Subgroups — #12070303

Order 1280.

662 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈×#676	C₂	1	1	yes	maximal, characteristic, complemented
2	#10611384	C₂	1	1	yes	maximal, characteristic
3	#10611156	C₂	1	1	yes	maximal, characteristic
4	C₅×SD₁₆⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
5	#10601729	C₂	1	1	yes	maximal, characteristic, complemented
6	#10601691	C₂	1	1	yes	maximal, characteristic, complemented
7	#10601636	C₂	1	1	yes	maximal, characteristic, complemented
8	#10599365	C₂	1	1	yes	maximal, characteristic, complemented
9	#10599354	C₂	1	1	yes	maximal, characteristic, complemented
10	D₅×Q₈⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
11	#10599007	C₂	1	1	yes	maximal, characteristic, complemented
12	#10598969	C₂	1	1	yes	maximal, characteristic
13	#10598955	C₂	1	1	yes	maximal, characteristic, complemented
14	#10598875	C₂	1	1	yes	maximal, characteristic, complemented
15	#10598863	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#4047	—	2	1	no	—
17	C₄×Q₈×D₅	C₂²	1	1	yes	characteristic
18	#65882	C₂²	1	1	yes	characteristic
19	C₅×C₈×Q₈	C₂²	1	1	yes	characteristic
20	C₄×C₅×SD₁₆	C₂²	1	1	yes	characteristic
21	C₅×C₈×D₄	C₂²	1	1	yes	characteristic
22	#65459	C₄	1	1	yes	characteristic
23	#65452	C₄	1	1	yes	characteristic
24	#65400	—	2	1	no	—
25	C₄×#688	C₂²	1	1	yes	characteristic
26	Q₈×#168	C₂²	1	1	yes	characteristic
27	C₄×#687	C₂²	1	1	yes	characteristic
28	#65301	C₂²	1	1	yes	characteristic
29	#65152	C₄	1	1	yes	characteristic
30	#65143	C₄	1	1	yes	characteristic
31	#65126	—	2	1	no	—
32	#65126	C₂²	1	1	yes	characteristic
33	#65123	C₂²	1	1	yes	characteristic
34	D₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
35	#65120	—	2	1	no	—
36	#65120	C₂²	1	1	yes	characteristic
37	#65095	C₄	1	1	yes	characteristic
38	#65080	C₄	1	1	yes	characteristic
39	#65066	C₄	1	1	yes	characteristic
40	#65051	C₄	1	1	yes	characteristic
41	#65017	—	2	1	no	—
42	#65016	—	2	1	no	—
43	C₄×#677	C₂²	1	1	yes	characteristic
44	#64977	C₂²	1	1	yes	characteristic
45	C₄×#676	—	2	1	no	—
46	C₄×#676	C₂²	1	1	yes	characteristic
47	#64974	C₂²	1	1	yes	characteristic
48	C₄×C₈×D₅	C₂²	1	1	yes	characteristic
49	#64968	—	2	1	no	—
50	#64968	C₂²	1	1	yes	characteristic
51	C₅×#335	C₂²	1	1	yes	characteristic
52	C₅×Q₈⋊C₈	C₂²	1	1	yes	characteristic
