Subgroups — C₅×#19912 #11942632

Order 1280.

684 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3394	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#3373	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#3324	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×D₄×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#1706	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#1702	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#1701	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1666	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1665	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1650	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1649	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#1620	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#1619	C₂	1	1	yes	maximal, characteristic
14	C₅×#1590	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×C₈×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₅×SD₁₆	—	2	1	no	—
17	C₅×#559	C₂²	1	1	yes	characteristic, complemented
18	C₅×#556	C₂²	1	1	yes	characteristic
19	C₅×D₄×Q₈	C₂²	1	1	yes	characteristic
20	C₅×D₄²	C₂²	1	1	yes	characteristic
21	C₅×#500	C₂²	1	1	yes	characteristic, complemented
22	C₅×#495	—	2	1	no	—
23	C₅×#493	C₂²	1	1	yes	characteristic
24	C₅×#492	C₂²	1	1	yes	characteristic
25	C₅×#492	C₂²	1	1	yes	characteristic, complemented
26	C₅×#489	—	2	1	no	—
27	C₅×#486	C₂²	1	1	yes	characteristic
28	C₅×#486	C₂²	1	1	yes	characteristic, complemented
29	C₅×#482	—	2	1	no	—
30	C₅×#476	—	2	1	no	—
31	C₅×#475	C₂²	1	1	yes	characteristic, complemented
32	C₅×#474	C₂²	1	1	yes	characteristic
33	C₅×#468	—	2	1	no	—
34	C₅×#465	—	2	1	no	—
35	C₅×#464	—	2	1	no	—
36	C₅×#463	—	2	1	no	—
37	C₅×#463	—	2	1	no	—
38	C₅×#462	C₂²	1	1	yes	characteristic, complemented
39	C₅×#461	C₂²	1	1	yes	characteristic
40	C₅×#460	C₂²	1	1	yes	characteristic
41	C₅×#460	C₂²	1	1	yes	characteristic
42	C₅×#459	C₂²	1	1	yes	characteristic
43	C₅×#459	C₂²	1	1	yes	characteristic
44	C₅×#450	—	2	1	no	—
45	C₅×#450	—	2	1	no	—
46	C₅×#448	—	2	1	no	—
47	C₅×#446	C₂²	1	1	yes	characteristic, complemented
48	C₅×C₈×Q₈	C₂²	1	1	yes	characteristic, complemented
49	C₅×#442	—	2	1	no	—
50	C₄×C₅×SD₁₆	—	2	1	no	—
51	C₄×C₅×SD₁₆	C₂²	1	1	yes	characteristic
52	C₄×C₅×SD₁₆	C₂²	1	1	yes	characteristic
53	C₅×#436	C₂²	1	1	yes	characteristic
54	C₅×C₈×D₄	C₂²	1	1	yes	characteristic
55	C₅×#418	—	2	1	no	—
56	C₅×#334	C₂²	1	1	yes	characteristic, complemented
57	C₅×#334	C₂²	1	1	yes	characteristic, complemented
58	C₅×#332	C₂²	1	1	yes	characteristic, complemented
59	C₅×#332	C₂²	1	1	yes	characteristic, complemented
60	C₅×#331	C₂²	1	1	yes	characteristic
61	C₅×#331	C₂²	1	1	yes	characteristic, complemented
