Subgroups — C₅×#9229 #11931949

Order 1280.

646 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#459	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#436	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#1957	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#1802	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₅×#331	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#1296	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#1277	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×C₅×D₈	—	2	1	no	—
9	C₂²×C₅×M₁₆	—	2	1	no	—
10	C₂×C₅×#127	C₂²	1	1	yes	characteristic
11	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
12	C₅×#459	—	2	2	no	—
13	C₅×#459	C₄	1	4	yes	complemented
14	C₅×#436	—	2	2	no	—
15	C₅×#436	—	2	2	no	—
16	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
17	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
18	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
19	C₂×C₅×#102	—	2	1	no	—
20	C₂×C₅×#102	—	2	1	no	—
21	C₂×C₅×#102	—	2	1	no	—
22	C₂×C₅×#102	—	2	1	no	—
23	C₂×C₅×C₂²⋊C₈	—	2	1	no	—
24	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
25	C₅×#384	C₂²	1	1	yes	characteristic
26	C₅×#340	—	2	1	no	—
27	C₅×#331	—	2	2	no	—
28	#9229	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
29	C₂²×C₅×D₄	—	2	1	no	—
30	C₂²×C₅×D₄	—	2	1	no	—
31	C₂²×C₅×D₄	—	2	1	no	—
32	C₂²×C₅×D₄	D₄	1	1	yes	characteristic
33	C₂³×C₄×C₅	—	2	1	no	—
34	C₂×C₅×D₈	—	2	4	no	—
35	C₂×C₅×D₈	—	4	2	no	—
36	C₂×C₅×D₈	—	4	2	no	—
37	C₂×C₅×M₁₆	—	2	4	no	—
38	C₂×C₅×M₁₆	—	4	2	no	—
39	C₂×C₅×M₁₆	—	4	2	no	—
40	C₂²×C₅×C₈	—	2	1	no	—
41	C₂²×C₅×C₈	—	2	1	no	—
42	C₂²×C₅×C₈	—	2	1	no	—
43	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
44	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
45	C₅×#127	—	2	1	no	—
46	C₅×#127	—	2	1	no	—
47	C₅×#127	—	2	1	no	—
48	C₅×#127	C₂×C₄	1	2	yes	—
49	C₄×C₅×D₄	—	2	1	no	—
50	C₄×C₅×D₄	—	2	1	no	—
51	C₄×C₅×D₄	C₂×C₄	1	2	yes	—
52	C₄×C₅×D₄	D₄	1	2	yes	—
53	C₂×C₅×C₄⋊C₄	—	2	1	no	—
54	C₂×C₅×C₄⋊C₄	—	2	1	no	—
55	C₂×C₅×C₄⋊C₄	—	2	1	no	—
56	C₂×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
57	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
58	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
59	C₅×C₄⋊C₈	—	2	1	no	—
60	C₅×C₄⋊C₈	—	2	1	no	—
61	C₅×C₄⋊C₈	—	2	1	no	—
62	C₅×C₄⋊C₈	—	2	1	no	—
63	C₅×C₄⋊C₈	C₂×C₄	1	2	yes	—
64	C₅×C₄⋊C₈	D₄	1	2	yes	—
65	C₅×#102	—	2	4	no	—
66	C₅×#102	—	4	2	no	—
67	C₅×#102	—	4	2	no	—
68	C₅×#102	—	4	2	no	—
69	C₅×C₂²⋊C₈	—	2	4	no	—
70	C₄×C₅×C₈	—	2	1	no	—
71	C₄×C₅×C₈	—	2	1	no	—