53	C₅×D₄⋊C₈	C₂²	1	1	yes	characteristic
54	C₅×#322	C₂²	1	1	yes	characteristic
55	Q₈⋊#168	C₂²	1	1	yes	characteristic
56	D₄⋊#168	C₂²	1	1	yes	characteristic
57	#64704	C₂²	1	1	yes	characteristic
58	#64703	C₂²	1	1	yes	characteristic
59	#64699	C₂²	1	1	yes	characteristic
60	#64699	C₂²	1	1	yes	characteristic
61	#64679	C₂²	1	1	yes	characteristic
62	#64678	C₂²	1	1	yes	characteristic
63	#64676	C₂²	1	1	yes	characteristic
64	#64674	C₂²	1	1	yes	characteristic
65	#64674	C₂²	1	1	yes	characteristic
66	#64674	C₂²	1	1	yes	characteristic
67	#18004	—	5	1	no	maximal, Sylow
68	C₂×Q₈×D₅	C₂×C₄	1	1	yes	characteristic
69	C₂×#709	—	2	1	no	—
70	C₂×C₅×SD₁₆	C₂×C₄	1	1	yes	characteristic
71	C₂²×C₅×C₈	—	2	1	no	—
72	C₄×C₅×Q₈	C₂³	1	1	yes	characteristic
73	C₄×C₅×D₄	C₂³	1	1	yes	characteristic
74	Q₈×Dic₅	C₂×C₄	1	1	yes	characteristic
75	C₂×#688	C₂×C₄	1	1	yes	characteristic
76	#4086	C₂×C₄	1	1	yes	characteristic
77	#4084	C₂×C₄	1	1	yes	characteristic
78	C₂×#687	C₂×C₄	1	1	yes	characteristic
79	C₄×C₂²⋊D₅	—	2	1	no	—
80	C₂×#681	—	2	1	no	—
81	C₂×#677	C₂×C₄	1	1	yes	characteristic
82	#4047	—	4	4	no	—
83	C₂×#676	—	2	1	no	—
84	C₂×#676	—	2	1	no	—
85	C₂×#676	D₄	1	1	yes	characteristic
86	C₂×#676	D₄	1	1	yes	characteristic
87	C₂×C₈×D₅	—	2	1	no	—
88	C₂×C₈×D₅	—	2	1	no	—
89	C₂×C₈×D₅	—	2	1	no	—
90	#4041	C₂×C₄	1	1	yes	characteristic
91	D₅×C₄⋊C₄	—	2	1	no	—
92	D₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
93	#4034	C₂×C₄	1	1	yes	characteristic
94	#4033	—	2	1	no	—
95	#4033	C₂×C₄	1	1	yes	characteristic
96	#4031	—	2	1	no	—
97	#4030	—	2	1	no	—
98	C₄×D₂₀	C₂³	1	1	yes	characteristic
99	C₄²×D₅	—	2	1	no	—
100	C₄²×D₅	C₂³	1	1	yes	characteristic
101	C₄×Dic₁₀	—	2	1	no	—
102	C₄×Dic₁₀	C₂³	1	1	yes	characteristic
103	C₅×#106	C₂×C₄	1	1	yes	characteristic
104	C₅×C₄⋊C₈	—	2	1	no	—
105	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
106	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
107	C₅×#103	C₂×C₄	1	1	yes	characteristic
108	C₅×#102	C₂×C₄	1	1	yes	characteristic
109	C₅×C₂²⋊C₈	—	2	1	no	—
110	C₄×C₅×C₈	—	2	1	no	—
111	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
112	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
113	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
114	#3967	C₂×C₄	1	1	yes	characteristic
115	#3964	C₂×C₄	1	1	yes	characteristic