62	C₅×Q₈⋊C₈	C₂²	1	1	yes	characteristic, complemented
63	C₅×Q₈⋊C₈	C₂²	1	1	yes	characteristic, complemented
64	C₅×D₄⋊C₈	C₂²	1	1	yes	characteristic
65	C₅×D₄⋊C₈	C₂²	1	1	yes	characteristic
66	C₅×C₈²	C₂²	1	1	yes	characteristic, complemented
67	#19912	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
68	C₂²×C₅×Q₈	—	2	1	no	—
69	C₂²×C₅×D₄	—	2	1	no	—
70	C₂²×C₅×D₄	—	2	1	no	—
71	C₂×C₅×Q₁₆	—	2	1	no	—
72	C₂×C₅×SD₁₆	—	2	1	no	—
73	C₂×C₅×SD₁₆	—	2	1	no	—
74	C₂×C₅×SD₁₆	—	2	1	no	—
75	C₂×C₅×SD₁₆	—	2	1	no	—
76	C₂×C₅×SD₁₆	—	2	1	no	—
77	C₂×C₅×SD₁₆	—	2	1	no	—
78	C₂×C₅×SD₁₆	—	2	1	no	—
79	C₂×C₅×SD₁₆	—	4	4	no	—
80	C₂×C₅×SD₁₆	D₄	1	1	yes	characteristic
81	C₂×C₅×SD₁₆	D₄	1	1	yes	characteristic
82	C₂×C₅×D₈	—	2	1	no	—
83	C₂×C₅×D₈	—	2	1	no	—
84	C₂×C₅×D₈	—	4	1	no	—
85	C₂×C₅×M₁₆	—	2	1	no	—
86	C₂²×C₅×C₈	—	2	1	no	—
87	C₅×C₄⋊Q₈	—	2	1	no	—
88	C₅×C₄⋊Q₈	C₂³	1	1	yes	characteristic
89	C₅×C₄⋊Q₈	C₂³	1	1	yes	characteristic
90	C₅×#127	C₂³	1	1	yes	characteristic
91	C₅×#127	C₂³	1	1	yes	characteristic
92	C₅×#126	—	4	1	no	—
93	C₅×#124	—	2	1	no	—
94	C₅×#124	—	2	1	no	—
95	C₅×#124	—	2	1	no	—
96	C₅×#123	—	4	1	no	—
97	C₅×C₂²⋊Q₈	—	2	1	no	—
98	C₅×C₂²⋊Q₈	—	2	1	no	—
99	C₅×C₂²⋊Q₈	—	4	1	no	—
100	C₅×#121	—	2	1	no	—
101	C₅×#121	—	2	1	no	—
102	C₅×#120	—	4	1	no	—
103	C₄×C₅×Q₈	—	2	1	no	—
104	C₄×C₅×Q₈	C₂³	1	1	yes	characteristic
105	C₄×C₅×Q₈	C₂³	1	1	yes	characteristic
106	C₄×C₅×D₄	—	2	1	no	—
107	C₄×C₅×D₄	—	2	1	no	—
108	C₄×C₅×D₄	—	2	1	no	—
109	C₄×C₅×D₄	C₂³	1	1	yes	characteristic
110	C₄×C₅×D₄	C₂³	1	1	yes	characteristic
111	C₅×#117	—	2	1	no	—
112	C₅×#107	—	2	1	no	—
113	C₅×#107	—	4	1	no	—
114	C₅×#106	—	2	1	no	—
115	C₅×#106	D₄	1	1	yes	characteristic
116	C₅×#106	D₄	1	1	yes	characteristic
117	C₅×C₄⋊C₈	—	2	1	no	—
118	C₅×C₄⋊C₈	—	2	1	no	—
119	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
120	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
121	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
122	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
123	C₅×#103	—	2	1	no	—
124	C₅×#103	—	2	1	no	—
125	C₅×#103	—	2	1	no	—
126	C₅×#103	D₄	1	1	yes	characteristic
127	C₅×#103	D₄	1	1	yes	characteristic
128	C₅×#102	—	2	1	no	—
129	C₅×#102	—	2	1	no	—
130	C₅×#102	—	2	1	no	—
131	C₅×#102	—	2	1	no	—
132	C₅×#102	—	2	1	no	—
133	C₅×#102	—	2	1	no	—
134	C₅×#102	—	2	1	no	—
135	C₅×#102	—	2	1	no	—
136	C₅×#102	—	2	1	no	—
137	C₅×#102	D₄	1	1	yes	characteristic
138	C₅×#102	D₄	1	1	yes	characteristic
139	C₅×C₂²⋊C₈	—	2	1	no	—
140	C₅×C₂²⋊C₈	—	2	1	no	—
141	C₅×#97	—	2	1	no	—
142	C₄×C₅×C₈	—	2	1	no	—
143	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
144	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
145	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
