Subgroups — C₅×#33790 #11956510

Order 1280.

606 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3175	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#3155	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#2250	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#2249	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#2243	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#2240	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#2211	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#2210	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#2207	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#2206	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#2189	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#2187	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#2186	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#2184	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#2164	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₅×AGL(1,ℤ/8)	—	2	1	no	—
17	C₂×C₅×#135	C₂²	1	1	yes	characteristic
18	C₂²×C₅×D₈	C₂²	1	1	yes	characteristic
19	C₅×#542	—	2	1	no	—
20	C₅×#535	—	2	1	no	—
21	C₂×C₅×Q₃₂	C₂²	1	1	yes	characteristic, complemented
22	C₂×C₅×SD₃₂	C₂²	1	1	yes	characteristic
23	C₂×C₅×SD₃₂	C₂²	1	1	yes	characteristic
24	C₂×C₅×SD₃₂	C₂²	1	1	yes	characteristic, complemented
25	C₂×C₅×SD₃₂	C₂²	1	1	yes	characteristic, complemented
26	C₂×C₅×D₁₆	C₂²	1	1	yes	characteristic
27	C₂×C₅×D₁₆	C₂²	1	1	yes	characteristic
28	C₂×C₅×D₁₆	C₂²	1	1	yes	characteristic, complemented
29	C₅×#500	C₂²	1	1	yes	characteristic, complemented
30	C₅×#496	—	2	1	no	—
31	C₅×#496	—	2	1	no	—
32	C₅×#495	C₂²	1	1	yes	characteristic
33	C₅×#495	C₂²	1	1	yes	characteristic
34	C₅×#495	C₂²	1	1	yes	characteristic, complemented
35	C₅×#493	C₂²	1	1	yes	characteristic
36	C₅×#493	C₂²	1	1	yes	characteristic
37	C₅×#489	—	2	1	no	—
38	C₅×#468	—	2	1	no	—
39	C₅×#467	C₂²	1	1	yes	characteristic
40	C₅×#466	C₂²	1	1	yes	characteristic
41	C₅×#440	—	2	1	no	—
42	C₄×C₅×Q₁₆	C₂²	1	1	yes	characteristic, complemented
43	C₄×C₅×D₈	C₂²	1	1	yes	characteristic, complemented
44	C₅×#405	C₂²	1	1	yes	characteristic
45	C₅×C₄⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
46	C₅×C₄⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
47	C₅×#358	C₂²	1	1	yes	characteristic, complemented
48	C₅×#358	C₂²	1	1	yes	characteristic, complemented
49	C₅×#357	C₂²	1	1	yes	characteristic
50	C₅×#357	C₂²	1	1	yes	characteristic
