Subgroups — #72253140

Order 12800.

2192 conjugacy classes of subgroups.

The subgroup lattice has 507 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72253138	C₂	1	2	yes	maximal
2	#72253135	C₂	1	2	yes	maximal
3	#72253133	—	2	2	no	—
4	C₈×C₄⋊#1043	—	2	2	no	—
5	#72242315	C₂	1	1	yes	maximal, characteristic
6	C₂×#13100227	C₄	1	1	yes	characteristic
7	#72242307	C₄	1	2	yes	—
8	C₂×#13100228	C₄	1	1	yes	characteristic
9	C₄×#11716862	C₂²	1	2	yes	—
10	#72242207	C₂	1	1	yes	maximal, characteristic
11	#72242201	C₄	1	1	yes	characteristic, complemented
12	#72242199	C₄	1	2	yes	complemented
13	#72242197	C₄	1	1	yes	characteristic, complemented
14	#72242195	C₂²	1	2	yes	—
15	C₅⋊D₅×#1313	C₂	1	1	yes	maximal, characteristic
16	#72242123	C₄	1	1	yes	characteristic, complemented
17	#72242120	C₄	1	1	yes	characteristic, complemented
18	#72242115	C₄	1	1	yes	characteristic, complemented
19	C₅²×#1313	C₄	1	1	yes	characteristic, complemented
20	C₅⋊D₅×#346	C₂²	1	1	yes	characteristic
21	C₅⋊D₅×#346	C₂²	1	1	yes	characteristic
22	#72242073	—	5	6	no	maximal
23	C₅⋊D₅×#322	C₂²	1	1	yes	characteristic
24	C₂×#11716862	C₂×C₄	1	2	yes	—
25	C₂×#11716862	C₂×C₄	1	2	yes	—
26	C₂×C₈×#1043	—	4	2	no	—
27	C₄×C₄⋊#1043	—	2	2	no	—
28	#13104690	—	2	2	no	—
29	C₂×C₁₆×C₅⋊D₅	—	2	1	no	—
30	C₂×C₁₆×C₅⋊D₅	C₂×C₄	1	1	yes	characteristic
31	C₂×C₁₆×C₅⋊D₅	C₂×C₄	1	1	yes	characteristic
32	C₄×C₈×C₅⋊D₅	D₄	1	2	yes	—
33	C₄×C₈×C₅⋊D₅	C₂³	1	1	yes	characteristic
34	#13100271	—	2	2	no	—
35	#13100270	—	4	2	no	—
36	#13100260	—	2	2	no	—
37	#13100259	C₂×C₄	1	2	yes	—
38	#13100259	C₂×C₄	1	2	yes	—
39	#13100228	C₈	1	4	yes	complemented
40	#13100227	C₈	1	4	yes	complemented
41	C₅²×#346	C₂×C₄	1	1	yes	characteristic
42	C₅²×#346	C₂×C₄	1	1	yes	characteristic
43	C₅²×#322	C₂×C₄	1	1	yes	characteristic
44	#13099536	—	2	1	no	—
45	#13099536	C₂×C₄	1	1	yes	characteristic
46	#13099536	C₂×C₄	1	1	yes	characteristic
47	#13099493	C₂×C₄	1	1	yes	characteristic