146	#3394	C₂×C₅	1	1	yes	characteristic, complemented
147	#3373	C₂×C₅	1	1	yes	characteristic, complemented
148	#3324	C₂×C₅	1	1	yes	characteristic, complemented
149	D₄×SD₁₆	C₂×C₅	1	1	yes	characteristic, complemented
150	#1706	C₂×C₅	1	1	yes	characteristic, complemented
151	#1702	C₂×C₅	1	1	yes	characteristic, complemented
152	#1701	C₂×C₅	1	1	yes	characteristic, complemented
153	#1666	C₂×C₅	1	1	yes	characteristic, complemented
154	#1665	C₂×C₅	1	1	yes	characteristic, complemented
155	#1650	C₂×C₅	1	1	yes	characteristic, complemented
156	#1649	C₂×C₅	1	1	yes	characteristic, complemented
157	#1620	C₂×C₅	1	1	yes	characteristic, complemented
158	#1619	C₂×C₅	1	1	yes	characteristic
159	#1590	C₂×C₅	1	1	yes	characteristic, complemented
160	C₈×SD₁₆	C₂×C₅	1	1	yes	characteristic, complemented
161	C₂⁴×C₅	—	4	1	no	—
162	C₂×C₅×Q₈	—	2	1	no	—
163	C₂×C₅×Q₈	—	2	1	no	—
164	C₂×C₅×Q₈	—	4	1	no	—
165	C₂×C₅×Q₈	—	4	2	no	—
166	C₂×C₅×Q₈	—	8	1	no	—
167	C₂×C₅×Q₈	C₂×D₄	1	1	yes	characteristic
168	C₂×C₅×Q₈	C₂×D₄	1	1	yes	characteristic
169	C₂×C₅×D₄	—	2	1	no	—
170	C₂×C₅×D₄	—	2	1	no	—
171	C₂×C₅×D₄	—	2	1	no	—
172	C₂×C₅×D₄	—	2	1	no	—
173	C₂×C₅×D₄	—	2	1	no	—
174	C₂×C₅×D₄	—	2	1	no	—
175	C₂×C₅×D₄	—	4	1	no	—
176	C₂×C₅×D₄	—	4	1	no	—
177	C₂×C₅×D₄	—	4	2	no	—
178	C₂×C₅×D₄	—	4	2	no	—
179	C₂×C₅×D₄	—	8	1	no	—
180	C₂×C₅×D₄	—	8	1	no	—
181	C₂×C₅×D₄	C₂×D₄	1	1	yes	characteristic
182	C₂×C₅×D₄	C₂×D₄	1	1	yes	characteristic
183	C₂²×C₄×C₅	—	2	1	no	—
184	C₂²×C₄×C₅	—	2	1	no	—
185	C₂²×C₄×C₅	—	4	1	no	—
186	C₂²×C₄×C₅	—	4	1	no	—
187	C₅×Q₁₆	—	8	1	no	—
188	C₅×SD₁₆	—	2	2	no	—
189	C₅×SD₁₆	—	2	2	no	—
190	C₅×SD₁₆	—	4	2	no	—
191	C₅×SD₁₆	—	4	2	no	—
192	C₅×SD₁₆	—	4	2	no	—
193	C₅×SD₁₆	—	4	2	no	—
194	C₅×SD₁₆	—	8	1	no	—
195	C₅×SD₁₆	—	8	1	no	—
196	C₅×SD₁₆	—	8	1	no	—
197	C₅×D₈	—	4	2	no	—
198	C₅×D₈	—	8	2	no	—
199	C₅×D₈	—	8	1	no	—
200	C₅×M₁₆	—	8	1	no	—
201	C₂×C₅×C₈	—	2	1	no	—
202	C₂×C₅×C₈	—	2	1	no	—
203	C₂×C₅×C₈	—	2	1	no	—
204	C₂×C₅×C₈	—	2	1	no	—
205	C₂×C₅×C₈	—	2	1	no	—
206	C₂×C₅×C₈	—	4	2	no	—
207	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
208	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
209	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
210	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
211	C₅×C₄⋊C₄	—	2	1	no	—
212	C₅×C₄⋊C₄	—	2	1	no	—
213	C₅×C₄⋊C₄	—	2	1	no	—
214	C₅×C₄⋊C₄	—	2	1	no	—
215	C₅×C₄⋊C₄	—	2	1	no	—
216	C₅×C₄⋊C₄	—	2	1	no	—
217	C₅×C₄⋊C₄	—	4	1	no	—
218	C₅×C₄⋊C₄	—	4	1	no	—
219	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
220	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
221	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
222	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
