Subgroups — C₅×#19451 #11942171

Order 1280.

618 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3229	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#3076	C₂	1	1	yes	maximal, characteristic
3	C₅×#3039	C₂	1	1	yes	maximal, characteristic
4	C₅×#2989	C₂	1	1	yes	maximal, characteristic
5	C₅×#1700	C₂	1	2	yes	maximal, complemented
6	C₅×#1699	C₂	1	2	yes	maximal, complemented
7	C₅×#1692	C₂	1	2	yes	maximal, complemented
8	C₅×#1691	C₂	1	2	yes	maximal, complemented
9	C₅×#1571	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1550	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₅×#332	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₅×#137	—	2	1	no	—
13	C₅×#533	C₂²	1	1	yes	characteristic
14	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
15	C₄×C₅×#41	C₂²	1	1	yes	characteristic
16	C₅×#498	C₂²	1	2	yes	—
17	C₅×#487	C₂²	1	2	yes	—
18	C₅×#483	—	2	2	no	—
19	C₅×#479	—	2	1	no	—
20	C₅×#478	—	2	1	no	—
21	C₅×#477	C₂²	1	1	yes	characteristic
22	C₅×#476	C₂²	1	1	yes	characteristic
23	C₅×#475	—	2	1	no	—
24	C₅×#475	—	2	1	no	—
25	C₅×#475	C₂²	1	1	yes	characteristic
26	C₅×#474	C₂²	1	1	yes	characteristic
27	C₅×#462	—	2	1	no	—
28	C₅×#462	C₂²	1	2	yes	—
29	C₅×#461	—	2	1	no	—
30	C₅×#461	C₂²	1	2	yes	—
31	C₅×#446	C₂²	1	2	yes	—
32	C₅×#436	C₂²	1	2	yes	—
33	C₅×#435	—	2	2	no	—
34	C₅×#432	—	2	1	no	—
35	C₅×#431	C₂²	1	1	yes	characteristic
36	C₅×#427	—	2	1	no	—
37	C₅×#423	—	2	1	no	—
38	C₅×#423	C₂²	1	1	yes	characteristic
39	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
40	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
41	C₅×#419	—	2	1	no	—
42	C₅×#416	—	2	1	no	—
43	C₅×#335	C₂²	1	2	yes	—
44	C₅×#335	C₂²	1	2	yes	—
45	C₅×#333	C₂²	1	2	yes	—
46	C₅×#332	C₂²	1	2	yes	—
47	C₅×#332	C₂²	1	2	yes	—
48	C₅×#332	C₂²	1	2	yes	—
49	#19451	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
50	C₂×C₅×#41	D₄	1	1	yes	characteristic
51	C₂²×C₅×Q₈	—	2	1	no	—
52	C₅×#137	—	4	4	no	—
53	C₂×C₅×Q₁₆	—	2	2	no	—
54	C₂×C₅×SD₁₆	—	2	2	no	—
55	C₂×C₅×M₁₆	—	2	1	no	—
56	C₂×C₅×M₁₆	—	2	2	no	—
57	C₂²×C₅×C₈	—	2	1	no	—
58	C₂²×C₅×C₈	—	2	1	no	—
59	C₅×C₄⋊Q₈	—	2	1	no	—
60	C₅×C₄⋊Q₈	—	2	1	no	—
61	C₅×C₄⋊Q₈	—	2	1	no	—
62	C₅×C₄⋊Q₈	C₂³	1	2	yes	—
63	C₅×C₄⋊Q₈	C₂³	1	1	yes	characteristic
64	C₅×C₄⋊Q₈	C₂³	1	1	yes	characteristic
65	C₅×#125	—	2	1	no	—
66	C₅×C₂²⋊Q₈	—	2	1	no	—
67	C₅×C₂²⋊Q₈	—	2	1	no	—
68	C₄×C₅×Q₈	—	2	1	no	—
69	C₄×C₅×Q₈	—	2	1	no	—
70	C₄×C₅×Q₈	D₄	1	1	yes	characteristic
71	C₄×C₅×Q₈	C₂³	1	1	yes	characteristic
72	C₄×C₅×D₄	—	2	1	no	—
