Subgroups — #13031600

Order 1280.

714 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10617195	C₂	1	1	yes	maximal, characteristic
2	Q₈×D₅⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	#10611560	C₂	1	1	yes	maximal, characteristic
4	#10604838	C₂	1	1	yes	maximal, characteristic, complemented
5	Q₁₆×#170	C₂	1	1	yes	maximal, characteristic, complemented
6	#10604438	C₂	1	1	yes	maximal, characteristic, complemented
7	#10604437	C₂	1	1	yes	maximal, characteristic
8	#10604040	C₂	1	1	yes	maximal, characteristic, complemented
9	#10604039	C₂	1	1	yes	maximal, characteristic, complemented
10	#10603970	C₂	1	1	yes	maximal, characteristic, complemented
11	#10603969	C₂	1	1	yes	maximal, characteristic, complemented
12	#10603968	C₂	1	1	yes	maximal, characteristic, complemented
13	#10603967	C₂	1	1	yes	maximal, characteristic, complemented
14	#10603865	C₂	1	1	yes	maximal, characteristic, complemented
15	#10603861	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#4064	C₄	1	1	yes	characteristic
17	C₄×#713	C₂²	1	1	yes	characteristic
18	C₄×Q₈×D₅	C₂²	1	1	yes	characteristic
19	Q₈×#170	C₂²	1	1	yes	characteristic
20	Q₈×#170	C₂²	1	1	yes	characteristic
21	Q₈×#170	C₂²	1	1	yes	characteristic
22	Q₈×#170	C₂²	1	1	yes	characteristic
23	#65703	—	2	1	no	—
24	#65703	—	2	1	no	—
25	#65703	C₂²	1	1	yes	characteristic
26	#65703	C₂²	1	1	yes	characteristic
27	#65702	—	2	1	no	—
28	#65702	—	2	1	no	—
29	#65702	C₂²	1	1	yes	characteristic
30	#65702	C₂²	1	1	yes	characteristic
31	#65680	—	2	1	no	—
32	#65680	C₂²	1	1	yes	characteristic
33	D₅⋊(C₄⋊C₈)	—	2	1	no	—
34	D₅⋊(C₄⋊C₈)	C₂²	1	1	yes	characteristic
35	#65678	C₂²	1	1	yes	characteristic
36	C₄×D₅⋊C₈	—	2	1	no	—
37	C₄×D₅⋊C₈	—	2	1	no	—
38	C₄×D₅⋊C₈	C₂²	1	1	yes	characteristic
39	C₅×#441	C₄	1	1	yes	characteristic
40	Q₁₆×Dic₅	C₂²	1	1	yes	characteristic
41	#65319	C₄	1	1	yes	characteristic
42	#65315	C₄	1	1	yes	characteristic
43	#65150	C₄	1	1	yes	characteristic
44	#65141	C₂²	1	1	yes	characteristic
45	#65092	C₄	1	1	yes	characteristic
46	#65091	C₄	1	1	yes	characteristic
47	#65079	C₂²	1	1	yes	characteristic
48	#65077	C₂²	1	1	yes	characteristic
49	#64999	C₄	1	1	yes	characteristic
50	#64996	C₂²	1	1	yes	characteristic
51	Q₈⋊#170	C₂²	1	1	yes	characteristic
52	Q₈⋊#170	C₂²	1	1	yes	characteristic