51	C₅×#357	C₂²	1	1	yes	characteristic
52	C₅×#357	C₂²	1	1	yes	characteristic
53	C₅×#357	C₂²	1	1	yes	characteristic, complemented
54	C₅×#357	C₂²	1	1	yes	characteristic, complemented
55	C₅×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
56	C₅×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
57	C₅×#346	C₂²	1	1	yes	characteristic, complemented
58	C₄×C₅×C₁₆	C₂²	1	1	yes	characteristic, complemented
59	#33790	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
60	C₂×C₅×#41	—	2	1	no	—
61	C₂²×C₅×D₄	—	2	1	no	—
62	C₅×AGL(1,ℤ/8)	—	4	4	no	—
63	C₅×#135	—	4	1	no	—
64	C₅×#135	—	4	1	no	—
65	C₂×C₅×Q₁₆	C₂³	1	1	yes	characteristic
66	C₂×C₅×Q₁₆	C₂³	1	1	yes	characteristic
67	C₂×C₅×SD₁₆	—	2	1	no	—
68	C₂×C₅×SD₁₆	—	2	1	no	—
69	C₂×C₅×SD₁₆	—	2	1	no	—
70	C₂×C₅×SD₁₆	—	2	1	no	—
71	C₂×C₅×D₈	—	2	1	no	—
72	C₂×C₅×D₈	—	2	1	no	—
73	C₂×C₅×D₈	—	2	1	no	—
74	C₂×C₅×D₈	—	4	1	no	—
75	C₂×C₅×D₈	—	4	1	no	—
76	C₂×C₅×D₈	C₂³	1	1	yes	characteristic
77	C₂×C₅×D₈	C₂³	1	1	yes	characteristic
78	C₂×C₅×D₈	C₂³	1	1	yes	characteristic
79	C₂×C₅×D₈	C₂³	1	1	yes	characteristic
80	C₂×C₅×M₁₆	D₄	1	1	yes	characteristic
81	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
82	C₅×C₄⋊Q₈	—	2	1	no	—
83	C₅×#127	—	2	1	no	—
84	C₅×#127	—	2	1	no	—
85	C₅×#126	—	4	1	no	—
86	C₅×#124	—	2	1	no	—
87	C₅×#124	—	2	1	no	—
88	C₅×#124	—	2	1	no	—
89	C₅×#124	—	4	1	no	—
90	C₅×#123	—	4	1	no	—
91	C₅×C₂²⋊Q₈	—	2	1	no	—
92	C₅×C₂²⋊Q₈	—	4	1	no	—
93	C₅×#121	—	2	1	no	—
94	C₅×#121	—	4	1	no	—
95	C₅×#121	—	4	1	no	—
96	C₅×#120	—	4	1	no	—
97	C₅×#120	—	4	1	no	—
98	C₄×C₅×Q₈	—	2	1	no	—
99	C₄×C₅×D₄	—	2	1	no	—
100	C₅×#117	D₄	1	1	yes	characteristic
101	C₅×Q₃₂	—	4	1	no	—
102	C₅×SD₃₂	—	4	1	no	—
103	C₅×SD₃₂	—	4	1	no	—
104	C₅×SD₃₂	—	4	1	no	—
105	C₅×SD₃₂	—	4	1	no	—
106	C₅×D₁₆	—	4	1	no	—
107	C₅×D₁₆	—	4	1	no	—
108	C₅×D₁₆	—	4	1	no	—
109	C₂×C₅×C₁₆	C₂³	1	1	yes	characteristic
110	C₂×C₅×C₁₆	C₂³	1	1	yes	characteristic
111	C₂×C₅×C₁₆	C₂³	1	1	yes	characteristic
112	C₂×C₅×C₁₆	C₂³	1	1	yes	characteristic
113	C₅×#107	—	2	1	no	—
114	C₅×#107	C₂³	1	1	yes	characteristic
115	C₅×#107	C₂³	1	1	yes	characteristic
116	C₅×#103	—	2	1	no	—
117	C₅×#103	—	2	1	no	—
118	C₅×#102	—	2	1	no	—
119	C₅×#102	—	2	1	no	—
120	C₅×#97	D₄	1	1	yes	characteristic
121	C₅×#97	D₄	1	1	yes	characteristic
122	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
123	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
124	#3175	C₂×C₅	1	1	yes	characteristic, complemented
125	#3155	C₂×C₅	1	1	yes	characteristic, complemented
