Subgroups — C₅×#33526 #11956246

Order 1280.

1150 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#576	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅×#509	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×#508	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#3061	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#2189	C₂	1	2	yes	maximal, complemented
6	C₅×#2187	C₂	1	2	yes	maximal, complemented
7	C₅×#2186	C₂	1	2	yes	maximal, complemented
8	C₅×#2184	C₂	1	2	yes	maximal, complemented
9	C₅×#2139	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₅×#357	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#2113	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₅×H(5,𝔽₂)	—	2	1	no	—
13	C₅×#576	—	2	4	no	—
14	C₅×#576	—	2	4	no	—
15	C₂×C₅×AGL(1,ℤ/8)	—	2	1	no	—
16	C₂×C₅×AGL(1,ℤ/8)	—	2	2	no	—
17	C₂×C₅×#135	C₂²	1	2	yes	—
18	C₂×C₅×#135	C₂²	1	1	yes	characteristic
19	C₂×C₅×#135	C₂²	1	1	yes	characteristic, complemented
20	C₂²×C₅×D₈	C₂²	1	2	yes	—
21	C₂²×C₅×D₈	C₂²	1	1	yes	characteristic
22	C₂×C₅×#131	C₂²	1	1	yes	characteristic
23	C₅×#537	—	2	1	no	—
24	C₅×#509	—	2	4	no	—
25	C₅×#508	—	2	4	no	—
26	C₂×C₅×Q₃₂	C₂²	1	1	yes	characteristic, complemented
27	C₂×C₅×SD₃₂	C₂²	1	1	yes	characteristic, complemented
28	C₂×C₅×SD₃₂	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₅×SD₃₂	C₂²	1	2	yes	complemented
30	C₂×C₅×D₁₆	C₂²	1	1	yes	characteristic, complemented
31	C₂×C₅×D₁₆	C₂²	1	2	yes	complemented
32	C₂×C₅×M₃₂	C₂²	1	1	yes	characteristic, complemented
33	C₂²×C₅×C₁₆	C₂²	1	1	yes	characteristic, complemented
34	C₅×#468	—	2	2	no	—
35	C₅×#467	C₂²	1	2	yes	complemented
36	C₅×#466	C₂²	1	2	yes	complemented
37	C₂×C₅×#107	C₂²	1	1	yes	characteristic, complemented
38	C₅×#417	—	2	1	no	—
39	C₅×#358	C₂²	1	2	yes	complemented
40	C₅×#357	C₂²	1	2	yes	complemented
41	C₅×#357	C₂²	1	2	yes	complemented
42	C₅×#357	C₂²	1	2	yes	complemented
43	C₅×C₂²⋊C₁₆	C₂²	1	2	yes	complemented
44	C₅×C₂²⋊C₁₆	C₂²	1	2	yes	complemented
45	#33526	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
46	C₅×H(5,𝔽₂)	—	2	8	no	—
47	C₅×H(5,𝔽₂)	—	4	4	no	—
48	C₂×C₅×#41	—	2	2	no	—
49	C₂×C₅×#41	—	2	1	no	—