223	C₅×C₂²⋊C₄	—	2	1	no	—
224	C₅×C₂²⋊C₄	—	2	1	no	—
225	C₅×C₂²⋊C₄	—	4	1	no	—
226	C₅×C₂²⋊C₄	—	4	1	no	—
227	C₅×C₂²⋊C₄	—	4	1	no	—
228	C₅×C₂²⋊C₄	—	4	1	no	—
229	C₅×C₂²⋊C₄	—	4	1	no	—
230	C₅×C₂²⋊C₄	—	4	1	no	—
231	C₅×C₂²⋊C₄	—	4	1	no	—
232	C₄²×C₅	—	2	1	no	—
233	C₄²×C₅	—	2	1	no	—
234	C₄²×C₅	—	4	1	no	—
235	C₄²×C₅	C₂⁴	1	1	yes	characteristic
236	C₂²×SD₁₆	—	2	1	no	—
237	#559	C₂²×C₅	1	1	yes	characteristic, complemented
238	#556	C₂²×C₅	1	1	yes	characteristic
239	D₄×Q₈	C₂²×C₅	1	1	yes	characteristic
240	D₄²	C₂²×C₅	1	1	yes	characteristic
241	#500	C₂²×C₅	1	1	yes	characteristic, complemented
242	#495	—	2	1	no	—
243	#493	C₂²×C₅	1	1	yes	characteristic
244	#492	C₂²×C₅	1	1	yes	characteristic
245	#492	C₂²×C₅	1	1	yes	characteristic, complemented
246	#489	—	2	1	no	—
247	#486	C₂²×C₅	1	1	yes	characteristic
248	#486	C₂²×C₅	1	1	yes	characteristic, complemented
249	#482	—	2	1	no	—
250	#476	—	2	1	no	—
251	#475	C₂²×C₅	1	1	yes	characteristic, complemented
252	#474	C₂²×C₅	1	1	yes	characteristic
253	#468	—	2	1	no	—
254	#465	—	2	1	no	—
255	#464	—	2	1	no	—
256	#463	—	2	1	no	—
257	#463	—	2	1	no	—
258	#462	C₂²×C₅	1	1	yes	characteristic, complemented
259	#461	C₂²×C₅	1	1	yes	characteristic
260	#460	C₂²×C₅	1	1	yes	characteristic
261	#460	C₂²×C₅	1	1	yes	characteristic
262	#459	C₂²×C₅	1	1	yes	characteristic
263	#459	C₂²×C₅	1	1	yes	characteristic
264	#450	—	2	1	no	—
265	#450	—	2	1	no	—
266	#448	—	2	1	no	—
267	#446	C₂²×C₅	1	1	yes	characteristic, complemented
268	C₈×Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
269	#442	—	2	1	no	—
270	C₄×SD₁₆	—	2	1	no	—
271	C₄×SD₁₆	C₂²×C₅	1	1	yes	characteristic
272	C₄×SD₁₆	C₂²×C₅	1	1	yes	characteristic
273	#436	C₂²×C₅	1	1	yes	characteristic
274	C₈×D₄	C₂²×C₅	1	1	yes	characteristic
275	#418	—	2	1	no	—
276	#334	C₂²×C₅	1	1	yes	characteristic, complemented
277	#334	C₂²×C₅	1	1	yes	characteristic, complemented
278	#332	C₂²×C₅	1	1	yes	characteristic, complemented
279	#332	C₂²×C₅	1	1	yes	characteristic, complemented
280	#331	C₂²×C₅	1	1	yes	characteristic
281	#331	C₂²×C₅	1	1	yes	characteristic, complemented
282	Q₈⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
283	Q₈⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
284	D₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
285	D₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
286	C₈²	C₂²×C₅	1	1	yes	characteristic, complemented
287	C₂³×C₅	—	2	1	no	—
288	C₂³×C₅	—	2	1	no	—
289	C₂³×C₅	—	4	1	no	—
290	C₂³×C₅	—	4	1	no	—
291	C₂³×C₅	—	8	2	no	—
292	C₂³×C₅	—	8	2	no	—
293	C₂³×C₅	—	16	1	no	—
294	C₅×Q₈	—	2	1	no	—
295	C₅×Q₈	—	2	1	no	—
296	C₅×Q₈	—	2	1	no	—
297	C₅×Q₈	—	2	1	no	—
298	C₅×Q₈	—	4	1	no	—
299	C₅×Q₈	—	4	1	no	—
300	C₅×Q₈	—	4	1	no	—
301	C₅×Q₈	—	4	1	no	—