53	Q₈⋊#170	C₂²	1	1	yes	characteristic
54	Q₈⋊#170	C₂²	1	1	yes	characteristic
55	#64884	C₂²	1	1	yes	characteristic
56	#64883	C₂²	1	1	yes	characteristic
57	#64882	C₂²	1	1	yes	characteristic
58	#64881	C₂²	1	1	yes	characteristic
59	#64879	C₂²	1	1	yes	characteristic
60	#64879	C₂²	1	1	yes	characteristic
61	C₈×#170	C₂²	1	1	yes	characteristic
62	C₈×#170	C₂²	1	1	yes	characteristic
63	#64872	C₂²	1	1	yes	characteristic
64	#64872	C₂²	1	1	yes	characteristic
65	#64871	C₂²	1	1	yes	characteristic
66	#64871	C₂²	1	1	yes	characteristic
67	C₈×#137	—	5	1	no	maximal, Sylow
68	C₂×#713	C₂×C₄	1	1	yes	characteristic
69	C₂×Q₈×D₅	C₂×C₄	1	1	yes	characteristic
70	C₂×D₅⋊C₈	—	2	1	no	—
71	C₂×D₅⋊C₈	—	2	1	no	—
72	C₂×D₅⋊C₈	—	2	1	no	—
73	C₂×D₅⋊C₈	D₄	1	1	yes	characteristic
74	C₂×D₅⋊C₈	D₄	1	1	yes	characteristic
75	C₂×C₅×Q₁₆	C₂×C₄	1	1	yes	characteristic
76	C₄×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
77	C₄×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
78	Q₈×Dic₅	C₂³	1	1	yes	characteristic
79	Q₈×Dic₅	C₂³	1	1	yes	characteristic
80	C₂×#689	C₂×C₄	1	1	yes	characteristic
81	C₂×#688	C₂×C₄	1	1	yes	characteristic
82	#4064	C₈	1	8	yes	complemented
83	C₂×#677	C₂×C₄	1	1	yes	characteristic
84	C₂×#676	C₂×C₄	1	1	yes	characteristic
85	C₂×#676	C₂×C₄	1	1	yes	characteristic
86	#4039	—	2	1	no	—
87	#4039	C₂³	1	1	yes	characteristic
88	#4038	—	2	1	no	—
89	#4038	C₂×C₄	1	1	yes	characteristic
90	D₅×C₄⋊C₄	—	2	1	no	—
91	D₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
92	#4033	—	2	1	no	—
93	#4033	C₂³	1	1	yes	characteristic
94	C₄×D₂₀	—	2	1	no	—
95	C₄×D₂₀	C₂×C₄	1	1	yes	characteristic
96	C₄²×D₅	—	2	1	no	—
97	C₄²×D₅	—	2	1	no	—
98	C₄²×D₅	C₂³	1	1	yes	characteristic
99	C₄×Dic₁₀	—	2	1	no	—
100	C₄×Dic₁₀	C₂×C₄	1	1	yes	characteristic
101	#4004	—	2	1	no	—
102	#4004	—	2	1	no	—
103	#4004	—	2	1	no	—
104	#4004	—	2	1	no	—
105	#4003	—	2	1	no	—
106	#4003	—	2	1	no	—
107	#4003	—	2	1	no	—
108	#4003	—	2	1	no	—
109	C₄⋊#170	—	2	1	no	—
110	C₄⋊#170	—	2	1	no	—
111	C₄⋊#170	—	2	1	no	—
112	C₄⋊#170	—	2	1	no	—
113	C₄⋊#170	C₂³	1	1	yes	characteristic
114	C₄⋊#170	C₂³	1	1	yes	characteristic
115	C₄⋊#170	C₂³	1	1	yes	characteristic
116	C₄⋊#170	C₂³	1	1	yes	characteristic
117	C₄×#170	—	2	1	no	—
118	C₄×#170	—	2	1	no	—
119	C₄×#170	—	2	1	no	—
120	C₄×#170	—	2	1	no	—