116	C₂²⋊#168	—	2	1	no	—
117	#3953	C₂×C₄	1	1	yes	characteristic
118	#3952	—	2	1	no	—
119	#3952	—	2	1	no	—
120	#3952	C₂×C₄	1	1	yes	characteristic
121	#3952	C₂×C₄	1	1	yes	characteristic
122	#3949	C₂×C₄	1	1	yes	characteristic
123	#3948	C₂×C₄	1	1	yes	characteristic
124	#3947	—	2	1	no	—
125	#3947	—	2	1	no	—
126	#3947	D₄	1	1	yes	characteristic
127	#3947	D₄	1	1	yes	characteristic
128	#3946	—	2	1	no	—
129	#3946	—	2	1	no	—
130	#3946	—	2	1	no	—
131	#3946	—	2	1	no	—
132	#3946	C₂×C₄	1	1	yes	characteristic
133	#3946	C₂×C₄	1	1	yes	characteristic
134	C₈×Dic₅	—	2	1	no	—
135	#3942	C₂×C₄	1	1	yes	characteristic
136	#3941	C₂×C₄	1	1	yes	characteristic
137	#3940	C₂×C₄	1	1	yes	characteristic
138	#3940	C₂×C₄	1	1	yes	characteristic
139	C₄⋊#168	—	2	1	no	—
140	C₄⋊#168	C₂³	1	1	yes	characteristic
141	C₄⋊#168	C₂³	1	1	yes	characteristic
142	C₄×#168	—	2	1	no	—
143	C₄×#168	C₂³	1	1	yes	characteristic
144	C₄×#168	C₂³	1	1	yes	characteristic
145	C₄×#168	C₂³	1	1	yes	characteristic
146	#3103	—	5	1	no	—
147	Q₈×M₁₆	—	5	1	no	—
148	#2935	—	5	1	no	—
149	#1592	—	5	1	no	—
150	#1592	—	5	1	no	—
151	#1588	—	5	1	no	—
152	#1588	—	5	1	no	—
153	#1585	—	5	1	no	—
154	#1585	—	5	1	no	—
155	SD₁₆⋊C₈	—	5	1	no	—
156	SD₁₆⋊C₈	D₅	1	1	yes	characteristic, complemented
157	#1571	—	5	1	no	—
158	#1492	—	5	1	no	—
159	C₂×Q₈⋊C₈	—	5	1	no	—
160	#1451	—	5	1	no	—
161	C₂×C₅×Q₈	C₂²×C₄	1	1	yes	characteristic
162	C₂×C₅×D₄	C₂²×C₄	1	1	yes	characteristic
163	C₂²×C₄×C₅	—	2	1	no	—
164	C₂×C₂²⋊D₅	—	2	1	no	—
165	C₂×C₂²⋊D₅	—	2	1	no	—
166	C₂×C₂²⋊D₅	—	2	1	no	—
167	Q₈×D₅	—	2	2	no	—
168	Q₈×D₅	—	4	1	no	—
169	#709	—	4	2	no	—
170	#709	—	4	2	no	—
171	C₂×D₂₀	—	2	1	no	—
172	C₂×D₂₀	C₂²×C₄	1	1	yes	characteristic
173	C₂×C₄×D₅	—	2	1	no	—
174	C₂×C₄×D₅	—	2	1	no	—
175	C₂×C₄×D₅	—	2	1	no	—
176	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
177	C₂×C₄×D₅	C₂×D₄	1	1	yes	characteristic
178	C₂×C₄×D₅	#41	1	1	yes	characteristic
179	C₂×Dic₁₀	—	2	1	no	—
180	C₂×Dic₁₀	—	2	1	no	—
181	C₂×Dic₁₀	C₂²×C₄	1	1	yes	characteristic
182	C₅×SD₁₆	—	2	2	no	—
183	C₂×C₅×C₈	—	2	1	no	—
184	C₂×C₅×C₈	—	2	1	no	—
185	C₂×C₅×C₈	—	2	1	no	—
186	C₂×C₅×C₈	—	4	2	no	—
187	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
188	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
189	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