50	C₂×C₅×#41	—	2	1	no	—
51	C₂×C₅×#41	—	4	1	no	—
52	C₂×C₅×#41	D₄	1	1	yes	characteristic
53	C₂²×C₅×D₄	—	2	2	no	—
54	C₂²×C₅×D₄	—	2	1	no	—
55	C₂²×C₅×D₄	—	4	2	no	—
56	C₂²×C₅×D₄	—	4	1	no	—
57	C₅×AGL(1,ℤ/8)	—	2	8	no	—
58	C₅×AGL(1,ℤ/8)	—	2	16	no	—
59	C₅×#135	—	2	4	no	—
60	C₅×#135	—	2	4	no	—
61	C₅×#135	—	2	2	no	—
62	C₅×#135	—	2	2	no	—
63	C₅×#135	—	2	2	no	—
64	C₅×#135	D₄	1	4	yes	complemented
65	C₂×C₅×Q₁₆	C₂³	1	1	yes	characteristic
66	C₂×C₅×Q₁₆	C₂³	1	1	yes	characteristic
67	C₂×C₅×SD₁₆	—	2	2	no	—
68	C₂×C₅×SD₁₆	—	2	1	no	—
69	C₂×C₅×SD₁₆	—	2	1	no	—
70	C₂×C₅×D₈	—	2	4	no	—
71	C₂×C₅×D₈	—	2	4	no	—
72	C₂×C₅×D₈	—	2	2	no	—
73	C₂×C₅×D₈	—	2	1	no	—
74	C₂×C₅×D₈	—	2	2	no	—
75	C₂×C₅×D₈	D₄	1	4	yes	complemented
76	C₂×C₅×D₈	C₂³	1	1	yes	characteristic
77	C₂×C₅×D₈	C₂³	1	1	yes	characteristic
78	C₂×C₅×D₈	C₂³	1	2	yes	—
79	C₅×#131	—	2	2	no	—
80	C₅×#131	—	2	2	no	—
81	C₂×C₅×M₁₆	D₄	1	1	yes	characteristic
82	C₂×C₅×M₁₆	D₄	1	2	yes	—
83	C₂²×C₅×C₈	C₂³	1	2	yes	—
84	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
85	C₅×C₂²⋊Q₈	—	2	2	no	—
86	C₅×C₂²⋊Q₈	—	4	1	no	—
87	C₅×#121	—	2	2	no	—
88	C₅×#121	—	4	1	no	—
89	C₅×#121	—	4	2	no	—
90	C₂×C₅×C₄⋊C₄	—	2	1	no	—
91	C₅×Q₃₂	—	2	2	no	—
92	C₅×SD₃₂	—	2	2	no	—
93	C₅×SD₃₂	—	2	2	no	—
94	C₅×SD₃₂	—	2	4	no	—
95	C₅×D₁₆	—	2	2	no	—
96	C₅×D₁₆	—	2	4	no	—
97	C₅×M₃₂	—	2	2	no	—
98	C₂×C₅×C₁₆	—	2	2	no	—
99	C₂×C₅×C₁₆	C₂³	1	1	yes	characteristic
100	C₂×C₅×C₁₆	C₂³	1	1	yes	characteristic
101	C₂×C₅×C₁₆	C₂³	1	2	yes	—
102	C₅×#107	—	2	1	no	—
103	C₅×#107	C₂³	1	2	yes	—
104	C₅×#103	—	2	2	no	—
105	C₅×#102	—	2	2	no	—
106	C₂×#576	C₂×C₅	1	1	yes	characteristic, complemented
107	C₂×#509	C₂×C₅	1	1	yes	characteristic, complemented
108	C₂×#508	C₂×C₅	1	1	yes	characteristic, complemented
109	#3061	C₂×C₅	1	1	yes	characteristic, complemented
110	#2189	C₂×C₅	1	2	yes	complemented
111	#2187	C₂×C₅	1	2	yes	complemented
112	#2186	C₂×C₅	1	2	yes	complemented
113	#2184	C₂×C₅	1	2	yes	complemented
114	#2139	C₂×C₅	1	1	yes	characteristic, complemented
115	C₂×#357	C₂×C₅	1	1	yes	characteristic, complemented
116	#2113	C₂×C₅	1	1	yes	characteristic, complemented
117	C₂⁴×C₅	—	4	2	no	—
118	C₂⁴×C₅	—	4	1	no	—
119	C₅×#41	—	2	2	no	—