72	C₂×#459	C₂×C₅	1	1	yes	characteristic
73	C₂×#436	C₂×C₅	1	1	yes	characteristic, complemented
74	#1957	C₂×C₅	1	1	yes	characteristic, complemented
75	#1802	C₂×C₅	1	1	yes	characteristic, complemented
76	C₂×#331	C₂×C₅	1	1	yes	characteristic, complemented
77	#1296	C₂×C₅	1	1	yes	characteristic, complemented
78	#1277	C₂×C₅	1	1	yes	characteristic, complemented
79	C₂⁴×C₅	—	2	1	no	—
80	C₂⁴×C₅	—	4	1	no	—
81	C₂×C₅×D₄	—	2	2	no	—
82	C₂×C₅×D₄	—	2	2	no	—
83	C₂×C₅×D₄	—	2	2	no	—
84	C₂×C₅×D₄	—	2	1	no	—
85	C₂×C₅×D₄	—	2	1	no	—
86	C₂×C₅×D₄	—	2	1	no	—
87	C₂×C₅×D₄	—	2	1	no	—
88	C₂×C₅×D₄	—	2	1	no	—
89	C₂×C₅×D₄	—	4	1	no	—
90	C₂×C₅×D₄	—	4	1	no	—
91	C₂×C₅×D₄	—	4	1	no	—
92	C₂×C₅×D₄	—	4	1	no	—
93	C₂×C₅×D₄	—	4	1	no	—
94	C₂×C₅×D₄	—	4	1	no	—
95	C₂×C₅×D₄	—	4	1	no	—
96	C₂×C₅×D₄	—	4	1	no	—
97	C₂×C₅×D₄	—	4	1	no	—
98	C₂×C₅×D₄	—	4	1	no	—
99	C₂×C₅×D₄	—	4	1	no	—
100	C₂×C₅×D₄	—	8	1	no	—
101	C₂×C₅×D₄	—	8	1	no	—
102	C₂×C₅×D₄	C₂²⋊C₄	1	2	yes	—
103	C₂²×C₄×C₅	—	2	1	no	—
104	C₂²×C₄×C₅	—	2	2	no	—
105	C₂²×C₄×C₅	—	2	2	no	—
106	C₂²×C₄×C₅	—	4	1	no	—
107	C₂²×C₄×C₅	—	4	1	no	—
108	C₂²×C₄×C₅	—	4	1	no	—
109	C₂²×C₄×C₅	—	4	1	no	—
110	C₂²×C₄×C₅	—	4	1	no	—
111	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₅	#41	1	1	yes	characteristic
114	C₅×D₈	—	4	8	no	—
115	C₅×M₁₆	—	4	8	no	—
116	C₂×C₅×C₈	—	2	1	no	—
117	C₂×C₅×C₈	—	2	1	no	—
118	C₂×C₅×C₈	—	2	2	no	—
119	C₂×C₅×C₈	—	2	2	no	—
120	C₂×C₅×C₈	—	2	1	no	—
121	C₂×C₅×C₈	—	2	1	no	—
122	C₂×C₅×C₈	—	2	1	no	—
123	C₂×C₅×C₈	—	4	1	no	—
124	C₂×C₅×C₈	—	4	1	no	—
125	C₂×C₅×C₈	—	4	1	no	—
126	C₂×C₅×C₈	—	4	1	no	—
127	C₂×C₅×C₈	—	4	1	no	—
128	C₂×C₅×C₈	—	4	1	no	—
129	C₂×C₅×C₈	—	4	1	no	—
130	C₂×C₅×C₈	D₈	1	2	yes	complemented
131	C₅×C₄⋊C₄	—	2	1	no	—
132	C₅×C₄⋊C₄	—	4	1	no	—
133	C₅×C₄⋊C₄	—	4	1	no	—
134	C₅×C₄⋊C₄	—	4	1	no	—
135	C₅×C₄⋊C₄	—	4	1	no	—
136	C₅×C₄⋊C₄	—	8	1	no	—
137	C₅×C₄⋊C₄	C₂²⋊C₄	1	2	yes	—
138	C₅×C₂²⋊C₄	—	2	2	no	—
139	C₅×C₂²⋊C₄	—	2	2	no	—
140	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
141	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
142	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
143	C₄²×C₅	#41	1	1	yes	characteristic
144	C₂²×D₈	—	2	1	no	—
145	C₂²×M₁₆	—	2	1	no	—
146	C₂×#127	C₂²×C₅	1	1	yes	characteristic
147	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
148	#459	—	2	2	no	—
149	#459	C₄×C₅	1	4	yes	complemented
150	#436	—	2	2	no	—
151	#436	—	2	2	no	—
152	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
153	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
154	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