126	#2250	C₂×C₅	1	1	yes	characteristic, complemented
127	#2249	C₂×C₅	1	1	yes	characteristic, complemented
128	#2243	C₂×C₅	1	1	yes	characteristic, complemented
129	#2240	C₂×C₅	1	1	yes	characteristic, complemented
130	#2211	C₂×C₅	1	1	yes	characteristic, complemented
131	#2210	C₂×C₅	1	1	yes	characteristic, complemented
132	#2207	C₂×C₅	1	1	yes	characteristic, complemented
133	#2206	C₂×C₅	1	1	yes	characteristic, complemented
134	#2189	C₂×C₅	1	1	yes	characteristic, complemented
135	#2187	C₂×C₅	1	1	yes	characteristic, complemented
136	#2186	C₂×C₅	1	1	yes	characteristic, complemented
137	#2184	C₂×C₅	1	1	yes	characteristic, complemented
138	#2164	C₂×C₅	1	1	yes	characteristic, complemented
139	C₂⁴×C₅	—	4	1	no	—
140	C₅×#41	—	4	2	no	—
141	C₅×#41	—	4	2	no	—
142	C₂×C₅×Q₈	—	2	1	no	—
143	C₂×C₅×Q₈	—	2	1	no	—
144	C₂×C₅×Q₈	—	4	1	no	—
145	C₂×C₅×D₄	—	2	1	no	—
146	C₂×C₅×D₄	—	2	1	no	—
147	C₂×C₅×D₄	—	2	1	no	—
148	C₂×C₅×D₄	—	2	1	no	—
149	C₂×C₅×D₄	—	4	2	no	—
150	C₂×C₅×D₄	—	4	2	no	—
151	C₂×C₅×D₄	—	4	1	no	—
152	C₂×C₅×D₄	—	4	1	no	—
153	C₂×C₅×D₄	—	4	1	no	—
154	C₂×C₅×D₄	—	4	1	no	—
155	C₂×C₅×D₄	—	4	1	no	—
156	C₂×C₅×D₄	—	4	1	no	—
157	C₂×C₅×D₄	—	4	1	no	—
158	C₂²×C₄×C₅	—	4	1	no	—
159	C₂²×C₄×C₅	—	4	1	no	—
160	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
161	C₅×Q₁₆	—	2	1	no	—
162	C₅×Q₁₆	—	2	1	no	—
163	C₅×Q₁₆	—	2	1	no	—
164	C₅×Q₁₆	—	2	1	no	—
165	C₅×SD₁₆	—	4	2	no	—
166	C₅×SD₁₆	—	4	2	no	—
167	C₅×SD₁₆	—	4	2	no	—
168	C₅×SD₁₆	—	4	2	no	—
169	C₅×D₈	—	2	1	no	—
170	C₅×D₈	—	2	1	no	—
171	C₅×D₈	—	2	1	no	—
172	C₅×D₈	—	2	1	no	—
173	C₅×D₈	—	2	1	no	—
174	C₅×D₈	—	2	1	no	—
175	C₅×D₈	—	2	1	no	—
176	C₅×D₈	—	2	1	no	—
177	C₅×D₈	—	4	2	no	—
178	C₅×D₈	—	4	2	no	—
179	C₅×D₈	—	4	2	no	—
180	C₅×M₁₆	—	2	2	no	—
181	C₂×C₅×C₈	—	2	1	no	—
182	C₂×C₅×C₈	—	2	1	no	—
183	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
184	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
185	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
186	C₂×C₅×C₈	C₂⁴	1	1	yes	characteristic
187	C₅×C₄⋊C₄	—	2	1	no	—
188	C₅×C₄⋊C₄	—	2	1	no	—
189	C₅×C₄⋊C₄	—	4	1	no	—
190	C₅×C₄⋊C₄	—	4	1	no	—
191	C₅×C₄⋊C₄	—	4	1	no	—
192	C₅×C₄⋊C₄	D₈	1	1	yes	characteristic
193	C₅×C₄⋊C₄	D₈	1	1	yes	characteristic
194	C₅×C₂²⋊C₄	—	4	1	no	—
195	C₅×C₂²⋊C₄	—	4	1	no	—
196	C₅×C₂²⋊C₄	—	4	1	no	—
197	C₅×C₂²⋊C₄	—	4	1	no	—
198	C₅×C₂²⋊C₄	—	4	1	no	—
199	C₅×C₂²⋊C₄	—	4	1	no	—
200	C₅×C₂²⋊C₄	—	4	1	no	—
201	C₅×C₂²⋊C₄	—	4	1	no	—
202	C₅×C₂²⋊C₄	—	4	1	no	—
203	C₅×C₂²⋊C₄	D₈	1	1	yes	characteristic
