Subgroups — C₅×#19282 #11942002

Order 1280.

684 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3167	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#3110	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#3109	C₂	1	1	yes	maximal, characteristic
4	C₂×C₅×#436	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#1703	C₂	1	2	yes	maximal, complemented
6	C₅×#1701	C₂	1	2	yes	maximal, complemented
7	C₅×#1691	C₂	1	2	yes	maximal, complemented
8	C₅×#1685	C₂	1	2	yes	maximal, complemented
9	C₅×#1568	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1552	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1551	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₅×M₁₆	—	2	1	no	—
13	C₅×#533	C₂²	1	1	yes	characteristic
14	C₅×#532	C₂²	1	1	yes	characteristic
15	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
16	C₅×#498	C₂²	1	1	yes	characteristic, complemented
17	C₅×#492	C₂²	1	1	yes	characteristic, complemented
18	C₅×#487	C₂²	1	1	yes	characteristic, complemented
19	C₅×#486	C₂²	1	1	yes	characteristic, complemented
20	C₅×#484	—	2	1	no	—
21	C₅×#481	—	2	1	no	—
22	C₅×#476	C₂²	1	2	yes	—
23	C₅×#474	C₂²	1	2	yes	—
24	C₅×#465	—	2	1	no	—
25	C₅×#465	—	2	1	no	—
26	C₅×#461	C₂²	1	2	yes	—
27	C₅×#459	C₂²	1	2	yes	—
28	C₅×#450	—	2	1	no	—
29	C₅×#447	—	2	1	no	—
30	C₅×#442	—	2	2	no	—
31	C₅×#440	—	2	2	no	—
32	C₄×C₅×SD₁₆	—	2	1	no	—
33	C₄×C₅×SD₁₆	—	2	1	no	—
34	C₅×#436	—	2	1	no	—
35	C₅×#436	—	2	1	no	—
36	C₅×#436	C₂²	1	2	yes	—
37	C₅×#436	C₂²	1	2	yes	—
38	C₅×#432	C₂²	1	1	yes	characteristic
39	C₅×#432	C₂²	1	1	yes	characteristic
40	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
41	C₂×C₅×C₂²⋊C₈	—	2	1	no	—
42	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
43	C₅×#335	C₂²	1	2	yes	complemented
44	C₅×#334	C₂²	1	2	yes	complemented
45	C₅×#333	C₂²	1	2	yes	complemented
46	C₅×#332	C₂²	1	2	yes	complemented
47	C₅×#332	C₂²	1	2	yes	complemented
48	C₅×#331	C₂²	1	2	yes	complemented
49	#19282	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
50	C₂×C₅×#41	—	2	1	no	—
51	C₂²×C₅×D₄	D₄	1	1	yes	characteristic
52	C₂³×C₄×C₅	—	2	1	no	—
53	C₂×C₅×SD₁₆	—	2	2	no	—
54	C₂×C₅×SD₁₆	—	2	1	no	—
55	C₂×C₅×SD₁₆	—	2	1	no	—
56	C₂×C₅×D₈	—	2	2	no	—
57	C₂×C₅×M₁₆	—	2	2	no	—
58	C₂×C₅×M₁₆	—	2	2	no	—
59	C₂×C₅×M₁₆	—	4	4	no	—
60	C₂²×C₅×C₈	—	2	1	no	—
61	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
62	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
63	C₅×C₄⋊Q₈	C₂³	1	1	yes	characteristic
64	C₅×C₄⋊Q₈	C₂³	1	1	yes	characteristic
65	C₅×C₄⋊Q₈	C₂³	1	1	yes	characteristic
66	C₅×#127	C₂³	1	1	yes	characteristic
67	C₅×#125	—	2	1	no	—
68	C₅×#124	—	2	1	no	—
69	C₅×C₂²⋊Q₈	—	2	1	no	—
70	C₅×C₂²⋊Q₈	—	2	1	no	—
71	C₅×#121	—	2	1	no	—