73	C₄×C₅×D₄	—	2	1	no	—
74	C₄×C₅×D₄	D₄	1	1	yes	characteristic
75	C₄×C₅×D₄	C₂³	1	1	yes	characteristic
76	C₅×#117	—	2	1	no	—
77	C₅×#117	—	2	1	no	—
78	C₅×#117	D₄	1	1	yes	characteristic
79	C₂×C₅×C₄⋊C₄	—	2	1	no	—
80	C₂×C₅×C₄⋊C₄	—	2	1	no	—
81	C₂×C₄²×C₅	—	2	1	no	—
82	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
83	C₅×#107	—	2	1	no	—
84	C₅×#107	—	2	1	no	—
85	C₅×#106	—	2	2	no	—
86	C₅×#106	—	2	2	no	—
87	C₅×#106	—	2	1	no	—
88	C₅×#106	—	2	1	no	—
89	C₅×C₄⋊C₈	—	2	2	no	—
90	C₅×C₄⋊C₈	—	2	1	no	—
91	C₅×C₄⋊C₈	—	2	1	no	—
92	C₅×C₄⋊C₈	—	2	1	no	—
93	C₅×C₄⋊C₈	D₄	1	1	yes	characteristic
94	C₅×C₄⋊C₈	D₄	1	1	yes	characteristic
95	C₅×C₄⋊C₈	C₂³	1	2	yes	—
96	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
97	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
98	C₅×C₄⋊C₈	C₂³	1	2	yes	—
99	C₅×#103	—	2	1	no	—
100	C₅×#103	—	2	1	no	—
101	C₅×#103	—	2	2	no	—
102	C₅×#103	—	2	2	no	—
103	C₅×#103	—	2	2	no	—
104	C₅×#103	—	2	2	no	—
105	C₅×#102	—	2	1	no	—
106	C₅×#102	—	2	1	no	—
107	C₅×C₂²⋊C₈	—	2	2	no	—
108	C₅×C₂²⋊C₈	D₄	1	2	yes	—
109	C₅×#97	—	2	2	no	—
110	C₄×C₅×C₈	C₂³	1	2	yes	—
111	#3229	C₂×C₅	1	1	yes	characteristic, complemented
112	#3076	C₂×C₅	1	1	yes	characteristic
113	#3039	C₂×C₅	1	1	yes	characteristic
114	#2989	C₂×C₅	1	1	yes	characteristic
115	#1700	C₂×C₅	1	2	yes	complemented
116	#1699	C₂×C₅	1	2	yes	complemented
117	#1692	C₂×C₅	1	2	yes	complemented
118	#1691	C₂×C₅	1	2	yes	complemented
119	#1571	C₂×C₅	1	1	yes	characteristic, complemented
120	#1550	C₂×C₅	1	1	yes	characteristic, complemented
121	C₂×#332	C₂×C₅	1	1	yes	characteristic, complemented
122	C₅×#41	—	2	2	no	—
123	C₅×#41	—	2	2	no	—
124	C₂×C₅×Q₈	—	2	1	no	—
125	C₂×C₅×Q₈	—	2	2	no	—
126	C₂×C₅×Q₈	—	2	1	no	—
127	C₂×C₅×Q₈	—	4	1	no	—
128	C₂×C₅×Q₈	—	4	2	no	—
129	C₂×C₅×Q₈	—	4	2	no	—
130	C₂×C₅×Q₈	C₂×D₄	1	1	yes	characteristic
131	C₂×C₅×D₄	—	2	1	no	—
132	C₂×C₅×D₄	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₅	—	2	1	no	—
134	C₂²×C₄×C₅	—	2	1	no	—
135	C₂²×C₄×C₅	—	2	1	no	—
136	C₂²×C₄×C₅	—	4	1	no	—
137	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
138	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
139	C₂²×C₄×C₅	#41	1	1	yes	characteristic
140	C₅×Q₁₆	—	4	4	no	—
141	C₅×SD₁₆	—	4	4	no	—
142	C₅×M₁₆	—	4	2	no	—
143	C₅×M₁₆	—	8	2	no	—
144	C₂×C₅×C₈	—	2	2	no	—
145	C₂×C₅×C₈	—	2	1	no	—
146	C₂×C₅×C₈	—	2	1	no	—
147	C₂×C₅×C₈	—	2	2	no	—
148	C₂×C₅×C₈	—	4	2	no	—
149	C₂×C₅×C₈	—	8	1	no	—
150	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