204	C₅×C₂²⋊C₄	D₈	1	1	yes	characteristic
205	C₄²×C₅	—	4	1	no	—
206	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
207	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
208	C₅×C₁₆	—	2	1	no	—
209	C₅×C₁₆	—	2	1	no	—
210	C₅×C₁₆	—	2	1	no	—
211	C₅×C₁₆	—	2	1	no	—
212	C₂×AGL(1,ℤ/8)	—	2	1	no	—
213	C₂×#135	C₂²×C₅	1	1	yes	characteristic
214	C₂²×D₈	C₂²×C₅	1	1	yes	characteristic
215	#542	—	2	1	no	—
216	#535	—	2	1	no	—
217	C₂×Q₃₂	C₂²×C₅	1	1	yes	characteristic, complemented
218	C₂×SD₃₂	C₂²×C₅	1	1	yes	characteristic
219	C₂×SD₃₂	C₂²×C₅	1	1	yes	characteristic
220	C₂×SD₃₂	C₂²×C₅	1	1	yes	characteristic, complemented
221	C₂×SD₃₂	C₂²×C₅	1	1	yes	characteristic, complemented
222	C₂×D₁₆	C₂²×C₅	1	1	yes	characteristic
223	C₂×D₁₆	C₂²×C₅	1	1	yes	characteristic
224	C₂×D₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
225	#500	C₂²×C₅	1	1	yes	characteristic, complemented
226	#496	—	2	1	no	—
227	#496	—	2	1	no	—
228	#495	C₂²×C₅	1	1	yes	characteristic
229	#495	C₂²×C₅	1	1	yes	characteristic
230	#495	C₂²×C₅	1	1	yes	characteristic, complemented
231	#493	C₂²×C₅	1	1	yes	characteristic
232	#493	C₂²×C₅	1	1	yes	characteristic
233	#489	—	2	1	no	—
234	#468	—	2	1	no	—
235	#467	C₂²×C₅	1	1	yes	characteristic
236	#466	C₂²×C₅	1	1	yes	characteristic
237	#440	—	2	1	no	—
238	C₄×Q₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
239	C₄×D₈	C₂²×C₅	1	1	yes	characteristic, complemented
240	#405	C₂²×C₅	1	1	yes	characteristic
241	C₄⋊C₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
242	C₄⋊C₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
243	#358	C₂²×C₅	1	1	yes	characteristic, complemented
244	#358	C₂²×C₅	1	1	yes	characteristic, complemented
245	#357	C₂²×C₅	1	1	yes	characteristic
246	#357	C₂²×C₅	1	1	yes	characteristic
247	#357	C₂²×C₅	1	1	yes	characteristic
248	#357	C₂²×C₅	1	1	yes	characteristic
249	#357	C₂²×C₅	1	1	yes	characteristic, complemented
250	#357	C₂²×C₅	1	1	yes	characteristic, complemented
251	C₂²⋊C₁₆	C₂²×C₅	1	1	yes	characteristic
252	C₂²⋊C₁₆	C₂²×C₅	1	1	yes	characteristic
253	#346	C₂²×C₅	1	1	yes	characteristic, complemented
254	C₄×C₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
255	C₂³×C₅	—	4	1	no	—
256	C₂³×C₅	—	4	1	no	—
257	C₂³×C₅	—	4	1	no	—
258	C₂³×C₅	—	4	1	no	—
259	C₂³×C₅	—	8	2	no	—
260	C₂³×C₅	—	16	1	no	—
261	C₂³×C₅	—	16	1	no	—
262	C₂³×C₅	C₂×D₈	1	1	yes	characteristic
263	C₅×Q₈	—	4	1	no	—
264	C₅×Q₈	—	4	1	no	—
265	C₅×Q₈	—	4	1	no	—
266	C₅×Q₈	—	4	1	no	—