302	C₅×Q₈	—	8	2	no	—
303	C₅×D₄	—	2	1	no	—
304	C₅×D₄	—	2	1	no	—
305	C₅×D₄	—	2	1	no	—
306	C₅×D₄	—	4	1	no	—
307	C₅×D₄	—	4	1	no	—
308	C₅×D₄	—	4	1	no	—
309	C₅×D₄	—	4	1	no	—
310	C₅×D₄	—	4	1	no	—
311	C₅×D₄	—	4	1	no	—
312	C₅×D₄	—	4	1	no	—
313	C₅×D₄	—	4	1	no	—
314	C₅×D₄	—	8	1	no	—
315	C₅×D₄	—	8	1	no	—
316	C₅×D₄	—	8	2	no	—
317	C₅×D₄	—	8	2	no	—
318	C₅×D₄	#135	1	2	yes	—
319	C₂×C₄×C₅	—	2	1	no	—
320	C₂×C₄×C₅	—	2	1	no	—
321	C₂×C₄×C₅	—	2	1	no	—
322	C₂×C₄×C₅	—	2	1	no	—
323	C₂×C₄×C₅	—	2	1	no	—
324	C₂×C₄×C₅	—	2	1	no	—
325	C₂×C₄×C₅	—	4	1	no	—
326	C₂×C₄×C₅	—	4	1	no	—
327	C₂×C₄×C₅	—	4	1	no	—
328	C₂×C₄×C₅	—	4	1	no	—
329	C₂×C₄×C₅	—	4	1	no	—
330	C₂×C₄×C₅	—	4	1	no	—
331	C₂×C₄×C₅	—	8	2	no	—
332	C₂×C₄×C₅	—	16	1	no	—
333	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
334	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
335	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
336	C₅×C₈	—	2	2	no	—
337	C₅×C₈	—	2	1	no	—
338	C₅×C₈	—	2	1	no	—
339	C₅×C₈	—	2	1	no	—
340	C₅×C₈	—	4	1	no	—
341	C₅×C₈	—	4	1	no	—
342	C₅×C₈	—	4	1	no	—
343	C₅×C₈	—	4	1	no	—
344	C₅×C₈	AGL(1,ℤ/8)	1	2	yes	—
345	C₂²×Q₈	—	2	1	no	—
346	C₂²×D₄	—	2	1	no	—
347	C₂²×D₄	—	2	1	no	—
348	C₂×Q₁₆	—	2	1	no	—
349	C₂×SD₁₆	—	2	1	no	—
350	C₂×SD₁₆	—	2	1	no	—
351	C₂×SD₁₆	—	2	1	no	—
352	C₂×SD₁₆	—	2	1	no	—
353	C₂×SD₁₆	—	2	1	no	—
354	C₂×SD₁₆	—	2	1	no	—
355	C₂×SD₁₆	—	2	1	no	—
356	C₂×SD₁₆	—	4	4	no	—
357	C₂×SD₁₆	C₅×D₄	1	1	yes	characteristic
358	C₂×SD₁₆	C₅×D₄	1	1	yes	characteristic
359	C₂×D₈	—	2	1	no	—
360	C₂×D₈	—	2	1	no	—
361	C₂×D₈	—	4	1	no	—
362	C₂×M₁₆	—	2	1	no	—
363	C₂²×C₈	—	2	1	no	—
364	C₄⋊Q₈	—	2	1	no	—
365	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
366	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
367	#127	C₂³×C₅	1	1	yes	characteristic
368	#127	C₂³×C₅	1	1	yes	characteristic
369	#126	—	4	1	no	—
370	#124	—	2	1	no	—
371	#124	—	2	1	no	—
372	#124	—	2	1	no	—
373	#123	—	4	1	no	—
374	C₂²⋊Q₈	—	2	1	no	—
375	C₂²⋊Q₈	—	2	1	no	—
376	C₂²⋊Q₈	—	4	1	no	—
377	#121	—	2	1	no	—
378	#121	—	2	1	no	—
379	#120	—	4	1	no	—
380	C₄×Q₈	—	2	1	no	—
381	C₄×Q₈	C₂³×C₅	1	1	yes	characteristic
382	C₄×Q₈	C₂³×C₅	1	1	yes	characteristic
383	C₄×D₄	—	2	1	no	—
384	C₄×D₄	—	2	1	no	—
385	C₄×D₄	—	2	1	no	—
386	C₄×D₄	C₂³×C₅	1	1	yes	characteristic
387	C₄×D₄	C₂³×C₅	1	1	yes	characteristic
388	#117	—	2	1	no	—
389	#107	—	2	1	no	—
390	#107	—	4	1	no	—
391	#106	—	2	1	no	—
392	#106	C₅×D₄	1	1	yes	characteristic
393	#106	C₅×D₄	1	1	yes	characteristic
394	C₄⋊C₈	—	2	1	no	—
395	C₄⋊C₈	—	2	1	no	—
396	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
397	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
398	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
399	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