120	C₅×#41	—	2	2	no	—
121	C₅×#41	—	2	8	no	—
122	C₅×#41	—	2	4	no	—
123	C₅×#41	—	4	4	no	—
124	C₅×#41	—	4	8	no	—
125	C₅×#41	—	4	2	no	—
126	C₅×#41	—	4	2	no	—
127	C₅×#41	—	4	2	no	—
128	C₂×C₅×Q₈	—	2	1	no	—
129	C₂×C₅×Q₈	—	2	1	no	—
130	C₂×C₅×Q₈	D₈	1	1	yes	characteristic
131	C₂×C₅×D₄	—	2	8	no	—
132	C₂×C₅×D₄	—	2	4	no	—
133	C₂×C₅×D₄	—	2	1	no	—
134	C₂×C₅×D₄	—	2	2	no	—
135	C₂×C₅×D₄	—	2	1	no	—
136	C₂×C₅×D₄	—	4	4	no	—
137	C₂×C₅×D₄	—	4	16	no	—
138	C₂×C₅×D₄	—	4	8	no	—
139	C₂×C₅×D₄	—	4	2	no	—
140	C₂×C₅×D₄	—	4	1	no	—
141	C₂×C₅×D₄	—	4	1	no	—
142	C₂×C₅×D₄	—	4	2	no	—
143	C₂×C₅×D₄	—	4	2	no	—
144	C₂×C₅×D₄	—	4	1	no	—
145	C₂×C₅×D₄	—	4	2	no	—
146	C₂×C₅×D₄	D₈	1	2	yes	—
147	C₂×C₅×D₄	D₈	1	1	yes	characteristic
148	C₂²×C₄×C₅	—	4	2	no	—
149	C₂²×C₄×C₅	—	4	1	no	—
150	C₂²×C₄×C₅	—	4	1	no	—
151	C₂²×C₄×C₅	—	4	1	no	—
152	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
153	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
154	C₅×Q₁₆	—	2	1	no	—
155	C₅×Q₁₆	—	2	1	no	—
156	C₅×Q₁₆	—	2	1	no	—
157	C₅×Q₁₆	C₂×D₄	1	2	yes	—
158	C₅×SD₁₆	—	2	8	no	—
159	C₅×SD₁₆	—	2	4	no	—
160	C₅×SD₁₆	—	4	2	no	—
161	C₅×D₈	—	2	8	no	—
162	C₅×D₈	—	2	4	no	—
163	C₅×D₈	—	2	2	no	—
164	C₅×D₈	—	2	1	no	—
165	C₅×D₈	—	2	1	no	—
166	C₅×D₈	—	2	1	no	—
167	C₅×D₈	C₂×D₄	1	2	yes	—
168	C₅×D₈	C₂×D₄	1	4	yes	—
169	C₅×M₁₆	—	2	2	no	—
170	C₅×M₁₆	—	2	4	no	—
171	C₂×C₅×C₈	—	2	2	no	—
172	C₂×C₅×C₈	—	2	2	no	—
173	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
174	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
175	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
176	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
177	C₂×C₅×C₈	C₂⁴	1	1	yes	characteristic
178	C₅×C₄⋊C₄	—	2	2	no	—
179	C₅×C₄⋊C₄	—	4	1	no	—
180	C₅×C₄⋊C₄	—	4	2	no	—
181	C₅×C₂²⋊C₄	—	4	2	no	—
182	C₅×C₂²⋊C₄	—	4	2	no	—
183	C₅×C₁₆	—	2	1	no	—
184	C₅×C₁₆	—	2	1	no	—
185	C₅×C₁₆	—	2	2	no	—
186	C₂×H(5,𝔽₂)	—	2	1	no	—
187	#576	—	2	4	no	—
188	#576	—	2	4	no	—
189	C₂×AGL(1,ℤ/8)	—	2	1	no	—
190	C₂×AGL(1,ℤ/8)	—	2	2	no	—
191	C₂×#135	C₂²×C₅	1	2	yes	—
192	C₂×#135	C₂²×C₅	1	1	yes	characteristic
193	C₂×#135	C₂²×C₅	1	1	yes	characteristic, complemented
194	C₂²×D₈	C₂²×C₅	1	2	yes	—