151	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
152	C₅×C₄⋊C₄	—	2	1	no	—
153	C₅×C₄⋊C₄	—	2	1	no	—
154	C₅×C₄⋊C₄	—	2	2	no	—
155	C₅×C₄⋊C₄	—	2	1	no	—
156	C₅×C₄⋊C₄	—	2	1	no	—
157	C₅×C₄⋊C₄	—	2	1	no	—
158	C₅×C₄⋊C₄	—	2	2	no	—
159	C₅×C₄⋊C₄	—	2	1	no	—
160	C₅×C₄⋊C₄	—	4	1	no	—
161	C₅×C₄⋊C₄	—	4	1	no	—
162	C₅×C₄⋊C₄	—	4	1	no	—
163	C₅×C₄⋊C₄	—	4	1	no	—
164	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
165	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
166	C₅×C₂²⋊C₄	—	2	1	no	—
167	C₅×C₂²⋊C₄	—	2	1	no	—
168	C₅×C₂²⋊C₄	—	2	1	no	—
169	C₅×C₂²⋊C₄	—	4	1	no	—
170	C₄²×C₅	—	2	1	no	—
171	C₄²×C₅	—	2	1	no	—
172	C₄²×C₅	—	2	1	no	—
173	C₄²×C₅	—	4	1	no	—
174	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
175	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
176	C₄²×C₅	#41	1	1	yes	characteristic
177	C₄²×C₅	C₂⁴	1	1	yes	characteristic
178	C₂×#137	—	2	1	no	—
179	#533	C₂²×C₅	1	1	yes	characteristic
180	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
181	C₄×#41	C₂²×C₅	1	1	yes	characteristic
182	#498	C₂²×C₅	1	2	yes	—
183	#487	C₂²×C₅	1	2	yes	—
184	#483	—	2	2	no	—
185	#479	—	2	1	no	—
186	#478	—	2	1	no	—
187	#477	C₂²×C₅	1	1	yes	characteristic
188	#476	C₂²×C₅	1	1	yes	characteristic
189	#475	—	2	1	no	—
190	#475	—	2	1	no	—
191	#475	C₂²×C₅	1	1	yes	characteristic
192	#474	C₂²×C₅	1	1	yes	characteristic
193	#462	—	2	1	no	—
194	#462	C₂²×C₅	1	2	yes	—
195	#461	—	2	1	no	—
196	#461	C₂²×C₅	1	2	yes	—
197	#446	C₂²×C₅	1	2	yes	—
198	#436	C₂²×C₅	1	2	yes	—
199	#435	—	2	2	no	—
200	#432	—	2	1	no	—
201	#431	C₂²×C₅	1	1	yes	characteristic
202	#427	—	2	1	no	—
203	#423	—	2	1	no	—
204	#423	C₂²×C₅	1	1	yes	characteristic
205	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
206	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
207	#419	—	2	1	no	—
208	#416	—	2	1	no	—
209	#335	C₂²×C₅	1	2	yes	—
210	#335	C₂²×C₅	1	2	yes	—
211	#333	C₂²×C₅	1	2	yes	—
212	#332	C₂²×C₅	1	2	yes	—
213	#332	C₂²×C₅	1	2	yes	—
214	#332	C₂²×C₅	1	2	yes	—
215	C₂³×C₅	—	2	1	no	—
216	C₂³×C₅	#121	1	1	yes	characteristic
217	C₅×Q₈	—	2	1	no	—
218	C₅×Q₈	—	2	1	no	—
219	C₅×Q₈	—	4	2	no	—
220	C₅×Q₈	—	4	2	no	—
221	C₅×Q₈	—	4	1	no	—
222	C₅×Q₈	—	4	1	no	—
223	C₅×Q₈	—	8	1	no	—
224	C₅×Q₈	—	8	2	no	—
225	C₅×D₄	—	2	1	no	—
226	C₅×D₄	—	2	1	no	—
227	C₅×D₄	—	4	2	no	—
228	C₂×C₄×C₅	—	2	1	no	—
229	C₂×C₄×C₅	—	2	1	no	—
230	C₂×C₄×C₅	—	2	1	no	—
231	C₂×C₄×C₅	—	2	1	no	—
232	C₂×C₄×C₅	—	2	1	no	—
233	C₂×C₄×C₅	—	4	1	no	—
234	C₂×C₄×C₅	—	4	1	no	—
235	C₂×C₄×C₅	—	4	1	no	—
236	C₂×C₄×C₅	—	4	2	no	—