72	C₅×#121	—	2	1	no	—
73	C₄×C₅×Q₈	—	2	1	no	—
74	C₄×C₅×Q₈	—	2	1	no	—
75	C₄×C₅×D₄	—	2	1	no	—
76	C₄×C₅×D₄	—	2	1	no	—
77	C₄×C₅×D₄	—	2	1	no	—
78	C₄×C₅×D₄	—	2	1	no	—
79	C₄×C₅×D₄	D₄	1	2	yes	—
80	C₄×C₅×D₄	C₂³	1	2	yes	—
81	C₅×#117	—	2	1	no	—
82	C₂×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
83	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
84	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
85	C₅×#107	—	2	2	no	—
86	C₅×#106	—	2	1	no	—
87	C₅×#106	—	2	1	no	—
88	C₅×#106	—	2	2	no	—
89	C₅×C₄⋊C₈	—	2	1	no	—
90	C₅×C₄⋊C₈	C₂³	1	2	yes	—
91	C₅×C₄⋊C₈	C₂³	1	2	yes	—
92	C₅×C₄⋊C₈	C₂³	1	2	yes	—
93	C₅×#103	—	2	1	no	—
94	C₅×#103	—	2	1	no	—
95	C₅×#103	—	2	2	no	—
96	C₅×#102	—	2	2	no	—
97	C₅×#102	—	2	2	no	—
98	C₅×#102	—	2	1	no	—
99	C₅×#102	—	2	1	no	—
100	C₅×#102	—	2	2	no	—
101	C₅×C₂²⋊C₈	—	2	1	no	—
102	C₅×C₂²⋊C₈	—	2	1	no	—
103	C₅×C₂²⋊C₈	—	2	2	no	—
104	C₅×C₂²⋊C₈	—	2	2	no	—
105	C₅×#97	—	2	1	no	—
106	C₅×#97	—	2	1	no	—
107	C₄×C₅×C₈	D₄	1	1	yes	characteristic
108	C₄×C₅×C₈	D₄	1	1	yes	characteristic
109	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
110	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
111	#3167	C₂×C₅	1	1	yes	characteristic, complemented
112	#3110	C₂×C₅	1	1	yes	characteristic, complemented
113	#3109	C₂×C₅	1	1	yes	characteristic
114	C₂×#436	C₂×C₅	1	1	yes	characteristic, complemented
115	#1703	C₂×C₅	1	2	yes	complemented
116	#1701	C₂×C₅	1	2	yes	complemented
117	#1691	C₂×C₅	1	2	yes	complemented
118	#1685	C₂×C₅	1	2	yes	complemented
119	#1568	C₂×C₅	1	1	yes	characteristic, complemented
120	#1552	C₂×C₅	1	1	yes	characteristic, complemented
121	#1551	C₂×C₅	1	1	yes	characteristic, complemented
122	C₂⁴×C₅	—	2	1	no	—
123	C₅×#41	—	8	2	no	—
124	C₂×C₅×Q₈	—	2	1	no	—
125	C₂×C₅×Q₈	—	2	1	no	—
126	C₂×C₅×Q₈	—	2	1	no	—
127	C₂×C₅×D₄	—	2	1	no	—
128	C₂×C₅×D₄	—	2	1	no	—
129	C₂×C₅×D₄	—	2	1	no	—
130	C₂×C₅×D₄	—	2	1	no	—
131	C₂×C₅×D₄	—	4	2	no	—
132	C₂×C₅×D₄	—	4	1	no	—
133	C₂×C₅×D₄	C₂×D₄	1	2	yes	—
134	C₂²×C₄×C₅	—	2	1	no	—
135	C₂²×C₄×C₅	—	2	2	no	—
136	C₂²×C₄×C₅	—	2	2	no	—
137	C₂²×C₄×C₅	—	4	2	no	—
138	C₂²×C₄×C₅	—	4	2	no	—
139	C₂²×C₄×C₅	—	4	1	no	—
140	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
141	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
142	C₂²×C₄×C₅	#41	1	1	yes	characteristic
143	C₅×SD₁₆	—	4	2	no	—
144	C₅×SD₁₆	—	4	4	no	—
145	C₅×SD₁₆	—	4	2	no	—
146	C₅×D₈	—	4	4	no	—
147	C₅×M₁₆	—	4	4	no	—
148	C₅×M₁₆	—	4	4	no	—
149	C₂×C₅×C₈	—	2	2	no	—
150	C₂×C₅×C₈	—	2	2	no	—
151	C₂×C₅×C₈	—	2	2	no	—
152	C₂×C₅×C₈	—	2	2	no	—
153	C₂×C₅×C₈	—	4	1	no	—
154	C₂×C₅×C₈	—	4	2	no	—
155	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
156	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