190	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
191	C₅×C₄⋊C₄	—	2	1	no	—
192	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
193	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
194	C₅×C₂²⋊C₄	—	2	1	no	—
195	C₄²×C₅	—	2	1	no	—
196	C₄²×C₅	C₂⁴	1	1	yes	characteristic
197	C₂²⋊Dic₅	—	2	1	no	—
198	#688	—	2	2	no	—
199	#687	—	4	1	no	—
200	#685	—	2	1	no	—
201	#685	—	2	1	no	—
202	C₄⋊Dic₅	—	2	1	no	—
203	C₄⋊Dic₅	C₂²×C₄	1	1	yes	characteristic
204	C₄⋊Dic₅	C₂²×C₄	1	1	yes	characteristic
205	#683	—	2	1	no	—
206	#683	—	2	1	no	—
207	#683	—	2	1	no	—
208	#683	—	2	1	no	—
209	C₄×Dic₅	—	2	1	no	—
210	C₄×Dic₅	—	2	1	no	—
211	C₄×Dic₅	—	2	1	no	—
212	C₄×Dic₅	C₂²×C₄	1	1	yes	characteristic
213	C₄×Dic₅	C₂×D₄	1	1	yes	characteristic
214	C₄×Dic₅	#41	1	1	yes	characteristic
215	#681	—	4	2	no	—
216	C₂×#168	—	2	1	no	—
217	C₂×#168	—	2	1	no	—
218	C₂×#168	—	2	1	no	—
219	C₂×#168	C₂²×C₄	1	1	yes	characteristic
220	C₂×#168	C₂²×C₄	1	1	yes	characteristic
221	C₂×#168	C₂×D₄	1	1	yes	characteristic
222	C₂×#168	C₂×D₄	1	1	yes	characteristic
223	#677	—	4	1	no	—
224	#676	—	2	2	no	—
225	#676	—	2	2	no	—
226	#676	—	4	2	no	—
227	#676	—	4	2	no	—
228	C₈×D₅	—	4	2	no	—
229	C₈×D₅	—	4	2	no	—
230	C₈×D₅	—	4	2	no	—
231	C₂×#131	—	10	1	no	—
232	#532	—	5	1	no	—
233	C₂×C₄×Q₈	—	5	1	no	—
234	#481	—	5	1	no	—
235	#481	—	5	1	no	—
236	#475	—	5	1	no	—
237	#475	—	5	1	no	—
238	#460	—	5	1	no	—
239	#460	—	5	1	no	—
240	#448	—	5	1	no	—
241	#448	—	5	1	no	—
242	#446	—	5	1	no	—
243	#446	—	5	1	no	—
244	#446	—	10	1	no	—
245	#446	—	10	1	no	—
246	C₈×Q₈	—	5	1	no	—
247	C₈×Q₈	C₂×D₅	1	1	yes	characteristic
248	C₄×SD₁₆	—	5	1	no	—
249	C₄×SD₁₆	—	5	1	no	—
250	C₄×SD₁₆	—	5	1	no	—
251	C₄×SD₁₆	C₂×D₅	1	1	yes	characteristic
252	#436	—	5	1	no	—
253	#436	—	5	1	no	—
254	#435	—	10	1	no	—
255	#435	—	10	1	no	—
256	C₈×D₄	—	5	1	no	—
257	C₈×D₄	C₂×D₅	1	1	yes	characteristic
258	#431	—	5	1	no	—
259	#423	—	5	1	no	—
260	#423	—	10	1	no	—
261	C₂×C₄⋊C₈	—	5	1	no	—
262	#408	—	10	1	no	—
263	C₄×M₁₆	—	5	1	no	—
264	C₄×M₁₆	—	10	1	no	—
265	C₂×C₄×C₈	—	5	1	no	—
266	#335	—	5	1	no	—
267	#335	—	5	1	no	—
268	#335	—	5	1	no	—
269	#335	C₂×D₅	1	1	yes	characteristic
270	Q₈⋊C₈	—	5	1	no	—
271	Q₈⋊C₈	—	5	1	no	—
272	Q₈⋊C₈	—	5	1	no	—
273	Q₈⋊C₈	C₂×D₅	1	1	yes	characteristic
274	D₄⋊C₈	—	5	1	no	—