237	C₂×C₄×C₅	—	4	1	no	—
238	C₂×C₄×C₅	—	4	1	no	—
239	C₂×C₄×C₅	—	4	2	no	—
240	C₂×C₄×C₅	—	8	1	no	—
241	C₂×C₄×C₅	—	8	2	no	—
242	C₂×C₄×C₅	#121	1	1	yes	characteristic
243	C₂×C₄×C₅	#121	1	1	yes	characteristic
244	C₂×C₄×C₅	#121	1	1	yes	characteristic
245	C₂×C₄×C₅	AGL(1,ℤ/8)	1	2	yes	—
246	C₂×C₄×C₅	#137	1	2	yes	—
247	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
248	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
249	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
250	C₅×C₈	—	2	2	no	—
251	C₅×C₈	—	2	2	no	—
252	C₅×C₈	—	4	1	no	—
253	C₅×C₈	—	4	1	no	—
254	C₅×C₈	—	4	2	no	—
255	C₅×C₈	—	4	2	no	—
256	C₂×#41	C₅×D₄	1	1	yes	characteristic
257	C₂²×Q₈	—	2	1	no	—
258	#137	—	4	4	no	—
259	C₂×Q₁₆	—	2	2	no	—
260	C₂×SD₁₆	—	2	2	no	—
261	C₂×M₁₆	—	2	1	no	—
262	C₂×M₁₆	—	2	2	no	—
263	C₂²×C₈	—	2	1	no	—
264	C₂²×C₈	—	2	1	no	—
265	C₄⋊Q₈	—	2	1	no	—
266	C₄⋊Q₈	—	2	1	no	—
267	C₄⋊Q₈	—	2	1	no	—
268	C₄⋊Q₈	C₂³×C₅	1	2	yes	—
269	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
270	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
271	#125	—	2	1	no	—
272	C₂²⋊Q₈	—	2	1	no	—
273	C₂²⋊Q₈	—	2	1	no	—
274	C₄×Q₈	—	2	1	no	—
275	C₄×Q₈	—	2	1	no	—
276	C₄×Q₈	C₅×D₄	1	1	yes	characteristic
277	C₄×Q₈	C₂³×C₅	1	1	yes	characteristic
278	C₄×D₄	—	2	1	no	—
279	C₄×D₄	—	2	1	no	—
280	C₄×D₄	C₅×D₄	1	1	yes	characteristic
281	C₄×D₄	C₂³×C₅	1	1	yes	characteristic
282	#117	—	2	1	no	—
283	#117	—	2	1	no	—
284	#117	C₅×D₄	1	1	yes	characteristic
285	C₂×C₄⋊C₄	—	2	1	no	—
286	C₂×C₄⋊C₄	—	2	1	no	—
287	C₂×C₄²	—	2	1	no	—
288	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
289	#107	—	2	1	no	—
290	#107	—	2	1	no	—
291	#106	—	2	2	no	—
292	#106	—	2	2	no	—
293	#106	—	2	1	no	—
294	#106	—	2	1	no	—
295	C₄⋊C₈	—	2	2	no	—
296	C₄⋊C₈	—	2	1	no	—
297	C₄⋊C₈	—	2	1	no	—
298	C₄⋊C₈	—	2	1	no	—
299	C₄⋊C₈	C₅×D₄	1	1	yes	characteristic
300	C₄⋊C₈	C₅×D₄	1	1	yes	characteristic
301	C₄⋊C₈	C₂³×C₅	1	2	yes	—
302	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
303	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
304	C₄⋊C₈	C₂³×C₅	1	2	yes	—
305	#103	—	2	1	no	—
306	#103	—	2	1	no	—
307	#103	—	2	2	no	—
308	#103	—	2	2	no	—
309	#103	—	2	2	no	—
310	#103	—	2	2	no	—
311	#102	—	2	1	no	—
312	#102	—	2	1	no	—
313	C₂²⋊C₈	—	2	2	no	—
314	C₂²⋊C₈	C₅×D₄	1	2	yes	—
315	#97	—	2	2	no	—
316	C₄×C₈	C₂³×C₅	1	2	yes	—
317	C₂²×C₅	—	2	1	no	—
318	C₂²×C₅	—	2	1	no	—
319	C₂²×C₅	—	4	1	no	—
320	C₂²×C₅	—	4	1	no	—
321	C₂²×C₅	—	4	1	no	—
322	C₂²×C₅	#468	1	2	yes	—
323	C₂²×C₅	C₂×#121	1	1	yes	characteristic