267	C₅×Q₈	—	16	1	no	—
268	C₅×D₄	—	4	1	no	—
269	C₅×D₄	—	4	1	no	—
270	C₅×D₄	—	4	1	no	—
271	C₅×D₄	—	4	1	no	—
272	C₅×D₄	—	4	1	no	—
273	C₅×D₄	—	4	1	no	—
274	C₅×D₄	—	4	1	no	—
275	C₅×D₄	—	4	1	no	—
276	C₅×D₄	—	8	2	no	—
277	C₅×D₄	—	8	2	no	—
278	C₅×D₄	—	16	1	no	—
279	C₅×D₄	—	16	1	no	—
280	C₅×D₄	—	16	1	no	—
281	C₅×D₄	—	16	1	no	—
282	C₅×D₄	—	16	1	no	—
283	C₂×C₄×C₅	—	2	1	no	—
284	C₂×C₄×C₅	—	2	1	no	—
285	C₂×C₄×C₅	—	4	1	no	—
286	C₂×C₄×C₅	—	4	1	no	—
287	C₂×C₄×C₅	—	4	1	no	—
288	C₂×C₄×C₅	—	4	1	no	—
289	C₂×C₄×C₅	—	8	2	no	—
290	C₂×C₄×C₅	—	16	1	no	—
291	C₂×C₄×C₅	C₂×D₈	1	1	yes	characteristic
292	C₂×C₄×C₅	C₂×D₈	1	1	yes	characteristic
293	C₂×C₄×C₅	C₂×D₈	1	1	yes	characteristic
294	C₂×C₄×C₅	C₂×D₈	1	1	yes	characteristic
295	C₂×C₄×C₅	C₂×D₈	1	1	yes	characteristic
296	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
297	C₅×C₈	—	2	1	no	—
298	C₅×C₈	—	2	1	no	—
299	C₅×C₈	AGL(1,ℤ/8)	1	2	yes	—
300	C₅×C₈	H(5,𝔽₂)	1	1	yes	characteristic
301	C₅×C₈	H(5,𝔽₂)	1	1	yes	characteristic
302	C₂×#41	—	2	1	no	—
303	C₂²×D₄	—	2	1	no	—
304	AGL(1,ℤ/8)	—	4	4	no	—
305	#135	—	4	1	no	—
306	#135	—	4	1	no	—
307	C₂×Q₁₆	C₂³×C₅	1	1	yes	characteristic
308	C₂×Q₁₆	C₂³×C₅	1	1	yes	characteristic
309	C₂×SD₁₆	—	2	1	no	—
310	C₂×SD₁₆	—	2	1	no	—
311	C₂×SD₁₆	—	2	1	no	—
312	C₂×SD₁₆	—	2	1	no	—
313	C₂×D₈	—	2	1	no	—
314	C₂×D₈	—	2	1	no	—
315	C₂×D₈	—	2	1	no	—
316	C₂×D₈	—	4	1	no	—
317	C₂×D₈	—	4	1	no	—
318	C₂×D₈	C₂³×C₅	1	1	yes	characteristic
319	C₂×D₈	C₂³×C₅	1	1	yes	characteristic
320	C₂×D₈	C₂³×C₅	1	1	yes	characteristic
321	C₂×D₈	C₂³×C₅	1	1	yes	characteristic
322	C₂×M₁₆	C₅×D₄	1	1	yes	characteristic
323	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
324	C₄⋊Q₈	—	2	1	no	—
325	#127	—	2	1	no	—
326	#127	—	2	1	no	—
327	#126	—	4	1	no	—
328	#124	—	2	1	no	—
329	#124	—	2	1	no	—
330	#124	—	2	1	no	—
331	#124	—	4	1	no	—
332	#123	—	4	1	no	—
333	C₂²⋊Q₈	—	2	1	no	—
334	C₂²⋊Q₈	—	4	1	no	—
335	#121	—	2	1	no	—
336	#121	—	4	1	no	—
337	#121	—	4	1	no	—
338	#120	—	4	1	no	—
339	#120	—	4	1	no	—
340	C₄×Q₈	—	2	1	no	—
341	C₄×D₄	—	2	1	no	—
342	#117	C₅×D₄	1	1	yes	characteristic
343	Q₃₂	—	4	1	no	—
344	SD₃₂	—	4	1	no	—
345	SD₃₂	—	4	1	no	—
346	SD₃₂	—	4	1	no	—
347	SD₃₂	—	4	1	no	—
348	D₁₆	—	4	1	no	—
349	D₁₆	—	4	1	no	—
350	D₁₆	—	4	1	no	—
351	C₂×C₁₆	C₂³×C₅	1	1	yes	characteristic
352	C₂×C₁₆	C₂³×C₅	1	1	yes	characteristic
353	C₂×C₁₆	C₂³×C₅	1	1	yes	characteristic
354	C₂×C₁₆	C₂³×C₅	1	1	yes	characteristic
355	#107	—	2	1	no	—
356	#107	C₂³×C₅	1	1	yes	characteristic