121	C₄×#170	—	2	1	no	—
122	C₄×#170	—	2	1	no	—
123	C₄×#170	—	2	1	no	—
124	C₄×#170	D₄	1	1	yes	characteristic
125	C₄×#170	D₄	1	1	yes	characteristic
126	C₄×#170	C₂³	1	1	yes	characteristic
127	C₄×#170	C₂³	1	1	yes	characteristic
128	C₄×#170	C₂³	1	1	yes	characteristic
129	C₄×#170	C₂³	1	1	yes	characteristic
130	C₅×#106	C₂×C₄	1	1	yes	characteristic
131	C₅×#103	C₂×C₄	1	1	yes	characteristic
132	C₅×#103	C₂×C₄	1	1	yes	characteristic
133	C₅×#97	C₂×C₄	1	1	yes	characteristic
134	#3967	C₂×C₄	1	1	yes	characteristic
135	#3967	C₂×C₄	1	1	yes	characteristic
136	#3953	C₂×C₄	1	1	yes	characteristic
137	#3950	C₂×C₄	1	1	yes	characteristic
138	#3948	C₂×C₄	1	1	yes	characteristic
139	C₈×Dic₅	C₂³	1	1	yes	characteristic
140	C₈×Dic₅	C₂³	1	1	yes	characteristic
141	#3942	C₂×C₄	1	1	yes	characteristic
142	#3941	C₂×C₄	1	1	yes	characteristic
143	#3940	C₂×C₄	1	1	yes	characteristic
144	#3939	C₂×C₄	1	1	yes	characteristic
145	#3935	C₂×C₄	1	1	yes	characteristic
146	C₈×#41	—	5	1	no	—
147	C₂×C₈×Q₈	—	5	1	no	—
148	C₄×#137	—	5	1	no	—
149	#1579	—	5	1	no	—
150	#1579	—	5	1	no	—
151	SD₁₆⋊C₈	—	5	1	no	—
152	SD₁₆⋊C₈	—	5	1	no	—
153	C₈×Q₁₆	—	5	1	no	—
154	C₈×Q₁₆	—	5	1	no	—
155	C₈×SD₁₆	—	5	1	no	—
156	C₈×SD₁₆	—	5	1	no	—
157	#1565	—	5	1	no	—
158	#1479	—	5	1	no	—
159	#1477	—	5	1	no	—
160	C₈×M₁₆	—	5	1	no	—
161	C₂×C₅×Q₈	C₂²×C₄	1	1	yes	characteristic
162	C₂×C₅×Q₈	C₂²×C₄	1	1	yes	characteristic
163	#713	—	2	2	no	—
164	#713	C₂×C₈	1	4	yes	—
165	Q₈×D₅	—	2	2	no	—
166	Q₈×D₅	C₂×C₈	1	4	yes	complemented
167	C₂×D₂₀	—	2	1	no	—
168	C₂×D₂₀	C₂²×C₄	1	1	yes	characteristic
169	C₂×C₄×D₅	—	2	1	no	—
170	C₂×C₄×D₅	—	2	1	no	—
171	C₂×C₄×D₅	—	2	1	no	—
172	C₂×C₄×D₅	—	2	1	no	—
173	C₂×C₄×D₅	—	2	1	no	—
174	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
175	C₂×C₄×D₅	C₂×D₄	1	1	yes	characteristic
176	C₂×C₄×D₅	#41	1	1	yes	characteristic
177	C₂×Dic₁₀	—	2	1	no	—
178	C₂×Dic₁₀	C₂²×C₄	1	1	yes	characteristic
179	C₂×#170	—	2	1	no	—
180	C₂×#170	—	2	1	no	—
181	C₂×#170	—	2	1	no	—
182	C₂×#170	—	2	1	no	—
183	C₂×#170	—	2	1	no	—
184	C₂×#170	—	2	1	no	—
185	C₂×#170	C₂×D₄	1	1	yes	characteristic
186	C₂×#170	C₂×D₄	1	1	yes	characteristic
187	C₂×#170	C₂×D₄	1	1	yes	characteristic
188	C₂×#170	C₂×D₄	1	1	yes	characteristic
189	D₅⋊C₈	—	2	2	no	—
190	D₅⋊C₈	—	4	1	no	—
191	D₅⋊C₈	—	4	2	no	—
192	D₅⋊C₈	—	4	2	no	—