195	C₂²×D₈	C₂²×C₅	1	1	yes	characteristic
196	C₂×#131	C₂²×C₅	1	1	yes	characteristic
197	#537	—	2	1	no	—
198	#509	—	2	4	no	—
199	#508	—	2	4	no	—
200	C₂×Q₃₂	C₂²×C₅	1	1	yes	characteristic, complemented
201	C₂×SD₃₂	C₂²×C₅	1	1	yes	characteristic, complemented
202	C₂×SD₃₂	C₂²×C₅	1	1	yes	characteristic, complemented
203	C₂×SD₃₂	C₂²×C₅	1	2	yes	complemented
204	C₂×D₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
205	C₂×D₁₆	C₂²×C₅	1	2	yes	complemented
206	C₂×M₃₂	C₂²×C₅	1	1	yes	characteristic, complemented
207	C₂²×C₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
208	#468	—	2	2	no	—
209	#467	C₂²×C₅	1	2	yes	complemented
210	#466	C₂²×C₅	1	2	yes	complemented
211	C₂×#107	C₂²×C₅	1	1	yes	characteristic, complemented
212	#417	—	2	1	no	—
213	#358	C₂²×C₅	1	2	yes	complemented
214	#357	C₂²×C₅	1	2	yes	complemented
215	#357	C₂²×C₅	1	2	yes	complemented
216	#357	C₂²×C₅	1	2	yes	complemented
217	C₂²⋊C₁₆	C₂²×C₅	1	2	yes	complemented
218	C₂²⋊C₁₆	C₂²×C₅	1	2	yes	complemented
219	C₂³×C₅	—	4	8	no	—
220	C₂³×C₅	—	4	2	no	—
221	C₂³×C₅	—	4	1	no	—
222	C₂³×C₅	—	4	4	no	—
223	C₂³×C₅	—	4	1	no	—
224	C₂³×C₅	—	16	1	no	—
225	C₂³×C₅	—	16	1	no	—
226	C₂³×C₅	—	16	2	no	—
227	C₂³×C₅	—	16	2	no	—
228	C₂³×C₅	C₂×D₈	1	2	yes	—
229	C₂³×C₅	C₂×D₈	1	1	yes	characteristic
230	C₅×Q₈	—	2	2	no	—
231	C₅×Q₈	—	2	2	no	—
232	C₅×Q₈	—	4	1	no	—
233	C₅×Q₈	—	4	1	no	—
234	C₅×Q₈	—	4	1	no	—
235	C₅×D₄	—	2	4	no	—
236	C₅×D₄	—	2	2	no	—
237	C₅×D₄	—	2	4	no	—
238	C₅×D₄	—	2	2	no	—
239	C₅×D₄	—	4	8	no	—
240	C₅×D₄	—	4	8	no	—
241	C₅×D₄	—	4	4	no	—
242	C₅×D₄	—	4	1	no	—
243	C₅×D₄	—	4	1	no	—
244	C₅×D₄	—	4	2	no	—
245	C₅×D₄	—	4	1	no	—
246	C₅×D₄	—	4	4	no	—
247	C₅×D₄	—	8	2	no	—
248	C₅×D₄	—	16	2	no	—
249	C₂×C₄×C₅	—	2	2	no	—
250	C₂×C₄×C₅	—	2	2	no	—
251	C₂×C₄×C₅	—	4	8	no	—
252	C₂×C₄×C₅	—	4	1	no	—
253	C₂×C₄×C₅	—	4	4	no	—
254	C₂×C₄×C₅	—	4	2	no	—
255	C₂×C₄×C₅	—	4	1	no	—
256	C₂×C₄×C₅	—	8	2	no	—
257	C₂×C₄×C₅	—	16	1	no	—
258	C₂×C₄×C₅	#120	1	2	yes	—
259	C₂×C₄×C₅	C₂×D₈	1	2	yes	—
260	C₂×C₄×C₅	C₂×D₈	1	1	yes	characteristic
261	C₂×C₄×C₅	AGL(1,ℤ/8)	1	2	yes	—
262	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
263	C₅×C₈	—	2	2	no	—
264	C₅×C₈	#120	1	2	yes	—