155	C₂×#102	—	2	1	no	—
156	C₂×#102	—	2	1	no	—
157	C₂×#102	—	2	1	no	—
158	C₂×#102	—	2	1	no	—
159	C₂×C₂²⋊C₈	—	2	1	no	—
160	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
161	#384	C₂²×C₅	1	1	yes	characteristic
162	#340	—	2	1	no	—
163	#331	—	2	2	no	—
164	C₂³×C₅	—	2	2	no	—
165	C₂³×C₅	—	4	1	no	—
166	C₂³×C₅	—	4	1	no	—
167	C₂³×C₅	—	4	1	no	—
168	C₂³×C₅	—	4	1	no	—
169	C₂³×C₅	—	4	1	no	—
170	C₂³×C₅	—	4	1	no	—
171	C₂³×C₅	—	4	2	no	—
172	C₂³×C₅	—	8	1	no	—
173	C₂³×C₅	—	8	1	no	—
174	C₂³×C₅	—	8	1	no	—
175	C₂³×C₅	—	8	1	no	—
176	C₂³×C₅	—	8	1	no	—
177	C₂³×C₅	—	8	1	no	—
178	C₂³×C₅	#121	1	1	yes	characteristic
179	C₅×D₄	—	2	2	no	—
180	C₅×D₄	—	2	2	no	—
181	C₅×D₄	—	4	2	no	—
182	C₅×D₄	—	4	2	no	—
183	C₅×D₄	—	4	2	no	—
184	C₅×D₄	—	4	2	no	—
185	C₅×D₄	—	4	1	no	—
186	C₅×D₄	—	4	1	no	—
187	C₅×D₄	—	8	2	no	—
188	C₅×D₄	—	8	2	no	—
189	C₅×D₄	—	8	1	no	—
190	C₅×D₄	—	8	1	no	—
191	C₅×D₄	—	8	1	no	—
192	C₅×D₄	—	8	1	no	—
193	C₂×C₄×C₅	—	2	1	no	—
194	C₂×C₄×C₅	—	2	1	no	—
195	C₂×C₄×C₅	—	2	2	no	—
196	C₂×C₄×C₅	—	4	1	no	—
197	C₂×C₄×C₅	—	4	1	no	—
198	C₂×C₄×C₅	—	4	2	no	—
199	C₂×C₄×C₅	—	4	2	no	—
200	C₂×C₄×C₅	—	4	2	no	—
201	C₂×C₄×C₅	—	4	2	no	—
202	C₂×C₄×C₅	—	8	1	no	—
203	C₂×C₄×C₅	—	8	1	no	—
204	C₂×C₄×C₅	—	8	1	no	—
205	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
206	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
207	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
208	C₂×C₄×C₅	#120	1	1	yes	characteristic
209	C₂×C₄×C₅	#121	1	1	yes	characteristic
210	C₂×C₄×C₅	#123	1	1	yes	characteristic
211	C₂×C₄×C₅	C₂×D₈	1	1	yes	characteristic
212	C₂×C₄×C₅	#135	1	1	yes	characteristic
213	C₂×C₄×C₅	AGL(1,ℤ/8)	1	1	yes	characteristic
214	C₂×C₄×C₅	AGL(1,ℤ/8)	1	1	yes	characteristic
215	C₂×C₄×C₅	AGL(1,ℤ/8)	1	1	yes	characteristic
216	C₂×C₄×C₅	AGL(1,ℤ/8)	1	1	yes	characteristic
217	C₂×C₄×C₅	AGL(1,ℤ/8)	1	1	yes	characteristic
218	C₂×C₄×C₅	#137	1	1	yes	characteristic
219	C₅×C₈	—	2	2	no	—
220	C₅×C₈	—	4	2	no	—
221	C₅×C₈	—	4	2	no	—
222	C₅×C₈	—	4	1	no	—
223	C₅×C₈	—	8	1	no	—
224	C₂²×D₄	—	2	1	no	—
225	C₂²×D₄	—	2	1	no	—
226	C₂²×D₄	—	2	1	no	—
227	C₂²×D₄	C₅×D₄	1	1	yes	characteristic
228	C₂³×C₄	—	2	1	no	—
229	C₂×D₈	—	2	4	no	—
230	C₂×D₈	—	4	2	no	—
231	C₂×D₈	—	4	2	no	—
232	C₂×M₁₆	—	2	4	no	—
233	C₂×M₁₆	—	4	2	no	—
234	C₂×M₁₆	—	4	2	no	—
235	C₂²×C₈	—	2	1	no	—
236	C₂²×C₈	—	2	1	no	—
237	C₂²×C₈	—	2	1	no	—
238	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
239	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
240	#127	—	2	1	no	—
241	#127	—	2	1	no	—
242	#127	—	2	1	no	—
243	#127	C₂×C₄×C₅	1	2	yes	—