193	D₅⋊C₈	—	4	2	no	—
194	C₅×Q₁₆	C₂×C₈	1	4	yes	complemented
195	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
196	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
197	C₅×C₄⋊C₄	—	2	1	no	—
198	C₅×C₄⋊C₄	—	2	1	no	—
199	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
200	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
201	C₄²×C₅	—	2	1	no	—
202	C₄²×C₅	—	2	1	no	—
203	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
204	#689	C₂×C₈	1	4	yes	complemented
205	#688	C₂×C₈	1	4	yes	complemented
206	#685	—	2	1	no	—
207	#685	—	2	1	no	—
208	#685	—	2	1	no	—
209	C₄⋊Dic₅	—	2	1	no	—
210	C₄⋊Dic₅	—	2	1	no	—
211	C₄⋊Dic₅	C₂²×C₄	1	1	yes	characteristic
212	C₄⋊Dic₅	C₂²×C₄	1	1	yes	characteristic
213	#683	—	2	1	no	—
214	#683	—	2	1	no	—
215	#683	—	2	1	no	—
216	C₄×Dic₅	—	2	1	no	—
217	C₄×Dic₅	—	2	1	no	—
218	C₄×Dic₅	—	2	1	no	—
219	C₄×Dic₅	—	2	1	no	—
220	C₄×Dic₅	—	2	1	no	—
221	C₄×Dic₅	C₂×D₄	1	1	yes	characteristic
222	C₄×Dic₅	#41	1	1	yes	characteristic
223	C₄×Dic₅	C₂⁴	1	1	yes	characteristic
224	C₂×#168	C₂²×C₄	1	1	yes	characteristic
225	C₂×#168	C₂²×C₄	1	1	yes	characteristic
226	#677	C₂×C₈	1	4	yes	complemented
227	#676	—	2	2	no	—
228	#676	C₂×C₈	1	4	yes	complemented
229	C₂×#137	—	5	1	no	—
230	C₄×#41	—	5	1	no	—
231	C₂×C₄×Q₈	—	5	1	no	—
232	C₈×Q₈	—	5	1	no	—
233	C₈×Q₈	—	5	1	no	—
234	C₈×Q₈	—	5	1	no	—
235	C₈×Q₈	—	5	1	no	—
236	C₈×Q₈	—	5	1	no	—
237	C₈×Q₈	—	5	1	no	—
238	C₈×Q₈	—	10	1	no	—
239	C₈×Q₈	—	10	1	no	—
240	#441	—	5	1	no	—
241	#441	AGL(1,𝔽₅)	1	1	yes	characteristic
242	#440	—	5	1	no	—
243	#440	—	5	1	no	—
244	C₄×Q₁₆	—	5	1	no	—
245	C₄×Q₁₆	—	5	1	no	—
246	C₄×SD₁₆	—	5	1	no	—
247	C₄×SD₁₆	—	5	1	no	—
248	C₈×D₄	—	5	1	no	—
249	C₈×D₄	—	5	1	no	—
250	C₈×D₄	—	10	1	no	—
251	C₈×D₄	—	10	1	no	—
252	#431	—	5	1	no	—
253	#431	—	5	1	no	—
254	#431	—	10	1	no	—
255	#428	—	5	1	no	—
256	C₂×C₄⋊C₈	—	5	1	no	—
257	C₂×C₄⋊C₈	—	10	1	no	—
258	#419	—	5	1	no	—
259	#417	—	5	1	no	—
260	C₄×M₁₆	—	5	1	no	—
261	C₂×C₄×C₈	—	5	1	no	—
262	C₂×C₄×C₈	—	10	1	no	—
263	C₂×C₄×C₈	—	10	1	no	—
264	#335	—	5	1	no	—
265	#335	—	5	1	no	—
266	#334	—	5	1	no	—
267	#334	—	5	1	no	—
268	Q₈⋊C₈	—	5	1	no	—
269	Q₈⋊C₈	—	5	1	no	—
270	Q₈⋊C₈	—	5	1	no	—
271	Q₈⋊C₈	—	5	1	no	—
272	Q₈⋊C₈	—	5	1	no	—
273	Q₈⋊C₈	—	5	1	no	—
274	D₄⋊C₈	—	5	1	no	—
275	D₄⋊C₈	—	5	1	no	—