275	D₄⋊C₈	—	5	1	no	—
276	D₄⋊C₈	—	5	1	no	—
277	D₄⋊C₈	C₂×D₅	1	1	yes	characteristic
278	#322	—	5	1	no	—
279	#322	—	5	1	no	—
280	#322	—	5	1	no	—
281	#322	C₂×D₅	1	1	yes	characteristic
282	C₂³×C₅	—	2	1	no	—
283	C₂²×D₅	—	2	1	no	—
284	C₂²×D₅	C₄×D₄	1	1	yes	characteristic
285	C₅×Q₈	—	2	1	no	—
286	C₅×Q₈	#131	1	2	yes	complemented
287	C₅×D₄	—	2	1	no	—
288	C₅×D₄	—	2	1	no	—
289	C₂×C₄×C₅	—	2	1	no	—
290	C₂×C₄×C₅	—	2	1	no	—
291	C₂×C₄×C₅	—	2	1	no	—
292	C₂×C₄×C₅	—	4	1	no	—
293	C₂×C₄×C₅	—	4	1	no	—
294	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
295	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
296	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
297	C₂²⋊D₅	—	4	2	no	—
298	C₂²⋊D₅	—	4	2	no	—
299	C₂²⋊D₅	—	8	1	no	—
300	C₂×Dic₅	—	2	1	no	—
301	C₂×Dic₅	—	2	1	no	—
302	C₂×Dic₅	—	2	1	no	—
303	C₂×Dic₅	C₄×D₄	1	1	yes	characteristic
304	C₂×Dic₅	C₄×D₄	1	1	yes	characteristic
305	C₂×Dic₅	C₄×D₄	1	1	yes	characteristic
306	D₂₀	—	2	1	no	—
307	D₂₀	—	2	1	no	—
308	D₂₀	—	4	2	no	—
309	C₄×D₅	—	2	1	no	—
310	C₄×D₅	—	2	1	no	—
311	C₄×D₅	—	4	1	no	—
312	C₄×D₅	—	4	2	no	—
313	C₄×D₅	—	4	1	no	—
314	C₄×D₅	—	4	1	no	—
315	C₄×D₅	—	8	1	no	—
316	C₄×D₅	AGL(1,ℤ/8)	1	2	yes	—
317	C₄×D₅	#137	1	2	yes	—
318	Dic₁₀	—	2	1	no	—
319	Dic₁₀	—	2	1	no	—
320	Dic₁₀	—	4	2	no	—
321	Dic₁₀	—	4	2	no	—
322	C₅×C₈	—	2	1	no	—
323	C₅×C₈	—	2	1	no	—
324	C₅×C₈	—	2	1	no	—
325	C₅×C₈	—	2	1	no	—
326	C₅×C₈	—	4	1	no	—
327	C₅×C₈	—	4	1	no	—
328	C₅×C₈	—	4	1	no	—
329	#168	—	2	2	no	—
330	#168	—	2	1	no	—
331	#168	—	2	1	no	—
332	#168	—	2	1	no	—
333	#168	—	2	1	no	—
334	#168	—	4	1	no	—
335	#168	—	4	1	no	—
336	C₂×#41	—	10	1	no	—
337	C₂²×Q₈	—	5	1	no	—
338	C₂×SD₁₆	—	5	1	no	—
339	C₂×SD₁₆	—	5	1	no	—
340	C₂×SD₁₆	—	5	1	no	—
341	C₂×SD₁₆	C₄×D₅	1	1	yes	characteristic
342	#131	—	20	4	no	—
343	C₂×M₁₆	—	5	1	no	—
344	C₂×M₁₆	—	5	1	no	—
345	C₂×M₁₆	—	10	1	no	—
346	C₂×M₁₆	—	10	1	no	—
347	C₂×M₁₆	—	10	1	no	—
348	C₂²×C₈	—	2	1	no	—
349	C₂²×C₈	—	10	1	no	—
350	C₂²×C₈	—	10	1	no	—
351	C₂²×C₈	—	10	1	no	—
352	C₄⋊Q₈	—	5	1	no	—
353	#127	—	5	1	no	—
354	#124	—	10	1	no	—
355	#121	—	5	1	no	—
356	#121	—	5	1	no	—
357	#121	—	10	1	no	—
358	C₄×Q₈	—	5	1	no	—
359	C₄×Q₈	—	5	1	no	—
360	C₄×Q₈	—	5	1	no	—
361	C₄×Q₈	—	10	1	no	—
362	C₄×Q₈	—	10	1	no	—
363	C₄×Q₈	C₂²×D₅	1	1	yes	characteristic
364	C₄×D₄	—	5	1	no	—
365	C₄×D₄	—	10	1	no	—