265	C₅×C₈	C₂²×D₄	1	1	yes	characteristic
266	C₅×C₈	C₂²×D₄	1	1	yes	characteristic
267	H(5,𝔽₂)	—	2	8	no	—
268	H(5,𝔽₂)	—	4	4	no	—
269	C₂×#41	—	2	2	no	—
270	C₂×#41	—	2	1	no	—
271	C₂×#41	—	2	1	no	—
272	C₂×#41	—	4	1	no	—
273	C₂×#41	C₅×D₄	1	1	yes	characteristic
274	C₂²×D₄	—	2	2	no	—
275	C₂²×D₄	—	2	1	no	—
276	C₂²×D₄	—	4	2	no	—
277	C₂²×D₄	—	4	1	no	—
278	AGL(1,ℤ/8)	—	2	8	no	—
279	AGL(1,ℤ/8)	—	2	16	no	—
280	#135	—	2	4	no	—
281	#135	—	2	4	no	—
282	#135	—	2	2	no	—
283	#135	—	2	2	no	—
284	#135	—	2	2	no	—
285	#135	C₅×D₄	1	4	yes	complemented
286	C₂×Q₁₆	C₂³×C₅	1	1	yes	characteristic
287	C₂×Q₁₆	C₂³×C₅	1	1	yes	characteristic
288	C₂×SD₁₆	—	2	2	no	—
289	C₂×SD₁₆	—	2	1	no	—
290	C₂×SD₁₆	—	2	1	no	—
291	C₂×D₈	—	2	4	no	—
292	C₂×D₈	—	2	4	no	—
293	C₂×D₈	—	2	2	no	—
294	C₂×D₈	—	2	1	no	—
295	C₂×D₈	—	2	2	no	—
296	C₂×D₈	C₅×D₄	1	4	yes	complemented
297	C₂×D₈	C₂³×C₅	1	1	yes	characteristic
298	C₂×D₈	C₂³×C₅	1	1	yes	characteristic
299	C₂×D₈	C₂³×C₅	1	2	yes	—
300	#131	—	2	2	no	—
301	#131	—	2	2	no	—
302	C₂×M₁₆	C₅×D₄	1	1	yes	characteristic
303	C₂×M₁₆	C₅×D₄	1	2	yes	—
304	C₂²×C₈	C₂³×C₅	1	2	yes	—
305	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
306	C₂²⋊Q₈	—	2	2	no	—
307	C₂²⋊Q₈	—	4	1	no	—
308	#121	—	2	2	no	—
309	#121	—	4	1	no	—
310	#121	—	4	2	no	—
311	C₂×C₄⋊C₄	—	2	1	no	—
312	Q₃₂	—	2	2	no	—
313	SD₃₂	—	2	2	no	—
314	SD₃₂	—	2	2	no	—
315	SD₃₂	—	2	4	no	—
316	D₁₆	—	2	2	no	—
317	D₁₆	—	2	4	no	—
318	M₃₂	—	2	2	no	—
319	C₂×C₁₆	—	2	2	no	—
320	C₂×C₁₆	C₂³×C₅	1	1	yes	characteristic
321	C₂×C₁₆	C₂³×C₅	1	1	yes	characteristic
322	C₂×C₁₆	C₂³×C₅	1	2	yes	—
323	#107	—	2	1	no	—
324	#107	C₂³×C₅	1	2	yes	—
325	#103	—	2	2	no	—
326	#102	—	2	2	no	—
327	C₂²×C₅	—	2	1	no	—
328	C₂²×C₅	—	2	1	no	—
329	C₂²×C₅	—	2	2	no	—
330	C₂²×C₅	—	2	2	no	—
331	C₂²×C₅	—	2	2	no	—
332	C₂²×C₅	—	4	4	no	—
333	C₂²×C₅	—	4	2	no	—
334	C₂²×C₅	—	8	2	no	—
335	C₂²×C₅	—	8	1	no	—
336	C₂²×C₅	—	8	2	no	—
337	C₂²×C₅	—	8	1	no	—
338	C₂²×C₅	—	8	1	no	—
339	C₂²×C₅	—	8	1	no	—
340	C₂²×C₅	—	8	1	no	—
341	C₂²×C₅	—	16	4	no	—
342	C₂²×C₅	—	16	8	no	—
343	C₂²×C₅	#447	1	2	yes	—
344	C₂²×C₅	C₂²×D₈	1	1	yes	characteristic
345	C₄×C₅	—	2	2	no	—
346	C₄×C₅	—	4	2	no	—
347	C₄×C₅	—	8	2	no	—