276	#322	—	5	1	no	—
277	#322	—	5	1	no	—
278	C₈²	—	5	1	no	—
279	C₈²	—	5	1	no	—
280	C₂²×D₅	—	2	1	no	—
281	C₂²×D₅	C₄×D₄	1	1	yes	characteristic
282	C₅×Q₈	—	2	1	no	—
283	C₅×Q₈	—	2	1	no	—
284	C₅×Q₈	C₂²×C₈	1	2	yes	—
285	C₅×Q₈	C₂²×C₈	1	2	yes	—
286	C₂×C₄×C₅	—	2	1	no	—
287	C₂×C₄×C₅	—	2	1	no	—
288	C₂×C₄×C₅	—	2	1	no	—
289	C₂×C₄×C₅	—	2	1	no	—
290	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
291	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
292	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
293	C₂×Dic₅	—	2	1	no	—
294	C₂×Dic₅	—	2	1	no	—
295	C₂×Dic₅	—	2	1	no	—
296	C₂×Dic₅	C₄×D₄	1	1	yes	characteristic
297	C₂×Dic₅	C₂²×D₄	1	1	yes	characteristic
298	C₂×Dic₅	C₂×#41	1	1	yes	characteristic
299	D₂₀	—	2	4	no	—
300	D₂₀	—	2	1	no	—
301	D₂₀	C₂²×C₈	1	2	yes	—
302	C₄×D₅	—	2	4	no	—
303	C₄×D₅	—	2	1	no	—
304	C₄×D₅	—	2	1	no	—
305	C₄×D₅	—	2	4	no	—
306	C₄×D₅	—	4	1	no	—
307	C₄×D₅	—	4	2	no	—
308	C₄×D₅	—	4	2	no	—
309	C₄×D₅	—	4	1	no	—
310	C₄×D₅	—	4	1	no	—
311	C₄×D₅	C₂²×C₈	1	2	yes	—
312	C₄×D₅	#131	1	2	yes	—
313	Dic₁₀	—	2	1	no	—
314	Dic₁₀	—	2	4	no	—
315	Dic₁₀	C₂²×C₈	1	2	yes	—
316	#170	—	2	1	no	—
317	#170	—	2	1	no	—
318	#170	—	2	1	no	—
319	#170	—	4	1	no	—
320	#170	—	4	1	no	—
321	#170	—	4	1	no	—
322	#170	—	4	1	no	—
323	#170	—	4	1	no	—
324	#170	—	4	1	no	—
325	#170	#137	1	2	yes	complemented
326	C₅×C₈	—	2	1	no	—
327	C₅×C₈	C₂²×C₈	1	2	yes	—
328	#168	—	2	1	no	—
329	#168	C₂²×C₈	1	2	yes	—
330	C₂×#41	—	5	1	no	—
331	C₂²×Q₈	—	5	1	no	—
332	#137	—	5	8	no	—
333	C₂×Q₁₆	—	5	1	no	—
334	C₂×Q₁₆	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
335	C₂×SD₁₆	—	5	1	no	—
336	C₂×SD₁₆	—	5	1	no	—
337	C₂×M₁₆	—	5	1	no	—
338	C₂×M₁₆	—	5	1	no	—
339	C₂²×C₈	—	5	1	no	—
340	C₂²×C₈	—	5	1	no	—
341	C₂²×C₈	—	10	1	no	—
342	C₂²×C₈	—	10	1	no	—
343	C₂²×C₈	—	10	1	no	—
344	C₄×Q₈	—	5	1	no	—
345	C₄×Q₈	—	5	1	no	—
346	C₄×Q₈	—	5	1	no	—
347	C₄×Q₈	—	5	1	no	—
348	C₄×Q₈	—	10	1	no	—
349	C₄×Q₈	—	10	1	no	—
350	C₄×Q₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
351	C₄×Q₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
352	C₄×D₄	—	5	1	no	—
353	C₄×D₄	—	5	1	no	—
354	C₄×D₄	—	10	1	no	—
355	C₄×D₄	—	10	1	no	—
356	#117	—	5	1	no	—
357	#117	—	10	1	no	—
358	C₂×C₄⋊C₄	—	5	1	no	—
359	C₂×C₄⋊C₄	—	10	1	no	—
360	C₂×C₄²	—	5	1	no	—
361	C₂×C₄²	—	10	1	no	—
362	C₂×C₄²	—	10	1	no	—