157	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
158	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
159	C₅×C₄⋊C₄	—	2	1	no	—
160	C₅×C₄⋊C₄	—	2	1	no	—
161	C₅×C₄⋊C₄	—	2	1	no	—
162	C₅×C₄⋊C₄	—	2	1	no	—
163	C₅×C₄⋊C₄	—	2	1	no	—
164	C₅×C₄⋊C₄	—	2	1	no	—
165	C₅×C₄⋊C₄	—	2	1	no	—
166	C₅×C₄⋊C₄	—	4	1	no	—
167	C₅×C₄⋊C₄	—	4	1	no	—
168	C₅×C₄⋊C₄	C₂×D₄	1	2	yes	—
169	C₅×C₂²⋊C₄	—	2	2	no	—
170	C₅×C₂²⋊C₄	—	2	2	no	—
171	C₅×C₂²⋊C₄	—	4	1	no	—
172	C₅×C₂²⋊C₄	—	4	1	no	—
173	C₅×C₂²⋊C₄	—	4	1	no	—
174	C₄²×C₅	—	4	1	no	—
175	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
176	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
177	C₄²×C₅	#41	1	1	yes	characteristic
178	C₄²×C₅	C₂⁴	1	1	yes	characteristic
179	C₂²×M₁₆	—	2	1	no	—
180	#533	C₂²×C₅	1	1	yes	characteristic
181	#532	C₂²×C₅	1	1	yes	characteristic
182	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
183	#498	C₂²×C₅	1	1	yes	characteristic, complemented
184	#492	C₂²×C₅	1	1	yes	characteristic, complemented
185	#487	C₂²×C₅	1	1	yes	characteristic, complemented
186	#486	C₂²×C₅	1	1	yes	characteristic, complemented
187	#484	—	2	1	no	—
188	#481	—	2	1	no	—
189	#476	C₂²×C₅	1	2	yes	—
190	#474	C₂²×C₅	1	2	yes	—
191	#465	—	2	1	no	—
192	#465	—	2	1	no	—
193	#461	C₂²×C₅	1	2	yes	—
194	#459	C₂²×C₅	1	2	yes	—
195	#450	—	2	1	no	—
196	#447	—	2	1	no	—
197	#442	—	2	2	no	—
198	#440	—	2	2	no	—
199	C₄×SD₁₆	—	2	1	no	—
200	C₄×SD₁₆	—	2	1	no	—
201	#436	—	2	1	no	—
202	#436	—	2	1	no	—
203	#436	C₂²×C₅	1	2	yes	—
204	#436	C₂²×C₅	1	2	yes	—
205	#432	C₂²×C₅	1	1	yes	characteristic
206	#432	C₂²×C₅	1	1	yes	characteristic
207	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
208	C₂×C₂²⋊C₈	—	2	1	no	—
209	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
210	#335	C₂²×C₅	1	2	yes	complemented
211	#334	C₂²×C₅	1	2	yes	complemented
212	#333	C₂²×C₅	1	2	yes	complemented
213	#332	C₂²×C₅	1	2	yes	complemented
214	#332	C₂²×C₅	1	2	yes	complemented
215	#331	C₂²×C₅	1	2	yes	complemented
216	C₂³×C₅	—	2	2	no	—
217	C₂³×C₅	—	4	2	no	—
218	C₂³×C₅	—	4	2	no	—
219	C₂³×C₅	—	4	2	no	—
220	C₂³×C₅	—	4	1	no	—
221	C₂³×C₅	#121	1	1	yes	characteristic
222	C₅×Q₈	—	4	1	no	—
223	C₅×Q₈	—	4	1	no	—
224	C₅×Q₈	—	4	2	no	—
225	C₅×Q₈	—	8	1	no	—
226	C₅×D₄	—	2	2	no	—
227	C₅×D₄	—	2	2	no	—
228	C₅×D₄	—	4	2	no	—
229	C₅×D₄	—	4	1	no	—
230	C₅×D₄	—	4	2	no	—
231	C₅×D₄	—	4	1	no	—
232	C₅×D₄	—	8	1	no	—
233	C₅×D₄	—	8	2	no	—
234	C₂×C₄×C₅	—	2	2	no	—
235	C₂×C₄×C₅	—	2	1	no	—
236	C₂×C₄×C₅	—	2	1	no	—
237	C₂×C₄×C₅	—	2	2	no	—
238	C₂×C₄×C₅	—	2	2	no	—
239	C₂×C₄×C₅	—	4	4	no	—
240	C₂×C₄×C₅	—	4	2	no	—
241	C₂×C₄×C₅	—	4	2	no	—
242	C₂×C₄×C₅	—	4	2	no	—
243	C₂×C₄×C₅	—	4	1	no	—
244	C₂×C₄×C₅	—	4	1	no	—
245	C₂×C₄×C₅	—	4	1	no	—