244	C₄×D₄	—	2	1	no	—
245	C₄×D₄	—	2	1	no	—
246	C₄×D₄	C₂×C₄×C₅	1	2	yes	—
247	C₄×D₄	C₅×D₄	1	2	yes	—
248	C₂×C₄⋊C₄	—	2	1	no	—
249	C₂×C₄⋊C₄	—	2	1	no	—
250	C₂×C₄⋊C₄	—	2	1	no	—
251	C₂×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
252	C₂×C₂²⋊C₄	—	2	1	no	—
253	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
254	C₄⋊C₈	—	2	1	no	—
255	C₄⋊C₈	—	2	1	no	—
256	C₄⋊C₈	—	2	1	no	—
257	C₄⋊C₈	—	2	1	no	—
258	C₄⋊C₈	C₂×C₄×C₅	1	2	yes	—
259	C₄⋊C₈	C₅×D₄	1	2	yes	—
260	#102	—	2	4	no	—
261	#102	—	4	2	no	—
262	#102	—	4	2	no	—
263	#102	—	4	2	no	—
264	C₂²⋊C₈	—	2	4	no	—
265	C₄×C₈	—	2	1	no	—
266	C₄×C₈	—	2	1	no	—
267	C₂²×C₅	—	4	2	no	—
268	C₂²×C₅	—	4	2	no	—
269	C₂²×C₅	—	4	2	no	—
270	C₂²×C₅	—	8	1	no	—
271	C₂²×C₅	—	8	1	no	—
272	C₂²×C₅	—	8	1	no	—
273	C₂²×C₅	—	8	1	no	—
274	C₂²×C₅	—	8	2	no	—
275	C₂²×C₅	—	8	2	no	—
276	C₂²×C₅	—	8	2	no	—
277	C₂²×C₅	—	16	1	no	—
278	C₂²×C₅	—	16	1	no	—
279	C₂²×C₅	—	16	1	no	—
280	C₂²×C₅	—	16	1	no	—
281	C₂²×C₅	#386	1	1	yes	characteristic
282	C₂²×C₅	#459	1	1	yes	characteristic
283	C₂²×C₅	#463	1	1	yes	characteristic
284	C₂²×C₅	#468	1	1	yes	characteristic
285	C₂²×C₅	#469	1	1	yes	characteristic
286	C₂²×C₅	#471	1	1	yes	characteristic
287	C₂²×C₅	#472	1	1	yes	characteristic
288	C₄×C₅	—	2	1	no	—
289	C₄×C₅	—	2	1	no	—
290	C₄×C₅	—	4	2	no	—
291	C₄×C₅	—	16	1	no	—
292	C₄×C₅	#417	1	1	yes	characteristic
293	C₄×C₅	#418	1	1	yes	characteristic
294	C₄×C₅	C₄×D₈	1	1	yes	characteristic
295	C₄×C₅	#442	1	1	yes	characteristic
296	C₄×C₅	#447	1	1	yes	characteristic
297	C₄×C₅	#449	1	1	yes	characteristic
298	C₄×C₅	#468	1	1	yes	characteristic
299	C₄×C₅	#469	1	1	yes	characteristic
300	C₂⁴	—	2	1	no	—
301	C₂⁴	—	4	1	no	—
302	C₂×D₄	—	2	2	no	—
303	C₂×D₄	—	2	2	no	—
304	C₂×D₄	—	2	2	no	—
305	C₂×D₄	—	2	1	no	—
306	C₂×D₄	—	2	1	no	—
307	C₂×D₄	—	2	1	no	—
308	C₂×D₄	—	2	1	no	—
309	C₂×D₄	—	2	1	no	—
310	C₂×D₄	—	4	1	no	—
311	C₂×D₄	—	4	1	no	—
312	C₂×D₄	—	4	1	no	—
313	C₂×D₄	—	4	1	no	—
314	C₂×D₄	—	4	1	no	—
315	C₂×D₄	—	4	1	no	—
316	C₂×D₄	—	4	1	no	—
317	C₂×D₄	—	4	1	no	—
318	C₂×D₄	—	4	1	no	—
319	C₂×D₄	—	4	1	no	—
320	C₂×D₄	—	4	1	no	—
321	C₂×D₄	—	8	1	no	—
322	C₂×D₄	—	8	1	no	—
323	C₂×D₄	C₅×C₂²⋊C₄	1	2	yes	—
324	C₂²×C₄	—	2	1	no	—
325	C₂²×C₄	—	2	2	no	—
326	C₂²×C₄	—	2	2	no	—
327	C₂²×C₄	—	4	1	no	—
328	C₂²×C₄	—	4	1	no	—
329	C₂²×C₄	—	4	1	no	—
330	C₂²×C₄	—	4	1	no	—
331	C₂²×C₄	—	4	1	no	—
332	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
333	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
334	C₂²×C₄	C₅×#41	1	1	yes	characteristic
335	D₈	—	4	8	no	—
336	M₁₆	—	4	8	no	—
337	C₂×C₈	—	2	1	no	—