348	C₄×C₅	—	8	1	no	—
349	C₄×C₅	#447	1	2	yes	—
350	C₄×C₅	C₂×#120	1	1	yes	characteristic
351	C₄×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
352	C₂⁴	—	4	2	no	—
353	C₂⁴	—	4	1	no	—
354	#41	—	2	2	no	—
355	#41	—	2	2	no	—
356	#41	—	2	8	no	—
357	#41	—	2	4	no	—
358	#41	—	4	4	no	—
359	#41	—	4	8	no	—
360	#41	—	4	2	no	—
361	#41	—	4	2	no	—
362	#41	—	4	2	no	—
363	C₂×Q₈	—	2	1	no	—
364	C₂×Q₈	—	2	1	no	—
365	C₂×Q₈	C₅×D₈	1	1	yes	characteristic
366	C₂×D₄	—	2	8	no	—
367	C₂×D₄	—	2	4	no	—
368	C₂×D₄	—	2	1	no	—
369	C₂×D₄	—	2	2	no	—
370	C₂×D₄	—	2	1	no	—
371	C₂×D₄	—	4	4	no	—
372	C₂×D₄	—	4	16	no	—
373	C₂×D₄	—	4	8	no	—
374	C₂×D₄	—	4	2	no	—
375	C₂×D₄	—	4	1	no	—
376	C₂×D₄	—	4	1	no	—
377	C₂×D₄	—	4	2	no	—
378	C₂×D₄	—	4	2	no	—
379	C₂×D₄	—	4	1	no	—
380	C₂×D₄	—	4	2	no	—
381	C₂×D₄	C₅×D₈	1	2	yes	—
382	C₂×D₄	C₅×D₈	1	1	yes	characteristic
383	C₂²×C₄	—	4	2	no	—
384	C₂²×C₄	—	4	1	no	—
385	C₂²×C₄	—	4	1	no	—
386	C₂²×C₄	—	4	1	no	—
387	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
388	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
389	Q₁₆	—	2	1	no	—
390	Q₁₆	—	2	1	no	—
391	Q₁₆	—	2	1	no	—
392	Q₁₆	C₂×C₅×D₄	1	2	yes	—
393	SD₁₆	—	2	8	no	—
394	SD₁₆	—	2	4	no	—
395	SD₁₆	—	4	2	no	—
396	D₈	—	2	8	no	—
397	D₈	—	2	4	no	—
398	D₈	—	2	2	no	—
399	D₈	—	2	1	no	—
400	D₈	—	2	1	no	—
401	D₈	—	2	1	no	—
402	D₈	C₂×C₅×D₄	1	2	yes	—
403	D₈	C₂×C₅×D₄	1	4	yes	—
404	M₁₆	—	2	2	no	—
405	M₁₆	—	2	4	no	—
406	C₂×C₈	—	2	2	no	—
407	C₂×C₈	—	2	2	no	—
408	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
409	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
410	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
411	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
412	C₂×C₈	C₂⁴×C₅	1	1	yes	characteristic
413	C₄⋊C₄	—	2	2	no	—
414	C₄⋊C₄	—	4	1	no	—
415	C₄⋊C₄	—	4	2	no	—
416	C₂²⋊C₄	—	4	2	no	—
417	C₂²⋊C₄	—	4	2	no	—
418	C₁₆	—	2	1	no	—
419	C₁₆	—	2	1	no	—
420	C₁₆	—	2	2	no	—
421	C₂×C₅	—	2	2	no	—
422	C₂×C₅	—	4	2	no	—
423	C₂×C₅	—	8	4	no	—
424	C₂×C₅	—	8	2	no	—
425	C₂×C₅	—	16	1	no	—
426	C₂×C₅	C₂×#447	1	1	yes	characteristic
427	C₂×C₅	#3415	1	1	yes	characteristic
428	C₂×C₅	#3416	1	1	yes	characteristic
429	C₂³	—	4	8	no	—