246	C₂×C₄×C₅	—	8	2	no	—
247	C₂×C₄×C₅	#121	1	1	yes	characteristic
248	C₂×C₄×C₅	#121	1	1	yes	characteristic
249	C₂×C₄×C₅	#121	1	1	yes	characteristic
250	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
251	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
252	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
253	C₅×C₈	—	2	1	no	—
254	C₅×C₈	—	2	1	no	—
255	C₅×C₈	—	2	1	no	—
256	C₅×C₈	—	4	2	no	—
257	C₅×C₈	—	4	2	no	—
258	C₅×C₈	—	4	2	no	—
259	C₅×C₈	AGL(1,ℤ/8)	1	2	yes	—
260	C₂×#41	—	2	1	no	—
261	C₂²×D₄	C₅×D₄	1	1	yes	characteristic
262	C₂³×C₄	—	2	1	no	—
263	C₂×SD₁₆	—	2	2	no	—
264	C₂×SD₁₆	—	2	1	no	—
265	C₂×SD₁₆	—	2	1	no	—
266	C₂×D₈	—	2	2	no	—
267	C₂×M₁₆	—	2	2	no	—
268	C₂×M₁₆	—	2	2	no	—
269	C₂×M₁₆	—	4	4	no	—
270	C₂²×C₈	—	2	1	no	—
271	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
272	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
273	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
274	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
275	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
276	#127	C₂³×C₅	1	1	yes	characteristic
277	#125	—	2	1	no	—
278	#124	—	2	1	no	—
279	C₂²⋊Q₈	—	2	1	no	—
280	C₂²⋊Q₈	—	2	1	no	—
281	#121	—	2	1	no	—
282	#121	—	2	1	no	—
283	C₄×Q₈	—	2	1	no	—
284	C₄×Q₈	—	2	1	no	—
285	C₄×D₄	—	2	1	no	—
286	C₄×D₄	—	2	1	no	—
287	C₄×D₄	—	2	1	no	—
288	C₄×D₄	—	2	1	no	—
289	C₄×D₄	C₅×D₄	1	2	yes	—
290	C₄×D₄	C₂³×C₅	1	2	yes	—
291	#117	—	2	1	no	—
292	C₂×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
293	C₂×C₂²⋊C₄	—	2	1	no	—
294	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
295	#107	—	2	2	no	—
296	#106	—	2	1	no	—
297	#106	—	2	1	no	—
298	#106	—	2	2	no	—
299	C₄⋊C₈	—	2	1	no	—
300	C₄⋊C₈	C₂³×C₅	1	2	yes	—
301	C₄⋊C₈	C₂³×C₅	1	2	yes	—
302	C₄⋊C₈	C₂³×C₅	1	2	yes	—
303	#103	—	2	1	no	—
304	#103	—	2	1	no	—
305	#103	—	2	2	no	—
306	#102	—	2	2	no	—
307	#102	—	2	2	no	—
308	#102	—	2	1	no	—
309	#102	—	2	1	no	—
310	#102	—	2	2	no	—
311	C₂²⋊C₈	—	2	1	no	—
312	C₂²⋊C₈	—	2	1	no	—
313	C₂²⋊C₈	—	2	2	no	—
314	C₂²⋊C₈	—	2	2	no	—
315	#97	—	2	1	no	—
316	#97	—	2	1	no	—
317	C₄×C₈	C₅×D₄	1	1	yes	characteristic
318	C₄×C₈	C₅×D₄	1	1	yes	characteristic
319	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
320	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
321	C₂²×C₅	—	2	1	no	—
322	C₂²×C₅	—	2	1	no	—
323	C₂²×C₅	—	4	2	no	—
324	C₂²×C₅	—	4	2	no	—
325	C₂²×C₅	—	4	2	no	—
326	C₂²×C₅	—	8	4	no	—
327	C₂²×C₅	—	8	1	no	—
328	C₂²×C₅	—	8	1	no	—
329	C₂²×C₅	—	8	1	no	—
330	C₂²×C₅	#471	1	2	yes	—
331	C₂²×C₅	C₂×#121	1	1	yes	characteristic
332	C₄×C₅	—	2	1	no	—
333	C₄×C₅	—	2	1	no	—
334	C₄×C₅	—	2	1	no	—
335	C₄×C₅	—	2	1	no	—
336	C₄×C₅	—	4	2	no	—
337	C₄×C₅	—	8	1	no	—
338	C₄×C₅	—	8	1	no	—
339	C₄×C₅	—	8	1	no	—