366	C₄×D₄	C₂²×D₅	1	1	yes	characteristic
367	C₂×C₄⋊C₄	—	5	1	no	—
368	C₂×C₄⋊C₄	—	10	1	no	—
369	C₂×C₄²	—	5	1	no	—
370	C₂×C₄²	—	10	1	no	—
371	#106	—	5	1	no	—
372	#106	—	5	1	no	—
373	#106	—	5	1	no	—
374	#106	C₄×D₅	1	1	yes	characteristic
375	C₄⋊C₈	—	2	1	no	—
376	C₄⋊C₈	—	5	1	no	—
377	C₄⋊C₈	—	5	1	no	—
378	C₄⋊C₈	—	5	1	no	—
379	C₄⋊C₈	—	5	1	no	—
380	C₄⋊C₈	—	10	1	no	—
381	C₄⋊C₈	—	10	1	no	—
382	C₄⋊C₈	—	10	1	no	—
383	C₄⋊C₈	—	10	1	no	—
384	C₄⋊C₈	—	10	1	no	—
385	C₄⋊C₈	C₂²×D₅	1	1	yes	characteristic
386	C₄⋊C₈	C₂²×D₅	1	1	yes	characteristic
387	#103	—	5	1	no	—
388	#103	—	5	1	no	—
389	#103	—	5	1	no	—
390	#103	C₄×D₅	1	1	yes	characteristic
391	#102	—	5	1	no	—
392	#102	—	5	1	no	—
393	#102	—	5	1	no	—
394	#102	C₄×D₅	1	1	yes	characteristic
395	C₂²⋊C₈	—	2	1	no	—
396	C₂²⋊C₈	—	5	1	no	—
397	C₂²⋊C₈	—	5	1	no	—
398	C₂²⋊C₈	—	10	1	no	—
399	C₂²⋊C₈	—	10	1	no	—
400	C₂²⋊C₈	—	10	1	no	—
401	#97	—	5	1	no	—
402	#97	—	5	1	no	—
403	#97	—	10	1	no	—
404	#97	—	10	1	no	—
405	C₄×C₈	—	2	1	no	—
406	C₄×C₈	—	5	1	no	—
407	C₄×C₈	—	5	1	no	—
408	C₄×C₈	—	5	1	no	—
409	C₄×C₈	—	10	1	no	—
410	C₄×C₈	—	10	1	no	—
411	C₄×C₈	C₂²×D₅	1	1	yes	characteristic
412	C₄×C₈	C₂²×D₅	1	1	yes	characteristic
413	C₄×C₈	C₂²×D₅	1	1	yes	characteristic
414	C₂²×C₅	—	4	1	no	—
415	C₂²×C₅	—	4	1	no	—
416	C₂²×C₅	—	4	1	no	—
417	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
418	C₂×D₅	—	2	1	no	—
419	C₂×D₅	—	2	1	no	—
420	C₂×D₅	—	4	1	no	—
421	C₂×D₅	—	4	1	no	—
422	C₂×D₅	—	4	1	no	—
423	C₂×D₅	#440	1	2	yes	—
424	C₄×C₅	—	2	2	no	—
425	C₄×C₅	—	2	1	no	—
426	C₄×C₅	—	4	1	no	—
427	C₄×C₅	—	4	1	no	—
428	C₄×C₅	C₂×#131	1	1	yes	characteristic
429	C₄×C₅	#568	1	1	yes	characteristic
430	C₄×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
431	C₄×C₅	C₂×#137	1	1	yes	characteristic
432	Dic₅	—	2	1	no	—
433	Dic₅	—	2	1	no	—
434	Dic₅	—	4	1	no	—
435	Dic₅	—	4	1	no	—
436	Dic₅	—	4	1	no	—
437	Dic₅	#440	1	2	yes	—
438	#41	—	20	2	no	—
439	#41	—	20	2	no	—
440	C₂×Q₈	—	5	1	no	—
441	C₂×Q₈	—	10	1	no	—
442	C₂×Q₈	—	10	1	no	—
443	C₂×Q₈	—	10	2	no	—
444	C₂×Q₈	—	20	1	no	—
445	C₂×Q₈	C₂×C₄×D₅	1	1	yes	characteristic
446	C₂×D₄	—	5	1	no	—
447	C₂×D₄	—	10	1	no	—
448	C₂×D₄	—	10	1	no	—
449	C₂×D₄	—	10	1	no	—
450	C₂×D₄	—	10	1	no	—
451	C₂×D₄	C₂×C₄×D₅	1	1	yes	characteristic
452	C₂²×C₄	—	2	1	no	—
453	C₂²×C₄	—	5	1	no	—
454	C₂²×C₄	—	5	1	no	—