430	C₂³	—	4	2	no	—
431	C₂³	—	4	1	no	—
432	C₂³	—	4	4	no	—
433	C₂³	—	4	1	no	—
434	C₂³	—	16	1	no	—
435	C₂³	—	16	1	no	—
436	C₂³	—	16	2	no	—
437	C₂³	—	16	2	no	—
438	C₂³	C₂×C₅×D₈	1	2	yes	—
439	C₂³	C₂×C₅×D₈	1	1	yes	characteristic
440	Q₈	—	2	2	no	—
441	Q₈	—	2	2	no	—
442	Q₈	—	4	1	no	—
443	Q₈	—	4	1	no	—
444	Q₈	—	4	1	no	—
445	D₄	—	2	4	no	—
446	D₄	—	2	2	no	—
447	D₄	—	2	2	no	—
448	D₄	—	2	4	no	—
449	D₄	—	4	8	no	—
450	D₄	—	4	8	no	—
451	D₄	—	4	4	no	—
452	D₄	—	4	4	no	—
453	D₄	—	4	1	no	—
454	D₄	—	4	1	no	—
455	D₄	—	4	2	no	—
456	D₄	—	4	1	no	—
457	D₄	—	8	2	no	—
458	D₄	—	16	2	no	—
459	C₂×C₄	—	2	2	no	—
460	C₂×C₄	—	2	2	no	—
461	C₂×C₄	—	4	8	no	—
462	C₂×C₄	—	4	1	no	—
463	C₂×C₄	—	4	4	no	—
464	C₂×C₄	—	4	2	no	—
465	C₂×C₄	—	4	1	no	—
466	C₂×C₄	—	8	2	no	—
467	C₂×C₄	—	16	1	no	—
468	C₂×C₄	C₅×#120	1	2	yes	—
469	C₂×C₄	C₂×C₅×D₈	1	2	yes	—
470	C₂×C₄	C₂×C₅×D₈	1	1	yes	characteristic
471	C₂×C₄	C₅×AGL(1,ℤ/8)	1	2	yes	—
472	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
473	C₈	—	2	2	no	—
474	C₈	C₅×#120	1	2	yes	—
475	C₈	C₂²×C₅×D₄	1	1	yes	characteristic
476	C₈	C₂²×C₅×D₄	1	1	yes	characteristic
477	C₅	#33526	1	1	yes	characteristic, direct product factor, Sylow
478	C₂²	—	2	1	no	—
479	C₂²	—	2	1	no	—
480	C₂²	—	2	2	no	—
481	C₂²	—	2	2	no	—
482	C₂²	—	2	2	no	—
483	C₂²	—	4	4	no	—
484	C₂²	—	4	2	no	—
485	C₂²	—	8	2	no	—
486	C₂²	—	8	1	no	—
487	C₂²	—	8	2	no	—
488	C₂²	—	8	1	no	—
489	C₂²	—	8	1	no	—
490	C₂²	—	8	1	no	—
491	C₂²	—	8	1	no	—
492	C₂²	—	16	4	no	—
493	C₂²	—	16	8	no	—
494	C₂²	C₅×#447	1	2	yes	—
495	C₂²	C₂²×C₅×D₈	1	1	yes	characteristic
496	C₄	—	2	2	no	—
497	C₄	—	4	2	no	—
498	C₄	—	8	1	no	—
499	C₄	—	8	2	no	—
500	C₄	C₅×#447	1	2	yes	—
501	C₄	C₂×C₅×#120	1	1	yes	characteristic
502	C₄	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
503	C₂	—	2	2	no	—
504	C₂	—	4	2	no	—
505	C₂	—	8	4	no	—
506	C₂	—	8	2	no	—
507	C₂	—	16	1	no	—
508	C₂	C₂×C₅×#447	1	1	yes	characteristic
509	C₂	C₅×#3415	1	1	yes	characteristic
510	C₂	C₅×#3416	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₅
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅ ◁ C₂×C₅×#41 ◁ C₂×C₅×#131 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×#576	C₂	semidirect