400	#103	—	2	1	no	—
401	#103	—	2	1	no	—
402	#103	—	2	1	no	—
403	#103	C₅×D₄	1	1	yes	characteristic
404	#103	C₅×D₄	1	1	yes	characteristic
405	#102	—	2	1	no	—
406	#102	—	2	1	no	—
407	#102	—	2	1	no	—
408	#102	—	2	1	no	—
409	#102	—	2	1	no	—
410	#102	—	2	1	no	—
411	#102	—	2	1	no	—
412	#102	—	2	1	no	—
413	#102	—	2	1	no	—
414	#102	C₅×D₄	1	1	yes	characteristic
415	#102	C₅×D₄	1	1	yes	characteristic
416	C₂²⋊C₈	—	2	1	no	—
417	C₂²⋊C₈	—	2	1	no	—
418	#97	—	2	1	no	—
419	C₄×C₈	—	2	1	no	—
420	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
421	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
422	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
423	C₂²×C₅	—	2	2	no	—
424	C₂²×C₅	—	4	1	no	—
425	C₂²×C₅	—	4	1	no	—
426	C₂²×C₅	—	4	1	no	—
427	C₂²×C₅	—	4	1	no	—
428	C₂²×C₅	—	4	1	no	—
429	C₂²×C₅	—	8	1	no	—
430	C₂²×C₅	—	8	1	no	—
431	C₂²×C₅	—	8	1	no	—
432	C₂²×C₅	—	8	1	no	—
433	C₂²×C₅	—	8	1	no	—
434	C₂²×C₅	—	8	1	no	—
435	C₂²×C₅	—	16	4	no	—
436	C₂²×C₅	D₄²	1	1	yes	characteristic
437	C₄×C₅	—	2	1	no	—
438	C₄×C₅	—	4	1	no	—
439	C₄×C₅	—	4	1	no	—
440	C₄×C₅	—	4	1	no	—
441	C₄×C₅	—	4	1	no	—
442	C₄×C₅	—	4	1	no	—
443	C₄×C₅	—	4	1	no	—
444	C₄×C₅	—	8	1	no	—
445	C₄×C₅	—	8	1	no	—
446	C₄×C₅	C₂×#135	1	1	yes	characteristic
447	C₄×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
448	C₄×C₅	#576	1	1	yes	characteristic
449	C₄×C₅	#577	1	1	yes	characteristic
450	C₂⁴	—	4	1	no	—
451	C₂×Q₈	—	2	1	no	—
452	C₂×Q₈	—	2	1	no	—
453	C₂×Q₈	—	4	1	no	—
454	C₂×Q₈	—	4	2	no	—
455	C₂×Q₈	—	8	1	no	—
456	C₂×Q₈	C₂×C₅×D₄	1	1	yes	characteristic
457	C₂×Q₈	C₂×C₅×D₄	1	1	yes	characteristic
458	C₂×D₄	—	2	1	no	—
459	C₂×D₄	—	2	1	no	—
460	C₂×D₄	—	2	1	no	—
461	C₂×D₄	—	2	1	no	—
462	C₂×D₄	—	2	1	no	—
463	C₂×D₄	—	2	1	no	—
464	C₂×D₄	—	4	1	no	—
465	C₂×D₄	—	4	1	no	—
466	C₂×D₄	—	4	2	no	—
467	C₂×D₄	—	4	2	no	—
468	C₂×D₄	—	8	1	no	—
469	C₂×D₄	—	8	1	no	—
470	C₂×D₄	C₂×C₅×D₄	1	1	yes	characteristic
471	C₂×D₄	C₂×C₅×D₄	1	1	yes	characteristic
472	C₂²×C₄	—	2	1	no	—
473	C₂²×C₄	—	2	1	no	—
474	C₂²×C₄	—	4	1	no	—
475	C₂²×C₄	—	4	1	no	—
476	Q₁₆	—	8	1	no	—
477	SD₁₆	—	2	2	no	—
478	SD₁₆	—	2	2	no	—
479	SD₁₆	—	4	2	no	—
480	SD₁₆	—	4	2	no	—
481	SD₁₆	—	4	2	no	—
482	SD₁₆	—	4	2	no	—
483	SD₁₆	—	8	1	no	—
484	SD₁₆	—	8	1	no	—
485	SD₁₆	—	8	1	no	—
486	D₈	—	4	2	no	—
487	D₈	—	8	2	no	—
488	D₈	—	8	1	no	—
489	M₁₆	—	8	1	no	—
490	C₂×C₈	—	2	1	no	—
491	C₂×C₈	—	2	1	no	—
492	C₂×C₈	—	2	1	no	—
493	C₂×C₈	—	2	1	no	—
494	C₂×C₈	—	2	1	no	—
495	C₂×C₈	—	4	2	no	—
496	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
497	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
498	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
499	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
