	C₂	semidirect
5. #3120	C₂	semidirect
6. #3118	C₂	semidirect
7. #3116	C₂	semidirect
8. #3114	C₂	semidirect
9. #3111	C₂	semidirect
10. #3110	C₂	semidirect
11. #3098	C₂	semidirect
12. #3097	C₂	semidirect
13. #3083	C₂	semidirect
14. #3081	C₂	semidirect
15. #3046	C₂	semidirect
16. #3042	C₂	semidirect
18. #3009	C₂	semidirect
19. C₄×#137	C₂	semidirect
20. C₄×AGL(1,ℤ/8)	C₂	semidirect
21. #2943	C₂	semidirect
22. C₂×#440	C₂	semidirect
23. #2923	C₂	semidirect
29. #544	C₂²	semidirect
31. #542	C₂²	semidirect
33. #541	C₂²	semidirect
37. #536	C₂²	semidirect
39. #533	C₂²	semidirect
42. #529	C₂²	semidirect
55. C₄×#41	C₂²	semidirect
56. C₂×C₄×Q₈	C₂²	semidirect
61. #485	C₂²	semidirect
62. #485	C₂²	semidirect
63. #485	C₂²	semidirect
64. #484	C₂²	semidirect
65. #484	C₂²	semidirect
66. #483	C₂²	semidirect
67. #482	C₂²	semidirect
68. #480	C₂²	semidirect
69. #479	C₂²	semidirect
70. #478	C₂²	semidirect
71. #478	C₂²	semidirect
72. #478	C₂²	semidirect
73. #477	C₂²	semidirect
74. #476	C₂²	semidirect
75. #474	C₂²	semidirect
76. #474	C₂²	semidirect
77. #464	C₂²	semidirect
78. #463	C₂²	semidirect
79. #463	C₂²	semidirect
80. #463	C₂²	semidirect
81. #462	C₂²	semidirect
82. #461	C₂²	semidirect
83. #461	C₂²	semidirect
84. #461	C₂²	semidirect
93. #442	C₂²	semidirect
94. #442	C₂²	semidirect
95. #442	C₂²	semidirect
96. #441	C₂²	semidirect
97. #441	C₂²	semidirect
98. #441	C₂²	semidirect
99. #440	C₂²	semidirect
100. #440	C₂²	semidirect
101. #440	C₂²	semidirect
102. #440	C₂²	semidirect
103. #440	C₂²	semidirect
104. #440	C₂²	semidirect
105. #440	C₂²	semidirect
106. #440	C₂²	semidirect
107. #440	C₂²	semidirect
108. #440	C₂²	semidirect
109. C₄×Q₁₆	C₂²	semidirect
110. C₄×SD₁₆	C₂²	semidirect
111. C₄×SD₁₆	C₂²	semidirect
112. C₄×D₈	C₂²	semidirect
113. #433	C₂²	semidirect
114. #433	C₂²	semidirect
115. #432	C₂²	semidirect
116. #432	C₂²	semidirect
117. #428	C₂²	semidirect
118. #428	C₂²	semidirect
119. #427	C₂²	semidirect
120. C₂×#107	C₂²	semidirect
121. #424	C₂²	semidirect
122. #424	C₂²	semidirect
123. #419	C₂²	semidirect
126. #417	C₂²	semidirect
128. #416	C₂²	semidirect
129. C₂×#103	C₂²	semidirect
133. C₄×M₁₆	C₂²	semidirect
134. C₂×#97	C₂²	semidirect

Maximal subgroups

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

subgroup	index
#3461	2
C₄×H(5,𝔽₂)	2
#3124	2
#3123	2
#3120	2
#3118	2
#3116	2
#3114	2
#3111	2
#3110	2
#3098	2
#3097	2
#3083	2
#3081	2
#3046	2
#3042	2
#3012	2
#3009	2
C₄×#137	2
C₄×AGL(1,ℤ/8)	2
#2943	2
C₂×#440	2
#2923	2