324	C₄×C₅	—	2	1	no	—
325	C₄×C₅	—	2	1	no	—
326	C₄×C₅	—	2	1	no	—
327	C₄×C₅	—	4	1	no	—
328	C₄×C₅	—	4	1	no	—
329	C₄×C₅	—	4	1	no	—
330	C₄×C₅	—	8	1	no	—
331	C₄×C₅	—	8	2	no	—
332	C₄×C₅	—	8	1	no	—
333	C₄×C₅	#468	1	2	yes	—
334	C₄×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
335	C₄×C₅	C₂×#137	1	1	yes	characteristic
336	C₄×C₅	#577	1	1	yes	characteristic
337	C₄×C₅	#578	1	1	yes	characteristic
338	#41	—	2	2	no	—
339	#41	—	2	2	no	—
340	C₂×Q₈	—	2	1	no	—
341	C₂×Q₈	—	2	2	no	—
342	C₂×Q₈	—	2	1	no	—
343	C₂×Q₈	—	4	1	no	—
344	C₂×Q₈	—	4	2	no	—
345	C₂×Q₈	—	4	2	no	—
346	C₂×Q₈	C₂×C₅×D₄	1	1	yes	characteristic
347	C₂×D₄	—	2	1	no	—
348	C₂×D₄	C₂×C₅×D₄	1	1	yes	characteristic
349	C₂²×C₄	—	2	1	no	—
350	C₂²×C₄	—	2	1	no	—
351	C₂²×C₄	—	2	1	no	—
352	C₂²×C₄	—	4	1	no	—
353	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
354	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
355	C₂²×C₄	C₅×#41	1	1	yes	characteristic
356	Q₁₆	—	4	4	no	—
357	SD₁₆	—	4	4	no	—
358	M₁₆	—	4	2	no	—
359	M₁₆	—	8	2	no	—
360	C₂×C₈	—	2	2	no	—
361	C₂×C₈	—	2	1	no	—
362	C₂×C₈	—	2	1	no	—
363	C₂×C₈	—	2	2	no	—
364	C₂×C₈	—	4	2	no	—
365	C₂×C₈	—	8	1	no	—
366	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
367	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
368	C₄⋊C₄	—	2	1	no	—
369	C₄⋊C₄	—	2	1	no	—
370	C₄⋊C₄	—	2	1	no	—
371	C₄⋊C₄	—	2	1	no	—
372	C₄⋊C₄	—	2	2	no	—
373	C₄⋊C₄	—	2	1	no	—
374	C₄⋊C₄	—	2	2	no	—
375	C₄⋊C₄	—	2	1	no	—
376	C₄⋊C₄	—	4	1	no	—
377	C₄⋊C₄	—	4	1	no	—
378	C₄⋊C₄	—	4	1	no	—
379	C₄⋊C₄	—	4	1	no	—
380	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
381	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
382	C₂²⋊C₄	—	2	1	no	—
383	C₂²⋊C₄	—	2	1	no	—
384	C₂²⋊C₄	—	2	1	no	—
385	C₂²⋊C₄	—	4	1	no	—
386	C₄²	—	2	1	no	—
387	C₄²	—	2	1	no	—
388	C₄²	—	2	1	no	—
389	C₄²	—	4	1	no	—
390	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
391	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
392	C₄²	C₅×#41	1	1	yes	characteristic
393	C₄²	C₂⁴×C₅	1	1	yes	characteristic
394	C₂×C₅	—	2	2	no	—
395	C₂×C₅	—	8	1	no	—
396	C₂×C₅	#3046	1	1	yes	characteristic
397	C₂×C₅	C₂×#468	1	1	yes	characteristic
398	C₂×C₅	#3069	1	1	yes	characteristic
399	C₂³	—	2	1	no	—
400	C₂³	C₅×#121	1	1	yes	characteristic
401	Q₈	—	2	1	no	—
402	Q₈	—	2	1	no	—
403	Q₈	—	4	2	no	—
404	Q₈	—	4	2	no	—
405	Q₈	—	4	1	no	—
406	Q₈	—	4	1	no	—
407	Q₈	—	8	1	no	—
408	Q₈	—	8	2	no	—
409	D₄	—	2	1	no	—
410	D₄	—	2	1	no	—
411	D₄	—	4	2	no	—
412	C₂×C₄	—	2	1	no	—
413	C₂×C₄	—	2	1	no	—