363	#107	—	5	1	no	—
364	#107	—	5	1	no	—
365	#106	—	5	1	no	—
366	#106	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
367	C₄⋊C₈	—	5	1	no	—
368	C₄⋊C₈	—	5	1	no	—
369	C₄⋊C₈	—	5	1	no	—
370	C₄⋊C₈	—	5	1	no	—
371	C₄⋊C₈	—	10	1	no	—
372	C₄⋊C₈	—	10	1	no	—
373	C₄⋊C₈	—	10	1	no	—
374	C₄⋊C₈	—	10	1	no	—
375	C₄⋊C₈	—	10	1	no	—
376	C₄⋊C₈	—	10	1	no	—
377	C₄⋊C₈	—	10	1	no	—
378	C₄⋊C₈	—	10	1	no	—
379	#103	—	5	1	no	—
380	#103	—	5	1	no	—
381	#103	—	5	1	no	—
382	#103	—	5	1	no	—
383	#103	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
384	#103	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
385	#102	—	5	1	no	—
386	#102	—	5	1	no	—
387	C₂²⋊C₈	—	10	1	no	—
388	C₂²⋊C₈	—	10	1	no	—
389	C₂²⋊C₈	—	10	1	no	—
390	C₂²⋊C₈	—	10	1	no	—
391	#97	—	5	1	no	—
392	#97	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
393	C₄×C₈	—	5	1	no	—
394	C₄×C₈	—	5	1	no	—
395	C₄×C₈	—	5	1	no	—
396	C₄×C₈	—	5	1	no	—
397	C₄×C₈	—	5	1	no	—
398	C₄×C₈	—	5	1	no	—
399	C₄×C₈	—	5	1	no	—
400	C₄×C₈	—	5	1	no	—
401	C₄×C₈	—	10	1	no	—
402	C₄×C₈	—	10	1	no	—
403	C₄×C₈	—	10	1	no	—
404	C₄×C₈	—	10	1	no	—
405	C₄×C₈	—	10	1	no	—
406	C₄×C₈	—	10	1	no	—
407	C₄×C₈	—	10	1	no	—
408	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
409	C₂×D₅	—	2	1	no	—
410	C₂×D₅	—	2	1	no	—
411	C₂×D₅	—	2	2	no	—
412	C₂×D₅	—	4	1	no	—
413	C₂×D₅	—	4	1	no	—
414	C₂×D₅	C₈×D₄	1	2	yes	—
415	C₄×C₅	—	2	2	no	—
416	C₄×C₅	—	2	2	no	—
417	C₄×C₅	—	2	1	no	—
418	C₄×C₅	—	2	1	no	—
419	C₄×C₅	—	4	1	no	—
420	C₄×C₅	—	4	1	no	—
421	C₄×C₅	C₂³×C₈	1	1	yes	characteristic
422	C₄×C₅	C₂×#131	1	1	yes	characteristic
423	Dic₅	—	2	2	no	—
424	Dic₅	—	2	1	no	—
425	Dic₅	—	4	1	no	—
426	Dic₅	—	4	1	no	—
427	Dic₅	C₈×D₄	1	2	yes	—
428	Dic₅	C₂×#137	1	1	yes	characteristic
429	Dic₅	#575	1	1	yes	characteristic
430	#41	—	5	4	no	—
431	#41	—	10	2	no	—
432	C₂×Q₈	—	5	4	no	—
433	C₂×Q₈	—	5	1	no	—
434	C₂×Q₈	—	10	1	no	—
435	C₂×Q₈	—	10	2	no	—
436	C₂×Q₈	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
437	C₂×Q₈	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
438	C₂×D₄	—	5	1	no	—
439	C₂×D₄	—	10	1	no	—
440	C₂²×C₄	—	5	1	no	—
441	C₂²×C₄	—	5	1	no	—
442	C₂²×C₄	—	5	1	no	—
443	C₂²×C₄	—	10	1	no	—
444	C₂²×C₄	—	10	1	no	—
445	C₂²×C₄	—	10	1	no	—
446	C₂²×C₄	—	10	1	no	—
447	C₂²×C₄	—	10	1	no	—
448	Q₁₆	—	5	4	no	—
449	Q₁₆	D₅⋊C₈	1	4	yes	complemented