340	C₄×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
341	C₄×C₅	#575	1	1	yes	characteristic
342	C₄×C₅	#575	1	2	yes	—
343	C₂⁴	—	2	1	no	—
344	#41	—	8	2	no	—
345	C₂×Q₈	—	2	1	no	—
346	C₂×Q₈	—	2	1	no	—
347	C₂×Q₈	—	2	1	no	—
348	C₂×D₄	—	2	1	no	—
349	C₂×D₄	—	2	1	no	—
350	C₂×D₄	—	2	1	no	—
351	C₂×D₄	—	2	1	no	—
352	C₂×D₄	—	4	2	no	—
353	C₂×D₄	—	4	1	no	—
354	C₂×D₄	C₂×C₅×D₄	1	2	yes	—
355	C₂²×C₄	—	2	1	no	—
356	C₂²×C₄	—	2	2	no	—
357	C₂²×C₄	—	2	2	no	—
358	C₂²×C₄	—	4	2	no	—
359	C₂²×C₄	—	4	2	no	—
360	C₂²×C₄	—	4	1	no	—
361	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
362	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
363	C₂²×C₄	C₅×#41	1	1	yes	characteristic
364	SD₁₆	—	4	2	no	—
365	SD₁₆	—	4	4	no	—
366	SD₁₆	—	4	2	no	—
367	D₈	—	4	4	no	—
368	M₁₆	—	4	4	no	—
369	M₁₆	—	4	4	no	—
370	C₂×C₈	—	2	2	no	—
371	C₂×C₈	—	2	2	no	—
372	C₂×C₈	—	2	2	no	—
373	C₂×C₈	—	2	2	no	—
374	C₂×C₈	—	4	1	no	—
375	C₂×C₈	—	4	2	no	—
376	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
377	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
378	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
379	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
380	C₄⋊C₄	—	2	1	no	—
381	C₄⋊C₄	—	2	1	no	—
382	C₄⋊C₄	—	2	1	no	—
383	C₄⋊C₄	—	2	1	no	—
384	C₄⋊C₄	—	2	1	no	—
385	C₄⋊C₄	—	2	1	no	—
386	C₄⋊C₄	—	2	1	no	—
387	C₄⋊C₄	—	4	1	no	—
388	C₄⋊C₄	—	4	1	no	—
389	C₄⋊C₄	C₂×C₅×D₄	1	2	yes	—
390	C₂²⋊C₄	—	2	2	no	—
391	C₂²⋊C₄	—	2	2	no	—
392	C₂²⋊C₄	—	4	1	no	—
393	C₂²⋊C₄	—	4	1	no	—
394	C₂²⋊C₄	—	4	1	no	—
395	C₄²	—	4	1	no	—
396	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
397	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
398	C₄²	C₅×#41	1	1	yes	characteristic
399	C₄²	C₂⁴×C₅	1	1	yes	characteristic
400	C₂×C₅	—	2	2	no	—
401	C₂×C₅	—	8	2	no	—
402	C₂×C₅	—	16	1	no	—
403	C₂×C₅	#3036	1	1	yes	characteristic
404	C₂×C₅	#3054	1	1	yes	characteristic
405	C₂×C₅	C₂×#471	1	1	yes	characteristic
406	C₂³	—	2	2	no	—
407	C₂³	—	4	2	no	—
408	C₂³	—	4	2	no	—
409	C₂³	—	4	2	no	—
410	C₂³	—	4	1	no	—
411	C₂³	C₅×#121	1	1	yes	characteristic
412	Q₈	—	4	1	no	—
413	Q₈	—	4	1	no	—
414	Q₈	—	4	2	no	—
415	Q₈	—	8	1	no	—
416	D₄	—	2	2	no	—
417	D₄	—	2	2	no	—
418	D₄	—	4	2	no	—
419	D₄	—	4	1	no	—
420	D₄	—	4	2	no	—
421	D₄	—	4	1	no	—
422	D₄	—	8	1	no	—
423	D₄	—	8	2	no	—
424	C₂×C₄	—	2	2	no	—
425	C₂×C₄	—	2	1	no	—
426	C₂×C₄	—	2	1	no	—
427	C₂×C₄	—	2	2	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	4	4	no	—
430	C₂×C₄	—	4	2	no	—
431	C₂×C₄	—	4	2	no	—
432	C₂×C₄	—	4	2	no	—
433	C₂×C₄	—	4	1	no	—
434	C₂×C₄	—	4	1	no	—
435	C₂×C₄	—	4	1	no	—
436	C₂×C₄	—	8	2	no	—
437	C₂×C₄	C₅×#121	1	1	yes	characteristic
438	C₂×C₄	C₅×#121	1	1	yes	characteristic
439	C₂×C₄	C₅×#121	1	1	yes	characteristic