414	C₂×C₄	—	2	1	no	—
415	C₂×C₄	—	2	1	no	—
416	C₂×C₄	—	2	1	no	—
417	C₂×C₄	—	4	1	no	—
418	C₂×C₄	—	4	2	no	—
419	C₂×C₄	—	4	1	no	—
420	C₂×C₄	—	4	1	no	—
421	C₂×C₄	—	4	1	no	—
422	C₂×C₄	—	4	1	no	—
423	C₂×C₄	—	4	2	no	—
424	C₂×C₄	—	8	1	no	—
425	C₂×C₄	—	8	2	no	—
426	C₂×C₄	C₅×#121	1	1	yes	characteristic
427	C₂×C₄	C₅×#121	1	1	yes	characteristic
428	C₂×C₄	C₅×#121	1	1	yes	characteristic
429	C₂×C₄	C₅×AGL(1,ℤ/8)	1	2	yes	—
430	C₂×C₄	C₅×#137	1	2	yes	—
431	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
432	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
433	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
434	C₈	—	2	2	no	—
435	C₈	—	2	2	no	—
436	C₈	—	4	1	no	—
437	C₈	—	4	1	no	—
438	C₈	—	4	2	no	—
439	C₈	—	4	2	no	—
440	C₅	#19451	1	1	yes	characteristic, direct product factor, Sylow
441	C₂²	—	2	1	no	—
442	C₂²	—	2	1	no	—
443	C₂²	—	4	1	no	—
444	C₂²	—	4	1	no	—
445	C₂²	—	4	1	no	—
446	C₂²	C₅×#468	1	2	yes	—
447	C₂²	C₂×C₅×#121	1	1	yes	characteristic
448	C₄	—	2	1	no	—
449	C₄	—	2	1	no	—
450	C₄	—	2	1	no	—
451	C₄	—	4	1	no	—
452	C₄	—	4	1	no	—
453	C₄	—	4	1	no	—
454	C₄	—	8	1	no	—
455	C₄	—	8	2	no	—
456	C₄	—	8	1	no	—
457	C₄	C₅×#468	1	2	yes	—
458	C₄	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
459	C₄	C₂×C₅×#137	1	1	yes	characteristic
460	C₄	C₅×#577	1	1	yes	characteristic
461	C₄	C₅×#578	1	1	yes	characteristic
462	C₂	—	2	2	no	—
463	C₂	—	8	1	no	—
464	C₂	C₅×#3046	1	1	yes	characteristic
465	C₂	C₂×C₅×#468	1	1	yes	characteristic
466	C₂	C₅×#3069	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₅
prime radical	C₂×C₅×#41	D₄
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₅ ◁ C₂×C₄²×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅×#3229	C₂	semidirect
5. C₅×#1700	C₂	semidirect
6. C₅×#1699	C₂	semidirect
7. C₅×#1692	C₂	semidirect
8. C₅×#1691	C₂	semidirect
9. C₅×#1571	C₂	semidirect
10. C₅×#1550	C₂	semidirect
11. C₂×C₅×#332	C₂	semidirect
49. #19451	C₅	direct (N × H)
111. #3229	C₂×C₅	semidirect
115. #1700	C₂×C₅	semidirect
116. #1699	C₂×C₅	semidirect
117. #1692	C₂×C₅	semidirect
118. #1691	C₂×C₅	semidirect
119. #1571	C₂×C₅	semidirect
120. #1550	C₂×C₅	semidirect
121. C₂×#332	C₂×C₅	semidirect
440. C₅	#19451	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×#3229	2
C₅×#3076	2
C₅×#3039	2
C₅×#2989	2
C₅×#1700	2
C₅×#1699	2
C₅×#1692	2
C₅×#1691	2
C₅×#1571	2
C₅×#1550	2
C₂×C₅×#332	2
#19451	5

Subgroups — C5×#19451 #11942171

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#19451 #11942171