48	#13099493	C₂×C₄	1	1	yes	characteristic
49	#13099489	C₂×C₄	1	1	yes	characteristic
50	#13099488	Q₈	1	2	yes	—
51	#13026041	—	5	6	no	—
52	D₅⋊#1368	—	5	6	no	—
53	#13017334	—	5	12	no	—
54	#13013595	—	5	12	no	—
55	D₅×#1313	—	5	6	no	—
56	C₂×C₄⋊#1043	—	2	2	no	—
57	C₂×C₄⋊#1043	—	2	2	no	—
58	C₂×C₄×#1043	—	4	2	no	—
59	C₂×#87855	—	4	2	no	—
60	C₂×C₈×C₅⋊D₅	—	2	2	no	—
61	C₂×C₈×C₅⋊D₅	C₂²×C₄	1	1	yes	characteristic
62	C₂×C₈×C₅⋊D₅	#41	1	1	yes	characteristic
63	C₄²×C₅⋊D₅	C₂×D₄	1	1	yes	characteristic
64	#11716874	—	4	2	no	—
65	#11716872	—	4	2	no	—
66	C₄⋊#6033	—	2	2	no	—
67	C₄⋊#6033	—	2	2	no	—
68	#11716862	—	2	2	no	—
69	#11716862	—	2	2	no	—
70	#11716862	C₂×C₈	1	4	yes	—
71	#11716862	C₂×C₈	1	4	yes	—
72	C₈×#1043	—	8	4	no	—
73	C₂×C₅²×C₁₆	—	2	1	no	—
74	C₂×C₅²×C₁₆	C₄²	1	1	yes	characteristic
75	C₂×C₅²×C₁₆	C₄²	1	1	yes	characteristic
76	C₄×C₅²×C₈	C₄⋊C₄	1	2	yes	—
77	C₄×C₅²×C₈	C₂²×C₄	1	1	yes	characteristic
78	C₈×#1039	—	2	2	no	—
79	C₈×#1039	C₂²×C₄	1	1	yes	characteristic
80	C₈×#1039	#41	1	1	yes	characteristic
81	C₂×#87756	—	2	1	no	—
82	C₂×#87756	C₄²	1	1	yes	characteristic
83	C₂×#87756	C₄²	1	1	yes	characteristic
84	C₄×#6029	C₄⋊C₄	1	2	yes	—
85	C₄×#6029	C₂×Q₈	1	1	yes	characteristic
86	C₁₆×C₅⋊D₅	—	2	1	no	—
87	C₁₆×C₅⋊D₅	—	2	1	no	—
88	C₁₆×C₅⋊D₅	—	4	1	no	—
89	C₁₆×C₅⋊D₅	—	4	1	no	—
90	C₁₆×C₅⋊D₅	C₂×C₈	1	2	yes	—
91	C₁₆×C₅⋊D₅	C₂×C₈	1	2	yes	—
92	C₂×#64850	—	5	6	no	—
93	C₂×#64849	—	5	6	no	—
94	C₄×#3994	—	5	12	no	—
95	C₈×C₄⋊AGL(1,𝔽₅)	—	10	12	no	—
96	D₅⋊#334	—	5	12	no	—
97	D₅×#346	—	5	6	no	—
98	D₅×#346	—	5	6	no	—
99	D₅×#322	—	5	6	no	—
100	#10598664	—	5	12	no	—
101	#10598643	—	5	12	no	—
102	#10598642	—	5	6	no	—
103	#10598641	—	5	6	no	—
104	#10598530	—	10	12	no	—
105	C₅×#1313	AGL(1,𝔽₅)	1	6	yes	complemented
106	#10598003	—	5	6	no	—
107	#10598002	—	5	6	no	—
108	#10597933	—	5	6	no	—
109	#129165	—	25	1	no	Sylow
110	C₂²×#1043	—	4	2	no	—
111	C₂²×#1043	—	4	2	no	—
112	C₂×C₄×C₅⋊D₅	C₄×D₄	1	1	yes	characteristic
113	C₂×C₄×C₅⋊D₅	AGL(1,ℤ/8)	1	2	yes	—