357	#107	C₂³×C₅	1	1	yes	characteristic
358	#103	—	2	1	no	—
359	#103	—	2	1	no	—
360	#102	—	2	1	no	—
361	#102	—	2	1	no	—
362	#97	C₅×D₄	1	1	yes	characteristic
363	#97	C₅×D₄	1	1	yes	characteristic
364	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
365	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
366	C₂²×C₅	—	2	1	no	—
367	C₂²×C₅	—	2	1	no	—
368	C₂²×C₅	—	2	1	no	—
369	C₂²×C₅	—	8	1	no	—
370	C₂²×C₅	—	8	1	no	—
371	C₂²×C₅	—	8	1	no	—
372	C₂²×C₅	—	8	1	no	—
373	C₂²×C₅	—	8	1	no	—
374	C₂²×C₅	—	8	1	no	—
375	C₂²×C₅	—	8	1	no	—
376	C₂²×C₅	—	8	1	no	—
377	C₂²×C₅	—	8	1	no	—
378	C₂²×C₅	—	8	1	no	—
379	C₂²×C₅	—	8	1	no	—
380	C₂²×C₅	—	8	1	no	—
381	C₂²×C₅	—	16	4	no	—
382	C₂²×C₅	C₂²×D₈	1	1	yes	characteristic
383	C₄×C₅	—	2	1	no	—
384	C₄×C₅	—	2	1	no	—
385	C₄×C₅	—	2	1	no	—
386	C₄×C₅	—	2	1	no	—
387	C₄×C₅	—	2	1	no	—
388	C₄×C₅	—	8	1	no	—
389	C₄×C₅	—	8	1	no	—
390	C₄×C₅	—	8	1	no	—
391	C₄×C₅	—	8	1	no	—
392	C₄×C₅	#535	1	1	yes	characteristic
393	C₄×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
394	C₂⁴	—	4	1	no	—
395	#41	—	4	2	no	—
396	#41	—	4	2	no	—
397	C₂×Q₈	—	2	1	no	—
398	C₂×Q₈	—	2	1	no	—
399	C₂×Q₈	—	4	1	no	—
400	C₂×D₄	—	2	1	no	—
401	C₂×D₄	—	2	1	no	—
402	C₂×D₄	—	2	1	no	—
403	C₂×D₄	—	2	1	no	—
404	C₂×D₄	—	4	2	no	—
405	C₂×D₄	—	4	2	no	—
406	C₂×D₄	—	4	1	no	—
407	C₂×D₄	—	4	1	no	—
408	C₂×D₄	—	4	1	no	—
409	C₂×D₄	—	4	1	no	—
410	C₂×D₄	—	4	1	no	—
411	C₂×D₄	—	4	1	no	—
412	C₂×D₄	—	4	1	no	—
413	C₂²×C₄	—	4	1	no	—
414	C₂²×C₄	—	4	1	no	—
415	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
416	Q₁₆	—	2	1	no	—
417	Q₁₆	—	2	1	no	—
418	Q₁₆	—	2	1	no	—
419	Q₁₆	—	2	1	no	—
420	SD₁₆	—	4	2	no	—
421	SD₁₆	—	4	2	no	—
422	SD₁₆	—	4	2	no	—
423	SD₁₆	—	4	2	no	—
424	D₈	—	2	1	no	—
425	D₈	—	2	1	no	—
426	D₈	—	2	1	no	—
427	D₈	—	2	1	no	—
428	D₈	—	2	1	no	—
429	D₈	—	2	1	no	—
430	D₈	—	2	1	no	—
431	D₈	—	2	1	no	—
432	D₈	—	4	2	no	—
433	D₈	—	4	2	no	—
434	D₈	—	4	2	no	—
435	M₁₆	—	2	2	no	—
436	C₂×C₈	—	2	1	no	—
437	C₂×C₈	—	2	1	no	—
438	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
439	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
440	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
441	C₂×C₈	C₂⁴×C₅	1	1	yes	characteristic
442	C₄⋊C₄	—	2	1	no	—
443	C₄⋊C₄	—	2	1	no	—
444	C₄⋊C₄	—	4	1	no	—
445	C₄⋊C₄	—	4	1	no	—
446	C₄⋊C₄	—	4	1	no	—
447	C₄⋊C₄	C₅×D₈	1	1	yes	characteristic
448	C₄⋊C₄	C₅×D₈	1	1	yes	characteristic
449	C₂²⋊C₄	—	4	1	no	—
450	C₂²⋊C₄	—	4	1	no	—
451	C₂²⋊C₄	—	4	1	no	—
452	C₂²⋊C₄	—	4	1	no	—
453	C₂²⋊C₄	—	4	1	no	—