455	C₂²×C₄	—	5	1	no	—
456	C₂²×C₄	—	10	1	no	—
457	C₂²×C₄	—	10	1	no	—
458	C₂²×C₄	—	10	1	no	—
459	SD₁₆	—	2	2	no	—
460	SD₁₆	—	10	2	no	—
461	SD₁₆	—	20	1	no	—
462	SD₁₆	—	20	1	no	—
463	M₁₆	—	10	2	no	—
464	M₁₆	—	10	2	no	—
465	M₁₆	—	20	2	no	—
466	M₁₆	—	20	2	no	—
467	M₁₆	—	20	2	no	—
468	C₂×C₈	—	2	1	no	—
469	C₂×C₈	—	2	1	no	—
470	C₂×C₈	—	2	1	no	—
471	C₂×C₈	—	4	2	no	—
472	C₂×C₈	—	5	1	no	—
473	C₂×C₈	—	5	1	no	—
474	C₂×C₈	—	5	1	no	—
475	C₂×C₈	—	5	1	no	—
476	C₂×C₈	—	10	1	no	—
477	C₂×C₈	—	10	1	no	—
478	C₂×C₈	—	10	1	no	—
479	C₂×C₈	—	20	2	no	—
480	C₂×C₈	—	20	2	no	—
481	C₂×C₈	—	20	2	no	—
482	C₂×C₈	C₂×C₄×D₅	1	1	yes	characteristic
483	C₂×C₈	C₂×C₄×D₅	1	1	yes	characteristic
484	C₂×C₈	D₄×D₅	1	1	yes	characteristic
485	C₂×C₈	D₄×D₅	1	1	yes	characteristic
486	C₄⋊C₄	—	2	1	no	—
487	C₄⋊C₄	—	5	1	no	—
488	C₄⋊C₄	—	5	1	no	—
489	C₄⋊C₄	—	10	1	no	—
490	C₄⋊C₄	—	10	1	no	—
491	C₄⋊C₄	—	10	1	no	—
492	C₄⋊C₄	—	10	1	no	—
493	C₄⋊C₄	—	10	1	no	—
494	C₄⋊C₄	C₂×C₄×D₅	1	1	yes	characteristic
495	C₄⋊C₄	C₂×C₄×D₅	1	1	yes	characteristic
496	C₂²⋊C₄	—	2	1	no	—
497	C₂²⋊C₄	—	10	1	no	—
498	C₂²⋊C₄	—	10	1	no	—
499	C₂²⋊C₄	—	10	1	no	—
500	C₄²	—	2	1	no	—
501	C₄²	—	5	1	no	—
502	C₄²	—	5	1	no	—
503	C₄²	—	5	1	no	—
504	C₄²	—	10	1	no	—
505	C₄²	—	10	1	no	—
506	C₄²	—	10	1	no	—
507	C₄²	C₂³×D₅	1	1	yes	characteristic
508	C₂×C₅	—	8	1	no	—
509	C₂×C₅	#2933	1	1	yes	characteristic
510	C₂×C₅	C₂×#440	1	1	yes	characteristic
511	C₂×C₅	#2956	1	1	yes	characteristic
512	D₅	—	2	2	no	—
513	D₅	—	8	1	no	—
514	C₂³	—	2	1	no	—
515	C₂³	—	5	1	no	—
516	C₂³	—	10	1	no	—
517	Q₈	—	2	1	no	—
518	Q₈	—	10	1	no	—
519	Q₈	—	10	1	no	—
520	Q₈	—	20	2	no	—
521	Q₈	—	20	2	no	—
522	Q₈	#4047	1	2	yes	complemented
523	D₄	—	2	1	no	—
524	D₄	—	2	1	no	—
525	D₄	—	10	1	no	—
526	D₄	—	10	1	no	—
527	D₄	—	20	2	no	—
528	D₄	—	20	2	no	—
529	D₄	—	20	2	no	—
530	D₄	—	40	1	no	—
531	C₂×C₄	—	2	1	no	—
532	C₂×C₄	—	2	1	no	—
533	C₂×C₄	—	2	1	no	—
534	C₂×C₄	—	4	1	no	—
535	C₂×C₄	—	4	1	no	—
536	C₂×C₄	—	5	1	no	—
537	C₂×C₄	—	5	2	no	—
538	C₂×C₄	—	5	2	no	—
539	C₂×C₄	—	5	1	no	—
540	C₂×C₄	—	5	1	no	—
541	C₂×C₄	—	10	1	no	—
542	C₂×C₄	—	10	1	no	—
543	C₂×C₄	—	10	1	no	—
544	C₂×C₄	—	10	1	no	—
545	C₂×C₄	—	10	1	no	—
546	C₂×C₄	—	20	1	no	—
547	C₂×C₄	—	20	2	no	—
548	C₂×C₄	—	20	1	no	—
549	C₂×C₄	—	20	1	no	—
550	C₂×C₄	—	40	1	no	—