114	C₂×#6033	—	4	2	no	—
115	C₂×#6033	—	4	2	no	—
116	C₄⋊#1043	—	2	4	no	—
117	C₄⋊#1043	—	2	4	no	—
118	C₄⋊#1043	—	4	2	no	—
119	C₄⋊#1043	—	4	2	no	—
120	C₄×#1043	—	8	2	no	—
121	C₄×#1043	—	8	2	no	—
122	#87855	—	8	2	no	—
123	#87855	—	8	2	no	—
124	C₂×C₅²×C₈	—	2	2	no	—
125	C₂×C₅²×C₈	C₂×C₄²	1	1	yes	characteristic
126	C₂×C₅²×C₈	#117	1	1	yes	characteristic
127	C₄²×C₅²	C₂×C₄⋊C₄	1	1	yes	characteristic
128	C₄×#1039	C₄×D₄	1	1	yes	characteristic
129	C₄×#1039	#137	1	2	yes	—
130	C₂×#6029	—	2	2	no	—
131	C₂×#6029	C₄×Q₈	1	1	yes	characteristic
132	C₂×#6029	C₄×Q₈	1	1	yes	characteristic
133	C₈×C₅⋊D₅	—	2	1	no	—
134	C₈×C₅⋊D₅	—	2	1	no	—
135	C₈×C₅⋊D₅	—	4	2	no	—
136	C₈×C₅⋊D₅	—	4	2	no	—
137	C₈×C₅⋊D₅	C₂²×C₈	1	1	yes	characteristic
138	C₈×C₅⋊D₅	C₂²×C₈	1	1	yes	characteristic
139	C₈×C₅⋊D₅	#131	1	1	yes	characteristic
140	C₈×C₅⋊D₅	#131	1	1	yes	characteristic
141	C₅²×C₁₆	—	2	1	no	—
142	C₅²×C₁₆	—	4	1	no	—
143	C₅²×C₁₆	C₄×C₈	1	2	yes	complemented
144	#87756	—	2	1	no	—
145	#87756	—	4	1	no	—
146	#87756	C₄×C₈	1	2	yes	complemented
147	C₂×#3994	—	5	12	no	—
148	C₂×#3994	—	5	12	no	—
149	C₂×C₈×AGL(1,𝔽₅)	—	20	12	no	—
150	C₄×C₄⋊AGL(1,𝔽₅)	—	10	12	no	—
151	D₅⋊(C₄⋊C₈)	—	10	12	no	—
152	C₂×D₅×C₁₆	—	5	6	no	—
153	C₂×D₅×C₁₆	—	5	6	no	—
154	C₂×D₅×C₁₆	—	10	6	no	—
155	C₄×C₈×D₅	—	5	6	no	—
156	C₄×C₈×D₅	—	5	12	no	—
157	#64893	—	10	12	no	—
158	(C₂×AGL(1,𝔽₅))⋊C₈	—	20	12	no	—
159	#64883	—	10	12	no	—
160	#64881	—	5	12	no	—
161	#64881	—	5	12	no	—
162	#64850	—	5	24	no	—
163	#64849	—	5	24	no	—
164	C₅×#346	C₂×AGL(1,𝔽₅)	1	6	yes	—
165	C₅×#346	C₂×AGL(1,𝔽₅)	1	6	yes	—
166	C₅×#322	C₂×AGL(1,𝔽₅)	1	6	yes	—
167	#64722	—	5	6	no	—
168	#64722	—	5	6	no	—
169	#64722	—	10	6	no	—
170	#64681	—	5	6	no	—
171	#64681	—	5	6	no	—
172	#64675	—	5	6	no	—
173	#64674	—	5	12	no	—
174	#12674	—	25	1	no	—
175	C₂×#1368	—	25	1	no	—
176	C₂×#1313	—	25	1	no	—
177	#8284	—	25	2	no	—
178	#7178	—	25	2	no	—
179	C₂²×C₅⋊D₅	#442	1	1	yes	characteristic
180	C₂×#1043	—	4	4	no	—
181	C₂×#1043	—	4	4	no	—