454	C₂²⋊C₄	—	4	1	no	—
455	C₂²⋊C₄	—	4	1	no	—
456	C₂²⋊C₄	—	4	1	no	—
457	C₂²⋊C₄	—	4	1	no	—
458	C₂²⋊C₄	C₅×D₈	1	1	yes	characteristic
459	C₂²⋊C₄	C₅×D₈	1	1	yes	characteristic
460	C₄²	—	4	1	no	—
461	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
462	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
463	C₁₆	—	2	1	no	—
464	C₁₆	—	2	1	no	—
465	C₁₆	—	2	1	no	—
466	C₁₆	—	2	1	no	—
467	C₂×C₅	—	4	1	no	—
468	C₂×C₅	—	16	1	no	—
469	C₂×C₅	—	16	1	no	—
470	C₂×C₅	—	16	1	no	—
471	C₂×C₅	—	16	1	no	—
472	C₂×C₅	#3205	1	1	yes	characteristic
473	C₂×C₅	#3415	1	1	yes	characteristic
474	C₂×C₅	#3416	1	1	yes	characteristic
475	C₂³	—	4	1	no	—
476	C₂³	—	4	1	no	—
477	C₂³	—	4	1	no	—
478	C₂³	—	4	1	no	—
479	C₂³	—	8	2	no	—
480	C₂³	—	16	1	no	—
481	C₂³	—	16	1	no	—
482	C₂³	C₂×C₅×D₈	1	1	yes	characteristic
483	Q₈	—	4	1	no	—
484	Q₈	—	4	1	no	—
485	Q₈	—	4	1	no	—
486	Q₈	—	4	1	no	—
487	Q₈	—	16	1	no	—
488	D₄	—	4	1	no	—
489	D₄	—	4	1	no	—
490	D₄	—	4	1	no	—
491	D₄	—	4	1	no	—
492	D₄	—	4	1	no	—
493	D₄	—	4	1	no	—
494	D₄	—	4	1	no	—
495	D₄	—	4	1	no	—
496	D₄	—	8	2	no	—
497	D₄	—	8	2	no	—
498	D₄	—	16	1	no	—
499	D₄	—	16	1	no	—
500	D₄	—	16	1	no	—
501	D₄	—	16	1	no	—
502	D₄	—	16	1	no	—
503	C₂×C₄	—	2	1	no	—
504	C₂×C₄	—	2	1	no	—
505	C₂×C₄	—	4	1	no	—
506	C₂×C₄	—	4	1	no	—
507	C₂×C₄	—	4	1	no	—
508	C₂×C₄	—	4	1	no	—
509	C₂×C₄	—	8	2	no	—
510	C₂×C₄	—	16	1	no	—
511	C₂×C₄	C₂×C₅×D₈	1	1	yes	characteristic
512	C₂×C₄	C₂×C₅×D₈	1	1	yes	characteristic
513	C₂×C₄	C₂×C₅×D₈	1	1	yes	characteristic
514	C₂×C₄	C₂×C₅×D₈	1	1	yes	characteristic
515	C₂×C₄	C₂×C₅×D₈	1	1	yes	characteristic
516	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
517	C₈	—	2	1	no	—
518	C₈	—	2	1	no	—
519	C₈	C₅×AGL(1,ℤ/8)	1	2	yes	—
520	C₈	C₅×H(5,𝔽₂)	1	1	yes	characteristic
521	C₈	C₅×H(5,𝔽₂)	1	1	yes	characteristic
522	C₅	#33790	1	1	yes	characteristic, direct product factor, Sylow
523	C₂²	—	2	1	no	—
524	C₂²	—	2	1	no	—
525	C₂²	—	2	1	no	—
526	C₂²	—	8	1	no	—
527	C₂²	—	8	1	no	—
528	C₂²	—	8	1	no	—
529	C₂²	—	8	1	no	—
530	C₂²	—	8	1	no	—
531	C₂²	—	8	1	no	—
532	C₂²	—	8	1	no	—
533	C₂²	—	8	1	no	—
534	C₂²	—	8	1	no	—
535	C₂²	—	8	1	no	—
536	C₂²	—	8	1	no	—
537	C₂²	—	8	1	no	—
538	C₂²	—	16	4	no	—
539	C₂²	C₂²×C₅×D₈	1	1	yes	characteristic
540	C₄	—	2	1	no	—
541	C₄	—	2	1	no	—
542	C₄	—	2	1	no	—
543	C₄	—	2	1	no	—
544	C₄	—	2	1	no	—
545	C₄	—	8	1	no	—
546	C₄	—	8	1	no	—
547	C₄	—	8	1	no	—
548	C₄	—	8	1	no	—
549	C₄	C₅×#535	1	1	yes	characteristic
550	C₄	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