450	SD₁₆	—	5	4	no	—
451	SD₁₆	—	5	4	no	—
452	M₁₆	—	5	4	no	—
453	M₁₆	—	10	2	no	—
454	C₂×C₈	—	5	1	no	—
455	C₂×C₈	—	5	1	no	—
456	C₂×C₈	—	5	1	no	—
457	C₂×C₈	—	5	1	no	—
458	C₂×C₈	—	5	1	no	—
459	C₂×C₈	—	5	1	no	—
460	C₂×C₈	—	10	2	no	—
461	C₂×C₈	—	10	1	no	—
462	C₂×C₈	—	10	1	no	—
463	C₂×C₈	—	10	1	no	—
464	C₂×C₈	—	10	1	no	—
465	C₂×C₈	—	10	1	no	—
466	C₂×C₈	—	10	1	no	—
467	C₂×C₈	—	20	2	no	—
468	C₂×C₈	—	20	1	no	—
469	C₂×C₈	—	20	2	no	—
470	C₂×C₈	—	20	2	no	—
471	C₂×C₈	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
472	C₂×C₈	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
473	C₄⋊C₄	—	2	1	no	—
474	C₄⋊C₄	—	2	1	no	—
475	C₄⋊C₄	—	5	1	no	—
476	C₄⋊C₄	—	5	1	no	—
477	C₄⋊C₄	—	10	1	no	—
478	C₄⋊C₄	—	10	1	no	—
479	C₄⋊C₄	—	10	1	no	—
480	C₄⋊C₄	—	10	1	no	—
481	C₄⋊C₄	—	10	1	no	—
482	C₄⋊C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
483	C₄⋊C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
484	C₂²⋊C₄	—	10	1	no	—
485	C₂²⋊C₄	—	10	1	no	—
486	C₂²⋊C₄	—	10	1	no	—
487	C₄²	—	2	1	no	—
488	C₄²	—	2	1	no	—
489	C₄²	—	5	1	no	—
490	C₄²	—	5	1	no	—
491	C₄²	—	5	1	no	—
492	C₄²	—	10	1	no	—
493	C₄²	—	10	1	no	—
494	C₄²	—	10	1	no	—
495	C₄²	—	10	1	no	—
496	C₄²	—	10	1	no	—
497	C₄²	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
498	C₂×C₅	C₂×C₈×D₄	1	1	yes	characteristic
499	C₂×C₅	C₄×#137	1	1	yes	characteristic
500	C₂×C₅	#2955	1	1	yes	characteristic
501	D₅	—	2	2	no	—
502	D₅	—	4	2	no	—
503	C₂³	—	5	1	no	—
504	C₂³	—	10	1	no	—
505	Q₈	—	2	1	no	—
506	Q₈	—	2	1	no	—
507	Q₈	—	5	2	no	—
508	Q₈	—	10	4	no	—
509	Q₈	—	10	1	no	—
510	Q₈	C₂×D₅⋊C₈	1	2	yes	—
511	Q₈	C₂×D₅⋊C₈	1	2	yes	—
512	D₄	—	5	2	no	—
513	D₄	—	10	4	no	—
514	D₄	—	10	1	no	—
515	C₂×C₄	—	2	1	no	—
516	C₂×C₄	—	2	1	no	—
517	C₂×C₄	—	2	1	no	—
518	C₂×C₄	—	2	1	no	—
519	C₂×C₄	—	5	1	no	—
520	C₂×C₄	—	5	1	no	—
521	C₂×C₄	—	5	2	no	—
522	C₂×C₄	—	5	2	no	—
523	C₂×C₄	—	5	1	no	—
524	C₂×C₄	—	10	1	no	—
525	C₂×C₄	—	10	1	no	—
526	C₂×C₄	—	10	4	no	—
527	C₂×C₄	—	10	4	no	—
528	C₂×C₄	—	10	1	no	—
529	C₂×C₄	—	10	1	no	—
530	C₂×C₄	—	10	1	no	—
531	C₂×C₄	—	20	1	no	—
532	C₂×C₄	—	20	2	no	—
533	C₂×C₄	—	20	1	no	—
534	C₂×C₄	—	20	1	no	—
535	C₂×C₄	—	20	2	no	—
536	C₂×C₄	D₄×AGL(1,𝔽₅)	1	1	yes	characteristic
537	C₂×C₄	D₄×AGL(1,𝔽₅)	1	1	yes	characteristic
538	C₂×C₄	C₂³×AGL(1,𝔽₅)	1	1	yes	characteristic