182	C₂×#1043	—	8	2	no	—
183	C₂×#1043	—	8	2	no	—
184	C₂×#1043	—	8	2	no	—
185	C₂×#1043	—	8	2	no	—
186	C₂×C₄×C₅²	C₄×C₄⋊C₄	1	1	yes	characteristic
187	C₂×C₄×C₅²	#428	1	2	yes	—
188	C₂×#1039	#440	1	2	yes	—
189	C₂×#1039	#441	1	1	yes	characteristic
190	C₄×C₅⋊D₅	—	2	2	no	—
191	C₄×C₅⋊D₅	—	2	2	no	—
192	C₄×C₅⋊D₅	C₈×D₄	1	1	yes	characteristic
193	C₄×C₅⋊D₅	C₈×D₄	1	1	yes	characteristic
194	C₄×C₅⋊D₅	#444	1	1	yes	characteristic
195	C₄×C₅⋊D₅	#444	1	1	yes	characteristic
196	#6033	—	8	2	no	—
197	#6033	—	8	2	no	—
198	C₅²×C₈	—	2	1	no	—
199	C₅²×C₈	—	4	2	no	—
200	C₅²×C₈	C₂×C₄×C₈	1	1	yes	characteristic
201	C₅²×C₈	#405	1	1	yes	characteristic
202	#6029	—	2	1	no	—
203	#6029	—	4	2	no	—
204	#6029	C₈×Q₈	1	1	yes	characteristic
205	#6029	C₈×Q₈	1	1	yes	characteristic
206	C₂×C₄⋊AGL(1,𝔽₅)	—	10	12	no	—
207	C₂×C₄⋊AGL(1,𝔽₅)	—	10	12	no	—
208	C₂×C₄×AGL(1,𝔽₅)	—	20	12	no	—
209	C₂×D₅⋊C₈	—	20	12	no	—
210	C₂×C₈×D₅	—	5	6	no	—
211	C₂×C₈×D₅	—	5	6	no	—
212	C₂×C₈×D₅	—	10	12	no	—
213	C₄²×D₅	—	5	6	no	—
214	(C₂×AGL(1,𝔽₅))⋊C₄	—	20	12	no	—
215	#4004	—	20	12	no	—
216	C₄⋊#170	—	10	12	no	—
217	C₄⋊#170	—	10	12	no	—
218	#3994	—	5	24	no	—
219	#3994	—	5	24	no	—
220	#3994	—	10	12	no	—
221	#3994	—	10	12	no	—
222	C₈×AGL(1,𝔽₅)	—	40	24	no	—
223	C₂×C₅×C₁₆	—	2	6	no	—
224	C₂×C₅×C₁₆	C₄×AGL(1,𝔽₅)	1	6	yes	—
225	C₂×C₅×C₁₆	C₄×AGL(1,𝔽₅)	1	6	yes	—
226	C₄×C₅×C₈	C₄⋊AGL(1,𝔽₅)	1	12	yes	—
227	C₄×C₅×C₈	C₂²×AGL(1,𝔽₅)	1	6	yes	—
228	C₈×Dic₅	—	5	6	no	—
229	C₈×Dic₅	—	5	6	no	—
230	C₈×Dic₅	—	10	12	no	—
231	C₂×#672	—	5	6	no	—
232	C₂×#672	—	5	6	no	—
233	C₂×#672	—	10	6	no	—
234	C₄×#168	—	5	6	no	—
235	C₄×#168	—	5	12	no	—
236	D₅×C₁₆	—	5	12	no	—
237	D₅×C₁₆	—	5	12	no	—
238	D₅×C₁₆	—	10	6	no	—
239	D₅×C₁₆	—	10	6	no	—
240	D₅×C₁₆	—	20	6	no	—
241	D₅×C₁₆	—	20	6	no	—
242	C₂×#367	—	25	1	no	—
243	C₂×#366	—	25	1	no	—
244	C₂×#346	—	25	1	no	—
245	C₂×#346	—	25	1	no	—
246	C₄×#107	—	25	2	no	—
247	C₈×C₄⋊C₄	—	50	2	no	—
248	C₂×#334	—	25	2	no	—
249	C₂×#322	—	25	1	no	—