338	C₂×C₈	—	2	1	no	—
339	C₂×C₈	—	2	2	no	—
340	C₂×C₈	—	2	1	no	—
341	C₂×C₈	—	2	2	no	—
342	C₂×C₈	—	2	1	no	—
343	C₂×C₈	—	2	1	no	—
344	C₂×C₈	—	4	1	no	—
345	C₂×C₈	—	4	1	no	—
346	C₂×C₈	—	4	1	no	—
347	C₂×C₈	—	4	1	no	—
348	C₂×C₈	—	4	1	no	—
349	C₂×C₈	—	4	1	no	—
350	C₂×C₈	—	4	1	no	—
351	C₂×C₈	C₅×D₈	1	2	yes	complemented
352	C₄⋊C₄	—	2	1	no	—
353	C₄⋊C₄	—	4	1	no	—
354	C₄⋊C₄	—	4	1	no	—
355	C₄⋊C₄	—	4	1	no	—
356	C₄⋊C₄	—	4	1	no	—
357	C₄⋊C₄	—	8	1	no	—
358	C₄⋊C₄	C₅×C₂²⋊C₄	1	2	yes	—
359	C₂²⋊C₄	—	2	2	no	—
360	C₂²⋊C₄	—	2	2	no	—
361	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
362	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
363	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
364	C₄²	C₅×#41	1	1	yes	characteristic
365	C₂×C₅	—	8	2	no	—
366	C₂×C₅	—	16	2	no	—
367	C₂×C₅	#1685	1	1	yes	characteristic
368	C₂×C₅	#1687	1	1	yes	characteristic
369	C₂×C₅	#1697	1	1	yes	characteristic
370	C₂×C₅	#1701	1	1	yes	characteristic
371	C₂×C₅	#1879	1	1	yes	characteristic
372	C₂×C₅	#1895	1	1	yes	characteristic
373	C₂×C₅	#1907	1	1	yes	characteristic
374	C₂³	—	2	2	no	—
375	C₂³	—	4	1	no	—
376	C₂³	—	4	1	no	—
377	C₂³	—	4	1	no	—
378	C₂³	—	4	1	no	—
379	C₂³	—	4	1	no	—
380	C₂³	—	4	1	no	—
381	C₂³	—	4	2	no	—
382	C₂³	—	8	1	no	—
383	C₂³	—	8	1	no	—
384	C₂³	—	8	1	no	—
385	C₂³	—	8	1	no	—
386	C₂³	—	8	1	no	—
387	C₂³	—	8	1	no	—
388	C₂³	C₅×#121	1	1	yes	characteristic
389	D₄	—	2	2	no	—
390	D₄	—	2	2	no	—
391	D₄	—	4	2	no	—
392	D₄	—	4	2	no	—
393	D₄	—	4	2	no	—
394	D₄	—	4	2	no	—
395	D₄	—	4	1	no	—
396	D₄	—	4	1	no	—
397	D₄	—	8	2	no	—
398	D₄	—	8	2	no	—
399	D₄	—	8	1	no	—
400	D₄	—	8	1	no	—
401	D₄	—	8	1	no	—
402	D₄	—	8	1	no	—
403	C₂×C₄	—	2	1	no	—
404	C₂×C₄	—	2	1	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	4	1	no	—
407	C₂×C₄	—	4	1	no	—
408	C₂×C₄	—	4	2	no	—
409	C₂×C₄	—	4	2	no	—
410	C₂×C₄	—	4	2	no	—
411	C₂×C₄	—	4	2	no	—
412	C₂×C₄	—	8	1	no	—
413	C₂×C₄	—	8	1	no	—
414	C₂×C₄	—	8	1	no	—
415	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
416	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
417	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
418	C₂×C₄	C₅×#120	1	1	yes	characteristic
419	C₂×C₄	C₅×#121	1	1	yes	characteristic
420	C₂×C₄	C₅×#123	1	1	yes	characteristic
421	C₂×C₄	C₂×C₅×D₈	1	1	yes	characteristic
422	C₂×C₄	C₅×#135	1	1	yes	characteristic
423	C₂×C₄	C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
424	C₂×C₄	C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
425	C₂×C₄	C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
426	C₂×C₄	C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