500	C₄⋊C₄	—	2	1	no	—
501	C₄⋊C₄	—	2	1	no	—
502	C₄⋊C₄	—	2	1	no	—
503	C₄⋊C₄	—	2	1	no	—
504	C₄⋊C₄	—	2	1	no	—
505	C₄⋊C₄	—	2	1	no	—
506	C₄⋊C₄	—	4	1	no	—
507	C₄⋊C₄	—	4	1	no	—
508	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
509	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
510	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
511	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
512	C₂²⋊C₄	—	2	1	no	—
513	C₂²⋊C₄	—	2	1	no	—
514	C₂²⋊C₄	—	4	1	no	—
515	C₂²⋊C₄	—	4	1	no	—
516	C₂²⋊C₄	—	4	1	no	—
517	C₂²⋊C₄	—	4	1	no	—
518	C₂²⋊C₄	—	4	1	no	—
519	C₂²⋊C₄	—	4	1	no	—
520	C₂²⋊C₄	—	4	1	no	—
521	C₄²	—	2	1	no	—
522	C₄²	—	2	1	no	—
523	C₄²	—	4	1	no	—
524	C₄²	C₂⁴×C₅	1	1	yes	characteristic
525	C₂×C₅	—	4	2	no	—
526	C₂×C₅	—	8	1	no	—
527	C₂×C₅	—	16	1	no	—
528	C₂×C₅	—	16	1	no	—
529	C₂×C₅	#3274	1	1	yes	characteristic
530	C₂×C₅	#3282	1	1	yes	characteristic
531	C₂×C₅	#3291	1	1	yes	characteristic
532	C₂³	—	2	1	no	—
533	C₂³	—	2	1	no	—
534	C₂³	—	4	1	no	—
535	C₂³	—	4	1	no	—
536	C₂³	—	8	2	no	—
537	C₂³	—	8	2	no	—
538	C₂³	—	16	1	no	—
539	Q₈	—	2	1	no	—
540	Q₈	—	2	1	no	—
541	Q₈	—	2	1	no	—
542	Q₈	—	2	1	no	—
543	Q₈	—	4	1	no	—
544	Q₈	—	4	1	no	—
545	Q₈	—	4	1	no	—
546	Q₈	—	4	1	no	—
547	Q₈	—	8	2	no	—
548	D₄	—	2	1	no	—
549	D₄	—	2	1	no	—
550	D₄	—	2	1	no	—
551	D₄	—	4	1	no	—
552	D₄	—	4	1	no	—
553	D₄	—	4	1	no	—
554	D₄	—	4	1	no	—
555	D₄	—	4	1	no	—
556	D₄	—	4	1	no	—
557	D₄	—	4	1	no	—
558	D₄	—	4	1	no	—
559	D₄	—	8	1	no	—
560	D₄	—	8	1	no	—
561	D₄	—	8	2	no	—
562	D₄	—	8	2	no	—
563	D₄	C₅×#135	1	2	yes	—
564	C₂×C₄	—	2	1	no	—
565	C₂×C₄	—	2	1	no	—
566	C₂×C₄	—	2	1	no	—
567	C₂×C₄	—	2	1	no	—
568	C₂×C₄	—	2	1	no	—
569	C₂×C₄	—	2	1	no	—
570	C₂×C₄	—	4	1	no	—
571	C₂×C₄	—	4	1	no	—
572	C₂×C₄	—	4	1	no	—
573	C₂×C₄	—	4	1	no	—
574	C₂×C₄	—	4	1	no	—
575	C₂×C₄	—	4	1	no	—
576	C₂×C₄	—	8	2	no	—
577	C₂×C₄	—	16	1	no	—
578	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
579	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
580	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
581	C₈	—	2	2	no	—
582	C₈	—	2	1	no	—
583	C₈	—	2	1	no	—
584	C₈	—	2	1	no	—
585	C₈	—	4	1	no	—
586	C₈	—	4	1	no	—
587	C₈	—	4	1	no	—
588	C₈	—	4	1	no	—
589	C₈	C₅×AGL(1,ℤ/8)	1	2	yes	—
590	C₅	#19912	1	1	yes	characteristic, direct product factor, Sylow
591	C₂²	—	2	2	no	—
592	C₂²	—	4	1	no	—
593	C₂²	—	4	1	no	—
594	C₂²	—	4	1	no	—
595	C₂²	—	4	1	no	—
596	C₂²	—	4	1	no	—
597	C₂²	—	8	1	no	—
598	C₂²	—	8	1	no	—
599	C₂²	—	8	1	no	—
600	C₂²	—	8	1	no	—
601	C₂²	—	8	1	no	—
602	C₂²	—	8	1	no	—
603	C₂²	—	16	4	no	—
604	C₂²	C₅×D₄²	1	1	yes	characteristic
605	C₄	—	2	1	no	—
606	C₄	—	4	1	no	—
607	C₄	—	4	1	no	—
608	C₄	—	4	1	no	—
609	C₄	—	4	1	no	—
610	C₄	—	4	1	no	—
611	C₄	—	4	1	no	—
612	C₄	—	8	1	no	—