250	#1380	—	25	2	no	—
251	#1368	—	25	1	no	—
252	#1368	—	25	1	no	—
253	#1368	—	25	2	no	—
254	#1313	—	25	1	no	—
255	#1313	—	25	1	no	—
256	#1313	—	25	1	no	—
257	#1313	#1043	1	1	yes	characteristic, complemented
258	#1279	—	50	2	no	—
259	C₂²×C₅²	#1776	1	1	yes	characteristic
260	C₂×C₅⋊D₅	#1580	1	1	yes	characteristic
261	C₂×C₅⋊D₅	#1580	1	1	yes	characteristic
262	C₂×C₅⋊D₅	#2180	1	2	yes	—
263	C₂×C₅⋊D₅	AGL(1,ℤ/16)	1	2	yes	—
264	#1043	—	8	4	no	—
265	#1043	—	8	4	no	—
266	C₄×C₅²	—	2	2	no	—
267	C₄×C₅²	C₈×C₄⋊C₄	1	1	yes	characteristic
268	C₄×C₅²	#1773	1	1	yes	characteristic
269	#1039	—	2	2	no	—
270	#1039	#1579	1	1	yes	characteristic
271	#1039	#1579	1	1	yes	characteristic
272	C₂²×AGL(1,𝔽₅)	—	20	12	no	—
273	C₂²×AGL(1,𝔽₅)	—	20	12	no	—
274	C₂×C₄×D₅	—	5	6	no	—
275	C₂×C₄×D₅	—	5	12	no	—
276	C₂×#170	—	20	12	no	—
277	C₂×#170	—	20	12	no	—
278	C₄⋊AGL(1,𝔽₅)	—	10	24	no	—
279	C₄⋊AGL(1,𝔽₅)	—	10	24	no	—
280	C₄⋊AGL(1,𝔽₅)	—	20	12	no	—
281	C₄⋊AGL(1,𝔽₅)	—	20	12	no	—
282	C₄×AGL(1,𝔽₅)	—	40	12	no	—
283	C₄×AGL(1,𝔽₅)	—	40	12	no	—
284	D₅⋊C₈	—	40	12	no	—
285	D₅⋊C₈	—	40	12	no	—
286	C₂×C₅×C₈	—	2	12	no	—
287	C₂×C₅×C₈	C₂×C₄×AGL(1,𝔽₅)	1	6	yes	—
288	C₂×C₅×C₈	#4130	1	6	yes	—
289	C₄²×C₅	C₂×C₄⋊AGL(1,𝔽₅)	1	6	yes	—
290	C₄×Dic₅	—	5	6	no	—
291	C₄×Dic₅	—	5	12	no	—
292	C₂×#168	—	5	6	no	—
293	C₂×#168	—	5	6	no	—
294	C₂×#168	—	10	12	no	—
295	C₈×D₅	—	5	6	no	—
296	C₈×D₅	—	5	6	no	—
297	C₈×D₅	—	5	6	no	—
298	C₈×D₅	—	5	6	no	—
299	C₈×D₅	—	10	6	no	—
300	C₈×D₅	—	10	6	no	—
301	C₈×D₅	—	20	12	no	—
302	C₈×D₅	—	20	12	no	—
303	C₅×C₁₆	—	2	6	no	—
304	C₅×C₁₆	—	4	6	no	—
305	C₅×C₁₆	C₈×AGL(1,𝔽₅)	1	12	yes	complemented
306	#672	—	5	12	no	—
307	#672	—	10	6	no	—
308	#672	—	20	6	no	—
309	C₂²×C₁₆	—	25	1	no	—
310	C₂²×C₁₆	—	25	1	no	—
311	C₂²×C₁₆	—	50	1	no	—
312	C₂×#107	—	25	2	no	—
313	C₂×#107	—	25	2	no	—
314	C₂×C₄⋊C₈	—	50	2	no	—
315	C₂×C₄×C₈	—	25	1	no	—
316	C₂×C₄×C₈	—	25	2	no	—
317	C₂×C₄×C₈	—	100	2	no	—
318	C₄×C₄⋊C₄	—	50	2	no	—
319	#367	—	25	4	no	—
320	#366	—	25	4	no	—