427	C₂×C₄	C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
428	C₂×C₄	C₅×#137	1	1	yes	characteristic
429	C₈	—	2	2	no	—
430	C₈	—	4	2	no	—
431	C₈	—	4	2	no	—
432	C₈	—	4	1	no	—
433	C₈	—	8	1	no	—
434	C₅	#9229	1	1	yes	characteristic, direct product factor, Sylow
435	C₂²	—	4	2	no	—
436	C₂²	—	4	2	no	—
437	C₂²	—	4	2	no	—
438	C₂²	—	8	1	no	—
439	C₂²	—	8	1	no	—
440	C₂²	—	8	1	no	—
441	C₂²	—	8	1	no	—
442	C₂²	—	8	2	no	—
443	C₂²	—	8	2	no	—
444	C₂²	—	8	2	no	—
445	C₂²	—	16	1	no	—
446	C₂²	—	16	1	no	—
447	C₂²	—	16	1	no	—
448	C₂²	—	16	1	no	—
449	C₂²	C₅×#386	1	1	yes	characteristic
450	C₂²	C₅×#459	1	1	yes	characteristic
451	C₂²	C₅×#463	1	1	yes	characteristic
452	C₂²	C₅×#468	1	1	yes	characteristic
453	C₂²	C₅×#469	1	1	yes	characteristic
454	C₂²	C₅×#471	1	1	yes	characteristic
455	C₂²	C₅×#472	1	1	yes	characteristic
456	C₄	—	2	1	no	—
457	C₄	—	2	1	no	—
458	C₄	—	4	2	no	—
459	C₄	—	16	1	no	—
460	C₄	C₅×#417	1	1	yes	characteristic
461	C₄	C₅×#418	1	1	yes	characteristic
462	C₄	C₄×C₅×D₈	1	1	yes	characteristic
463	C₄	C₅×#442	1	1	yes	characteristic
464	C₄	C₅×#447	1	1	yes	characteristic
465	C₄	C₅×#449	1	1	yes	characteristic
466	C₄	C₅×#468	1	1	yes	characteristic
467	C₄	C₅×#469	1	1	yes	characteristic
468	C₂	—	8	2	no	—
469	C₂	—	16	2	no	—
470	C₂	C₅×#1685	1	1	yes	characteristic
471	C₂	C₅×#1687	1	1	yes	characteristic
472	C₂	C₅×#1697	1	1	yes	characteristic
473	C₂	C₅×#1701	1	1	yes	characteristic
474	C₂	C₅×#1879	1	1	yes	characteristic
475	C₂	C₅×#1895	1	1	yes	characteristic
476	C₂	C₅×#1907	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅	#121
commutator	C₄²	C₂²×C₄×C₅
Frattini, cosocle	C₂×C₄²	C₂³×C₅
prime radical	C₂×C₅×#459	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₅ ◁ C₂×C₄²×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₅×#436	C₂	semidirect
3. C₅×#1957	C₂	semidirect
4. C₅×#1802	C₂	semidirect
5. C₂×C₅×#331	C₂	semidirect
6. C₅×#1296	C₂	semidirect
7. C₅×#1277	C₂	semidirect
13. C₅×#459	C₄	semidirect
28. #9229	C₅	direct (N × H)
73. C₂×#436	C₂×C₅	semidirect
74. #1957	C₂×C₅	semidirect
75. #1802	C₂×C₅	semidirect
76. C₂×#331	C₂×C₅	semidirect
77. #1296	C₂×C₅	semidirect
78. #1277	C₂×C₅	semidirect
130. C₂×C₅×C₈	D₈	semidirect
149. #459	C₄×C₅	semidirect
351. C₂×C₈	C₅×D₈	semidirect
434. C₅	#9229	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₅×#459	2
C₂×C₅×#436	2
C₅×#1957	2
C₅×#1802	2
C₂×C₅×#331	2
C₅×#1296	2
C₅×#1277	2
#9229	5

Subgroups — C5×#9229 #11931949

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#9229 #11931949