440	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
441	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
442	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
443	C₈	—	2	1	no	—
444	C₈	—	2	1	no	—
445	C₈	—	2	1	no	—
446	C₈	—	4	2	no	—
447	C₈	—	4	2	no	—
448	C₈	—	4	2	no	—
449	C₈	C₅×AGL(1,ℤ/8)	1	2	yes	—
450	C₅	#19282	1	1	yes	characteristic, direct product factor, Sylow
451	C₂²	—	2	1	no	—
452	C₂²	—	2	1	no	—
453	C₂²	—	4	2	no	—
454	C₂²	—	4	2	no	—
455	C₂²	—	4	2	no	—
456	C₂²	—	8	4	no	—
457	C₂²	—	8	1	no	—
458	C₂²	—	8	1	no	—
459	C₂²	—	8	1	no	—
460	C₂²	C₅×#471	1	2	yes	—
461	C₂²	C₂×C₅×#121	1	1	yes	characteristic
462	C₄	—	2	1	no	—
463	C₄	—	2	1	no	—
464	C₄	—	2	1	no	—
465	C₄	—	2	1	no	—
466	C₄	—	4	2	no	—
467	C₄	—	8	1	no	—
468	C₄	—	8	1	no	—
469	C₄	—	8	1	no	—
470	C₄	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
471	C₄	C₅×#575	1	1	yes	characteristic
472	C₄	C₅×#575	1	2	yes	—
473	C₂	—	2	2	no	—
474	C₂	—	8	2	no	—
475	C₂	—	16	1	no	—
476	C₂	C₅×#3036	1	1	yes	characteristic
477	C₂	C₅×#3054	1	1	yes	characteristic
478	C₂	C₂×C₅×#471	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₅
prime radical	C₅×#3109	C₂
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×#3167	C₂	semidirect
2. C₅×#3110	C₂	semidirect
4. C₂×C₅×#436	C₂	semidirect
5. C₅×#1703	C₂	semidirect
6. C₅×#1701	C₂	semidirect
7. C₅×#1691	C₂	semidirect
8. C₅×#1685	C₂	semidirect
9. C₅×#1568	C₂	semidirect
10. C₅×#1552	C₂	semidirect
11. C₅×#1551	C₂	semidirect
16. C₅×#498	C₂²	semidirect
17. C₅×#492	C₂²	semidirect
18. C₅×#487	C₂²	semidirect
19. C₅×#486	C₂²	semidirect
43. C₅×#335	C₂²	semidirect
44. C₅×#334	C₂²	semidirect
45. C₅×#333	C₂²	semidirect
46. C₅×#332	C₂²	semidirect
47. C₅×#332	C₂²	semidirect
48. C₅×#331	C₂²	semidirect
49. #19282	C₅	direct (N × H)
111. #3167	C₂×C₅	semidirect
112. #3110	C₂×C₅	semidirect
114. C₂×#436	C₂×C₅	semidirect
115. #1703	C₂×C₅	semidirect
116. #1701	C₂×C₅	semidirect
117. #1691	C₂×C₅	semidirect
118. #1685	C₂×C₅	semidirect
119. #1568	C₂×C₅	semidirect
120. #1552	C₂×C₅	semidirect
121. #1551	C₂×C₅	semidirect
183. #498	C₂²×C₅	semidirect
184. #492	C₂²×C₅	semidirect
185. #487	C₂²×C₅	semidirect
186. #486	C₂²×C₅	semidirect
210. #335	C₂²×C₅	semidirect
211. #334	C₂²×C₅	semidirect
212. #333	C₂²×C₅	semidirect
213. #332	C₂²×C₅	semidirect
214. #332	C₂²×C₅	semidirect
215. #331	C₂²×C₅	semidirect
450. C₅	#19282	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×#3167	2
C₅×#3110	2
C₅×#3109	2
C₂×C₅×#436	2
C₅×#1703	2
C₅×#1701	2
C₅×#1691	2
C₅×#1685	2
C₅×#1568	2
C₅×#1552	2
C₅×#1551	2
#19282	5

Subgroups — C5×#19282 #11942002

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#19282 #11942002