321	#346	—	25	1	no	—
322	#346	—	25	1	no	—
323	#346	—	25	1	no	—
324	#346	—	25	1	no	—
325	#346	—	50	1	no	—
326	#346	C₂×#1043	1	1	yes	characteristic
327	#346	C₂×#1043	1	1	yes	characteristic
328	#340	—	50	2	no	—
329	#336	—	100	2	no	—
330	#334	—	25	2	no	—
331	#334	—	25	2	no	—
332	#334	—	50	2	no	—
333	#322	—	25	2	no	—
334	#322	—	25	1	no	—
335	#322	C₂×#1043	1	1	yes	characteristic
336	C₂×C₅²	#8284	1	1	yes	characteristic
337	C₂×C₅²	#12677	1	2	yes	—
338	C₅⋊D₅	#12065	1	2	yes	—
339	C₅⋊D₅	#12066	1	1	yes	characteristic
340	C₅⋊D₅	#12067	1	1	yes	characteristic
341	C₂²×D₅	—	5	6	no	—
342	C₂×AGL(1,𝔽₅)	—	20	24	no	—
343	C₂×AGL(1,𝔽₅)	—	20	24	no	—
344	C₂×AGL(1,𝔽₅)	—	40	12	no	—
345	C₂×AGL(1,𝔽₅)	—	40	12	no	—
346	C₂×AGL(1,𝔽₅)	—	40	12	no	—
347	C₂×AGL(1,𝔽₅)	—	40	12	no	—
348	C₂×C₄×C₅	C₄×C₄⋊AGL(1,𝔽₅)	1	6	yes	—
349	C₂×C₄×C₅	#65727	1	12	yes	—
350	C₂×Dic₅	—	5	6	no	—
351	C₂×Dic₅	—	5	12	no	—
352	C₄×D₅	—	5	6	no	—
353	C₄×D₅	—	5	6	no	—
354	C₄×D₅	—	5	6	no	—
355	C₄×D₅	—	5	6	no	—
356	C₄×D₅	—	10	12	no	—
357	C₄×D₅	—	10	12	no	—
358	#170	—	40	12	no	—
359	#170	—	40	12	no	—
360	C₅×C₈	—	2	6	no	—
361	C₅×C₈	—	4	12	no	—
362	C₅×C₈	C₂×C₈×AGL(1,𝔽₅)	1	6	yes	—
363	C₅×C₈	#65718	1	6	yes	—
364	#168	—	5	6	no	—
365	#168	—	5	6	no	—
366	#168	—	10	6	no	—
367	#168	—	20	12	no	—
368	C₂²×C₈	—	25	1	no	—
369	C₂²×C₈	—	25	1	no	—
370	C₂²×C₈	—	50	2	no	—
371	C₂²×C₈	—	100	2	no	—
372	C₂×C₄⋊C₄	—	50	2	no	—
373	C₂×C₄⋊C₄	—	50	2	no	—
374	C₂×C₄²	—	25	1	no	—
375	C₂×C₄²	—	100	2	no	—
376	C₂×C₁₆	—	2	1	no	—
377	C₂×C₁₆	—	25	1	no	—
378	C₂×C₁₆	—	25	2	no	—
379	C₂×C₁₆	—	25	2	no	—
380	C₂×C₁₆	—	25	1	no	—
381	C₂×C₁₆	—	50	1	no	—
382	C₂×C₁₆	—	50	1	no	—
383	C₂×C₁₆	—	50	1	no	—
384	C₂×C₁₆	—	100	1	no	—
385	C₂×C₁₆	—	100	1	no	—
386	C₂×C₁₆	C₄×#1043	1	1	yes	characteristic
387	C₂×C₁₆	C₄×#1043	1	1	yes	characteristic
388	#107	—	25	4	no	—
389	#107	—	25	4	no	—
390	#107	—	50	2	no	—
391	#107	—	50	2	no	—
392	C₄⋊C₈	—	50	2	no	—
393	C₄⋊C₈	—	50	2	no	—
394	C₄⋊C₈	—	100	2	no	—