539	C₈	—	2	1	no	—
540	C₈	—	5	2	no	—
541	C₈	—	5	2	no	—
542	C₈	—	10	1	no	—
543	C₈	—	10	1	no	—
544	C₈	—	10	1	no	—
545	C₈	—	10	1	no	—
546	C₈	—	20	1	no	—
547	C₈	—	20	1	no	—
548	C₈	—	20	1	no	—
549	C₈	—	20	1	no	—
550	C₈	—	20	1	no	—
551	C₈	—	20	1	no	—
552	C₈	C₂×D₅⋊C₈	1	2	yes	—
553	C₅	C₈×#137	1	1	yes	characteristic, complemented, Sylow
554	C₂²	—	5	2	no	—
555	C₂²	—	10	1	no	—
556	C₂²	—	10	1	no	—
557	C₂²	—	10	2	no	—
558	C₂²	—	20	1	no	—
559	C₂²	—	20	1	no	—
560	C₂²	C₂×D₄×AGL(1,𝔽₅)	1	1	yes	characteristic
561	C₄	—	2	2	no	—
562	C₄	—	2	2	no	—
563	C₄	—	2	1	no	—
564	C₄	—	2	1	no	—
565	C₄	—	4	1	no	—
566	C₄	—	4	1	no	—
567	C₄	—	5	2	no	—
568	C₄	—	5	1	no	—
569	C₄	—	5	1	no	—
570	C₄	—	10	2	no	—
571	C₄	—	10	1	no	—
572	C₄	—	20	1	no	—
573	C₄	—	20	1	no	—
574	C₄	C₂²×D₅⋊C₈	1	1	yes	characteristic
575	C₄	D₅⋊#131	1	1	yes	characteristic
576	C₂	—	10	2	no	—
577	C₂	—	20	2	no	—
578	C₂	D₄×D₅⋊C₈	1	1	yes	characteristic
579	C₂	AGL(1,𝔽₅)×#137	1	1	yes	characteristic
580	C₂	#10617452	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×AGL(1,𝔽₅)
commutator	C₄×C₅	C₂³×C₈
Frattini	C₂×C₄	C₂³×AGL(1,𝔽₅)
Fitting	C₅×#441	C₄
socle	C₂²×C₅	C₂×C₄×D₄
prime radical	C₂×#713	C₂×C₄
cosocle	C₄×Dic₅	C₂⁴
hypercenter	#441	AGL(1,𝔽₅)
hypocenter	C₅	C₈×#137
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #441

Complements

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

N	H ≅ G/N	type
2. Q₈×D₅⋊C₈	C₂	semidirect
4. #10604838	C₂	semidirect
5. Q₁₆×#170	C₂	semidirect
6. #10604438	C₂	semidirect
8. #10604040	C₂	semidirect
9. #10604039	C₂	semidirect
10. #10603970	C₂	semidirect
11. #10603969	C₂	semidirect
12. #10603968	C₂	semidirect
13. #10603967	C₂	semidirect
14. #10603865	C₂	semidirect
15. #10603861	C₂	semidirect
82. #4064	C₈	semidirect
166. Q₈×D₅	C₂×C₈	semidirect
194. C₅×Q₁₆	C₂×C₈	semidirect
204. #689	C₂×C₈	semidirect
205. #688	C₂×C₈	semidirect
226. #677	C₂×C₈	semidirect
228. #676	C₂×C₈	semidirect
325. #170	#137	semidirect
449. Q₁₆	D₅⋊C₈	semidirect
553. C₅	C₈×#137	semidirect

Maximal subgroups

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

subgroup	index
#10617195	2
Q₈×D₅⋊C₈	2
#10611560	2
#10604838	2
Q₁₆×#170	2
#10604438	2
#10604437	2
#10604040	2
#10604039	2
#10603970	2
#10603969	2
#10603968	2
#10603967	2
#10603865	2
#10603861	2
C₈×#137	5