551	C₂×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
552	C₂×C₄	C₂×D₄×D₅	1	1	yes	characteristic
553	C₂×C₄	D₅×#41	1	1	yes	characteristic
554	C₈	—	2	1	no	—
555	C₈	—	2	1	no	—
556	C₈	—	2	1	no	—
557	C₈	—	2	1	no	—
558	C₈	—	4	1	no	—
559	C₈	—	4	1	no	—
560	C₈	—	4	1	no	—
561	C₈	—	10	2	no	—
562	C₈	—	10	1	no	—
563	C₈	—	10	1	no	—
564	C₈	—	10	1	no	—
565	C₈	—	10	1	no	—
566	C₈	—	20	1	no	—
567	C₈	—	20	1	no	—
568	C₅	#18004	1	1	yes	characteristic, complemented, Sylow
569	C₂²	—	4	1	no	—
570	C₂²	—	4	1	no	—
571	C₂²	—	4	1	no	—
572	C₂²	—	5	2	no	—
573	C₂²	—	10	1	no	—
574	C₂²	—	10	1	no	—
575	C₂²	—	20	1	no	—
576	C₂²	—	20	1	no	—
577	C₂²	—	20	1	no	—
578	C₂²	C₄×D₄×D₅	1	1	yes	characteristic
579	C₄	—	2	1	no	—
580	C₄	—	2	2	no	—
581	C₄	—	4	1	no	—
582	C₄	—	4	1	no	—
583	C₄	—	5	2	no	—
584	C₄	—	10	1	no	—
585	C₄	—	10	1	no	—
586	C₄	—	20	1	no	—
587	C₄	—	20	1	no	—
588	C₄	—	20	1	no	—
589	C₄	C₂×#4047	1	1	yes	characteristic
590	C₄	#66084	1	1	yes	characteristic
591	C₄	D₅×AGL(1,ℤ/8)	1	1	yes	characteristic
592	C₄	D₅×#137	1	1	yes	characteristic
593	C₂	—	8	1	no	—
594	C₂	—	10	2	no	—
595	C₂	—	40	1	no	—
596	C₂	#10611154	1	1	yes	characteristic
597	C₂	D₅×#440	1	1	yes	characteristic
598	C₂	#10611629	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₅
commutator	C₂×C₄×C₅	C₂³×C₄
Frattini	C₄²	C₂³×D₅
Fitting	C₅×SD₁₆⋊C₈	C₂
socle	C₂²×C₅	C₂×C₄×D₄
prime radical	#65882	C₂²
cosocle	C₄²×C₅	C₂⁴
hypercenter	SD₁₆⋊C₈	D₅
hypocenter	C₅	#18004
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ SD₁₆⋊C₈

Complements

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

N	H ≅ G/N	type
1. Q₈×#676	C₂	semidirect
4. C₅×SD₁₆⋊C₈	C₂	semidirect
5. #10601729	C₂	semidirect
6. #10601691	C₂	semidirect
7. #10601636	C₂	semidirect
8. #10599365	C₂	semidirect
9. #10599354	C₂	semidirect
10. D₅×Q₈⋊C₈	C₂	semidirect
11. #10599007	C₂	semidirect
13. #10598955	C₂	semidirect
14. #10598875	C₂	semidirect
15. #10598863	C₂	semidirect
156. SD₁₆⋊C₈	D₅	semidirect
286. C₅×Q₈	#131	semidirect
522. Q₈	#4047	semidirect
568. C₅	#18004	semidirect

Maximal subgroups

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

subgroup	index
Q₈×#676	2
#10611384	2
#10611156	2
C₅×SD₁₆⋊C₈	2
#10601729	2
#10601691	2
#10601636	2
#10599365	2
#10599354	2
D₅×Q₈⋊C₈	2
#10599007	2
#10598969	2
#10598955	2
#10598875	2
#10598863	2
#18004	5