395	C₄×C₈	—	25	1	no	—
396	C₄×C₈	—	25	1	no	—
397	C₄×C₈	—	25	1	no	—
398	C₄×C₈	—	25	2	no	—
399	C₄×C₈	—	50	2	no	—
400	C₄×C₈	—	200	4	no	—
401	C₄×C₈	C₄⋊#1043	1	2	yes	—
402	C₄×C₈	C₂²×#1043	1	1	yes	characteristic
403	#95	—	100	2	no	—
404	C₅²	#129165	1	1	yes	characteristic, complemented, Sylow
405	C₂²×C₅	#10603881	1	6	yes	—
406	C₂×D₅	—	5	12	no	—
407	C₂×D₅	—	5	12	no	—
408	C₂×D₅	—	5	6	no	—
409	C₂×D₅	—	5	6	no	—
410	AGL(1,𝔽₅)	—	40	24	no	—
411	AGL(1,𝔽₅)	—	40	24	no	—
412	C₄×C₅	—	2	12	no	—
413	C₄×C₅	C₈×C₄⋊AGL(1,𝔽₅)	1	6	yes	—
414	C₄×C₅	#10603885	1	6	yes	—
415	Dic₅	—	5	6	no	—
416	Dic₅	—	5	6	no	—
417	Dic₅	—	10	12	no	—
418	C₂²×C₄	—	25	1	no	—
419	C₂²×C₄	—	25	2	no	—
420	C₂²×C₄	—	100	2	no	—
421	C₂²×C₄	—	100	2	no	—
422	C₂×C₈	—	2	2	no	—
423	C₂×C₈	—	25	1	no	—
424	C₂×C₈	—	25	1	no	—
425	C₂×C₈	—	25	1	no	—
426	C₂×C₈	—	25	1	no	—
427	C₂×C₈	—	25	1	no	—
428	C₂×C₈	—	25	1	no	—
429	C₂×C₈	—	50	1	no	—
430	C₂×C₈	—	50	1	no	—
431	C₂×C₈	—	50	2	no	—
432	C₂×C₈	—	100	2	no	—
433	C₂×C₈	—	100	2	no	—
434	C₂×C₈	—	100	2	no	—
435	C₂×C₈	—	100	2	no	—
436	C₂×C₈	—	200	2	no	—
437	C₂×C₈	—	200	2	no	—
438	C₂×C₈	C₂×C₄×#1043	1	1	yes	characteristic
439	C₂×C₈	#11717438	1	1	yes	characteristic
440	C₄⋊C₄	—	50	4	no	—
441	C₄⋊C₄	—	50	4	no	—
442	C₄⋊C₄	—	100	2	no	—
443	C₄⋊C₄	—	100	2	no	—
444	C₄²	—	25	1	no	—
445	C₄²	—	25	2	no	—
446	C₄²	—	200	2	no	—
447	C₄²	—	200	2	no	—
448	C₄²	C₂×C₄⋊#1043	1	1	yes	characteristic
449	C₁₆	—	2	1	no	—
450	C₁₆	—	4	1	no	—
451	C₁₆	—	25	2	no	—
452	C₁₆	—	50	1	no	—
453	C₁₆	—	100	1	no	—
454	C₁₆	C₈×#1043	1	2	yes	complemented
455	C₂×C₅	#13017334	1	6	yes	—
456	C₂×C₅	#13026049	1	12	yes	—
457	D₅	—	5	12	no	—
458	D₅	—	5	6	no	—
459	D₅	—	5	6	no	—
460	C₂³	—	25	1	no	—
461	C₂×C₄	—	25	1	no	—
462	C₂×C₄	—	25	1	no	—
463	C₂×C₄	—	25	1	no	—
464	C₂×C₄	—	25	1	no	—
465	C₂×C₄	—	25	1	no	—
466	C₂×C₄	—	25	2	no	—
467	C₂×C₄	—	50	2	no	—
468	C₂×C₄	—	50	2	no	—
469	C₂×C₄	—	100	4	no	—
470	C₂×C₄	—	100	4	no	—
471	C₂×C₄	—	200	2	no	—
472	C₂×C₄	—	200	2	no	—