613	C₄	—	8	1	no	—
614	C₄	C₂×C₅×#135	1	1	yes	characteristic
615	C₄	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
616	C₄	C₅×#576	1	1	yes	characteristic
617	C₄	C₅×#577	1	1	yes	characteristic
618	C₂	—	4	2	no	—
619	C₂	—	8	1	no	—
620	C₂	—	16	1	no	—
621	C₂	—	16	1	no	—
622	C₂	C₅×#3274	1	1	yes	characteristic
623	C₂	C₅×#3282	1	1	yes	characteristic
624	C₂	C₅×#3291	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅	D₄²
commutator, Frattini, cosocle	C₄²	C₂⁴×C₅
prime radical	C₅×#1619	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₅ ◁ C₄²×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅×#3394	C₂	semidirect
2. C₅×#3373	C₂	semidirect
3. C₅×#3324	C₂	semidirect
4. C₅×D₄×SD₁₆	C₂	semidirect
5. C₅×#1706	C₂	semidirect
6. C₅×#1702	C₂	semidirect
7. C₅×#1701	C₂	semidirect
8. C₅×#1666	C₂	semidirect
9. C₅×#1665	C₂	semidirect
10. C₅×#1650	C₂	semidirect
11. C₅×#1649	C₂	semidirect
12. C₅×#1620	C₂	semidirect
14. C₅×#1590	C₂	semidirect
15. C₅×C₈×SD₁₆	C₂	semidirect
17. C₅×#559	C₂²	semidirect
21. C₅×#500	C₂²	semidirect
25. C₅×#492	C₂²	semidirect
28. C₅×#486	C₂²	semidirect
31. C₅×#475	C₂²	semidirect
38. C₅×#462	C₂²	semidirect
47. C₅×#446	C₂²	semidirect
48. C₅×C₈×Q₈	C₂²	semidirect
56. C₅×#334	C₂²	semidirect
57. C₅×#334	C₂²	semidirect
58. C₅×#332	C₂²	semidirect
59. C₅×#332	C₂²	semidirect
61. C₅×#331	C₂²	semidirect
62. C₅×Q₈⋊C₈	C₂²	semidirect
63. C₅×Q₈⋊C₈	C₂²	semidirect
66. C₅×C₈²	C₂²	semidirect
67. #19912	C₅	direct (N × H)
146. #3394	C₂×C₅	semidirect
147. #3373	C₂×C₅	semidirect
148. #3324	C₂×C₅	semidirect
149. D₄×SD₁₆	C₂×C₅	semidirect
150. #1706	C₂×C₅	semidirect
151. #1702	C₂×C₅	semidirect
152. #1701	C₂×C₅	semidirect
153. #1666	C₂×C₅	semidirect
154. #1665	C₂×C₅	semidirect
155. #1650	C₂×C₅	semidirect
156. #1649	C₂×C₅	semidirect
157. #1620	C₂×C₅	semidirect
159. #1590	C₂×C₅	semidirect
160. C₈×SD₁₆	C₂×C₅	semidirect
237. #559	C₂²×C₅	semidirect
241. #500	C₂²×C₅	semidirect
245. #492	C₂²×C₅	semidirect
248. #486	C₂²×C₅	semidirect
251. #475	C₂²×C₅	semidirect
258. #462	C₂²×C₅	semidirect
267. #446	C₂²×C₅	semidirect
268. C₈×Q₈	C₂²×C₅	semidirect
276. #334	C₂²×C₅	semidirect
277. #334	C₂²×C₅	semidirect
278. #332	C₂²×C₅	semidirect
279. #332	C₂²×C₅	semidirect
281. #331	C₂²×C₅	semidirect
282. Q₈⋊C₈	C₂²×C₅	semidirect
283. Q₈⋊C₈	C₂²×C₅	semidirect
286. C₈²	C₂²×C₅	semidirect
590. C₅	#19912	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×#3394	2
C₅×#3373	2
C₅×#3324	2
C₅×D₄×SD₁₆	2
C₅×#1706	2
C₅×#1702	2
C₅×#1701	2
C₅×#1666	2
C₅×#1665	2
C₅×#1650	2
C₅×#1649	2
C₅×#1620	2
C₅×#1619	2
C₅×#1590	2
C₅×C₈×SD₁₆	2
#19912	5

Subgroups — C5×#19912 #11942632

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#19912 #11942632