2. C₂×C₅×#509	C₂	semidirect
3. C₂×C₅×#508	C₂	semidirect
4. C₅×#3061	C₂	semidirect
5. C₅×#2189	C₂	semidirect
6. C₅×#2187	C₂	semidirect
7. C₅×#2186	C₂	semidirect
8. C₅×#2184	C₂	semidirect
9. C₅×#2139	C₂	semidirect
10. C₂×C₅×#357	C₂	semidirect
11. C₅×#2113	C₂	semidirect
19. C₂×C₅×#135	C₂²	semidirect
26. C₂×C₅×Q₃₂	C₂²	semidirect
27. C₂×C₅×SD₃₂	C₂²	semidirect
28. C₂×C₅×SD₃₂	C₂²	semidirect
29. C₂×C₅×SD₃₂	C₂²	semidirect
30. C₂×C₅×D₁₆	C₂²	semidirect
31. C₂×C₅×D₁₆	C₂²	semidirect
32. C₂×C₅×M₃₂	C₂²	semidirect
33. C₂²×C₅×C₁₆	C₂²	semidirect
35. C₅×#467	C₂²	semidirect
36. C₅×#466	C₂²	semidirect
37. C₂×C₅×#107	C₂²	semidirect
39. C₅×#358	C₂²	semidirect
40. C₅×#357	C₂²	semidirect
41. C₅×#357	C₂²	semidirect
42. C₅×#357	C₂²	semidirect
43. C₅×C₂²⋊C₁₆	C₂²	semidirect
44. C₅×C₂²⋊C₁₆	C₂²	semidirect
45. #33526	C₅	direct (N × H)
64. C₅×#135	D₄	semidirect
75. C₂×C₅×D₈	D₄	semidirect
106. C₂×#576	C₂×C₅	semidirect
107. C₂×#509	C₂×C₅	semidirect
108. C₂×#508	C₂×C₅	semidirect
109. #3061	C₂×C₅	semidirect
110. #2189	C₂×C₅	semidirect
111. #2187	C₂×C₅	semidirect
112. #2186	C₂×C₅	semidirect
113. #2184	C₂×C₅	semidirect
114. #2139	C₂×C₅	semidirect
115. C₂×#357	C₂×C₅	semidirect
116. #2113	C₂×C₅	semidirect
193. C₂×#135	C₂²×C₅	semidirect
200. C₂×Q₃₂	C₂²×C₅	semidirect
201. C₂×SD₃₂	C₂²×C₅	semidirect
202. C₂×SD₃₂	C₂²×C₅	semidirect
203. C₂×SD₃₂	C₂²×C₅	semidirect
204. C₂×D₁₆	C₂²×C₅	semidirect
205. C₂×D₁₆	C₂²×C₅	semidirect
206. C₂×M₃₂	C₂²×C₅	semidirect
207. C₂²×C₁₆	C₂²×C₅	semidirect
209. #467	C₂²×C₅	semidirect
210. #466	C₂²×C₅	semidirect
211. C₂×#107	C₂²×C₅	semidirect
213. #358	C₂²×C₅	semidirect
214. #357	C₂²×C₅	semidirect
215. #357	C₂²×C₅	semidirect
216. #357	C₂²×C₅	semidirect
217. C₂²⋊C₁₆	C₂²×C₅	semidirect
218. C₂²⋊C₁₆	C₂²×C₅	semidirect
285. #135	C₅×D₄	semidirect
296. C₂×D₈	C₅×D₄	semidirect
477. C₅	#33526	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×#576	2
C₂×C₅×#509	2
C₂×C₅×#508	2
C₅×#3061	2
C₅×#2189	2
C₅×#2187	2
C₅×#2186	2
C₅×#2184	2
C₅×#2139	2
C₂×C₅×#357	2
C₅×#2113	2
#33526	5

Subgroups — C5×#33526 #11956246

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#33526 #11956246