473	C₂×C₄	—	200	2	no	—
474	C₂×C₄	—	200	2	no	—
475	C₂×C₄	C₄×C₄⋊#1043	1	1	yes	characteristic
476	C₂×C₄	#13104740	1	2	yes	—
477	C₈	—	2	1	no	—
478	C₈	—	4	2	no	—
479	C₈	—	25	1	no	—
480	C₈	—	25	1	no	—
481	C₈	—	50	1	no	—
482	C₈	—	100	2	no	—
483	C₈	—	200	2	no	—
484	C₈	—	200	2	no	—
485	C₈	C₂×C₈×#1043	1	1	yes	characteristic
486	C₈	#13104730	1	1	yes	characteristic
487	C₅	#72242073	1	6	yes	complemented
488	C₂²	—	25	1	no	—
489	C₂²	—	25	1	no	—
490	C₂²	—	25	2	no	—
491	C₂²	—	25	2	no	—
492	C₂²	#72220671	1	1	yes	characteristic
493	C₄	—	2	2	no	—
494	C₄	—	25	1	no	—
495	C₄	—	25	1	no	—
496	C₄	—	50	2	no	—
497	C₄	—	200	4	no	—
498	C₄	—	200	4	no	—
499	C₄	C₈×C₄⋊#1043	1	1	yes	characteristic
500	C₄	#72253134	1	1	yes	characteristic
501	C₂	—	25	1	no	—
502	C₂	—	25	2	no	—
503	C₂	—	25	1	no	—
504	C₂	#72253135	1	1	yes	characteristic
505	C₂	#72253139	1	2	yes	—

	subgroup	G/H
center	C₂²	#72220671
commutator	C₅²×C₈	C₂×C₄×C₈
Frattini	C₄×C₈	C₂²×#1043
Fitting	C₅²×#1313	C₄
socle	C₂²×C₅²	#1776
prime radical	C₂²×C₅⋊D₅	#442
cosocle	C₄×C₈×C₅⋊D₅	C₂³
hypercenter	#1313	#1043
hypocenter	C₅²	#129165
LCS	G ▷ C₅²×C₈ ▷ C₄×C₅² ▷ C₂×C₅² ▷ C₅²
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #322 ◁ #1313

Complements

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

N	H ≅ G/N	type
11. #72242201	C₄	semidirect
12. #72242199	C₄	semidirect
13. #72242197	C₄	semidirect
16. #72242123	C₄	semidirect
17. #72242120	C₄	semidirect
18. #72242115	C₄	semidirect
19. C₅²×#1313	C₄	semidirect
39. #13100228	C₈	semidirect
40. #13100227	C₈	semidirect
105. C₅×#1313	AGL(1,𝔽₅)	semidirect
143. C₅²×C₁₆	C₄×C₈	semidirect
146. #87756	C₄×C₈	semidirect
257. #1313	#1043	semidirect
305. C₅×C₁₆	C₈×AGL(1,𝔽₅)	semidirect
404. C₅²	#129165	semidirect
454. C₁₆	C₈×#1043	semidirect
487. C₅	#72242073	semidirect

Maximal subgroups

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

subgroup	index
#72253138	2
#72253135	2
#72242315	2
#72242207	2
C₅⋊D₅×#1313	2
#72242073	5