551	C₂	—	4	1	no	—
552	C₂	—	16	1	no	—
553	C₂	—	16	1	no	—
554	C₂	—	16	1	no	—
555	C₂	—	16	1	no	—
556	C₂	C₅×#3205	1	1	yes	characteristic
557	C₂	C₅×#3415	1	1	yes	characteristic
558	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 ◁ C₅×#117 ◁ C₅×#405 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅×#3175	C₂	semidirect
2. C₅×#3155	C₂	semidirect
3. C₅×#2250	C₂	semidirect
4. C₅×#2249	C₂	semidirect
5. C₅×#2243	C₂	semidirect
6. C₅×#2240	C₂	semidirect
7. C₅×#2211	C₂	semidirect
8. C₅×#2210	C₂	semidirect
9. C₅×#2207	C₂	semidirect
10. C₅×#2206	C₂	semidirect
11. C₅×#2189	C₂	semidirect
12. C₅×#2187	C₂	semidirect
13. C₅×#2186	C₂	semidirect
14. C₅×#2184	C₂	semidirect
15. C₅×#2164	C₂	semidirect
21. C₂×C₅×Q₃₂	C₂²	semidirect
24. C₂×C₅×SD₃₂	C₂²	semidirect
25. C₂×C₅×SD₃₂	C₂²	semidirect
28. C₂×C₅×D₁₆	C₂²	semidirect
29. C₅×#500	C₂²	semidirect
34. C₅×#495	C₂²	semidirect
42. C₄×C₅×Q₁₆	C₂²	semidirect
43. C₄×C₅×D₈	C₂²	semidirect
45. C₅×C₄⋊C₁₆	C₂²	semidirect
46. C₅×C₄⋊C₁₆	C₂²	semidirect
47. C₅×#358	C₂²	semidirect
48. C₅×#358	C₂²	semidirect
53. C₅×#357	C₂²	semidirect
54. C₅×#357	C₂²	semidirect
57. C₅×#346	C₂²	semidirect
58. C₄×C₅×C₁₆	C₂²	semidirect
59. #33790	C₅	direct (N × H)
124. #3175	C₂×C₅	semidirect
125. #3155	C₂×C₅	semidirect
126. #2250	C₂×C₅	semidirect
127. #2249	C₂×C₅	semidirect
128. #2243	C₂×C₅	semidirect
129. #2240	C₂×C₅	semidirect
130. #2211	C₂×C₅	semidirect
131. #2210	C₂×C₅	semidirect
132. #2207	C₂×C₅	semidirect
133. #2206	C₂×C₅	semidirect
134. #2189	C₂×C₅	semidirect
135. #2187	C₂×C₅	semidirect
136. #2186	C₂×C₅	semidirect
137. #2184	C₂×C₅	semidirect
138. #2164	C₂×C₅	semidirect
217. C₂×Q₃₂	C₂²×C₅	semidirect
220. C₂×SD₃₂	C₂²×C₅	semidirect
221. C₂×SD₃₂	C₂²×C₅	semidirect
224. C₂×D₁₆	C₂²×C₅	semidirect
225. #500	C₂²×C₅	semidirect
230. #495	C₂²×C₅	semidirect
238. C₄×Q₁₆	C₂²×C₅	semidirect
239. C₄×D₈	C₂²×C₅	semidirect
241. C₄⋊C₁₆	C₂²×C₅	semidirect
242. C₄⋊C₁₆	C₂²×C₅	semidirect
243. #358	C₂²×C₅	semidirect
244. #358	C₂²×C₅	semidirect
249. #357	C₂²×C₅	semidirect
250. #357	C₂²×C₅	semidirect
253. #346	C₂²×C₅	semidirect
254. C₄×C₁₆	C₂²×C₅	semidirect
522. C₅	#33790	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×#3175	2
C₅×#3155	2
C₅×#2250	2
C₅×#2249	2
C₅×#2243	2
C₅×#2240	2
C₅×#2211	2
C₅×#2210	2
C₅×#2207	2
C₅×#2206	2
C₅×#2189	2
C₅×#2187	2
C₅×#2186	2
C₅×#2184	2
C₅×#2164	2
#33790	5

Subgroups — C5×#33790 #11956510

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#33790 #11956510