Subgroups — C₅×#19891 #11942611

Order 1280.

686 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3384	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#3298	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#3295	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#3272	C₂	1	1	yes	maximal, characteristic
5	C₅×#1708	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#1691	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#1686	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1679	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1677	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1643	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1639	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#1635	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#1627	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#1590	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×C₈×D₈	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₅×AGL(1,ℤ/8)	—	2	1	no	—
17	C₅×#554	C₂²	1	1	yes	characteristic
18	C₅×D₄×Q₈	C₂²	1	1	yes	characteristic, complemented
19	C₅×#547	C₂²	1	1	yes	characteristic
20	C₅×D₄²	C₂²	1	1	yes	characteristic
21	C₅×#501	—	2	1	no	—
22	C₅×#498	C₂²	1	1	yes	characteristic, complemented
23	C₅×#492	C₂²	1	1	yes	characteristic
24	C₅×#487	C₂²	1	1	yes	characteristic, complemented
25	C₅×#487	C₂²	1	1	yes	characteristic, complemented
26	C₅×#486	C₂²	1	1	yes	characteristic
27	C₅×#486	C₂²	1	1	yes	characteristic
28	C₅×#483	—	2	1	no	—
29	C₅×#481	—	2	1	no	—
30	C₅×#478	—	2	1	no	—
31	C₅×#476	—	2	1	no	—
32	C₅×#476	C₂²	1	1	yes	characteristic
33	C₅×#476	C₂²	1	1	yes	characteristic, complemented
34	C₅×#475	C₂²	1	1	yes	characteristic, complemented
35	C₅×#474	C₂²	1	1	yes	characteristic
36	C₅×#468	—	2	1	no	—
37	C₅×#465	—	2	1	no	—
38	C₅×#465	—	2	1	no	—
39	C₅×#461	C₂²	1	1	yes	characteristic
40	C₅×#461	C₂²	1	1	yes	characteristic
41	C₅×#460	C₂²	1	1	yes	characteristic
42	C₅×#459	C₂²	1	1	yes	characteristic
43	C₅×#450	—	2	1	no	—
44	C₅×#450	—	2	1	no	—
45	C₅×#449	—	2	1	no	—
46	C₅×#448	—	2	1	no	—
47	C₅×#446	C₂²	1	1	yes	characteristic, complemented
48	C₅×#442	—	2	1	no	—
49	C₄×C₅×SD₁₆	C₂²	1	1	yes	characteristic
50	C₄×C₅×D₈	C₂²	1	1	yes	characteristic
51	C₅×#436	C₂²	1	1	yes	characteristic
52	C₅×C₈×D₄	C₂²	1	1	yes	characteristic
53	C₅×C₈×D₄	C₂²	1	1	yes	characteristic, complemented
54	C₂×C₅×#103	—	2	1	no	—
55	C₂×C₅×#102	—	2	1	no	—
56	C₅×#335	C₂²	1	1	yes	characteristic, complemented
57	C₅×#334	C₂²	1	1	yes	characteristic, complemented
58	C₅×#333	C₂²	1	1	yes	characteristic, complemented
59	C₅×#332	C₂²	1	1	yes	characteristic, complemented
60	C₅×#332	C₂²	1	1	yes	characteristic, complemented
61	C₅×#331	C₂²	1	1	yes	characteristic
62	C₅×Q₈⋊C₈	C₂²	1	1	yes	characteristic, complemented
63	C₅×D₄⋊C₈	C₂²	1	1	yes	characteristic
64	C₅×D₄⋊C₈	C₂²	1	1	yes	characteristic
65	C₅×D₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
66	C₅×C₈²	C₂²	1	1	yes	characteristic, complemented
67	#19891	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
68	C₂×C₅×#41	—	2	1	no	—
69	C₂²×C₅×Q₈	—	2	1	no	—
70	C₂²×C₅×D₄	—	2	1	no	—
71	C₂²×C₅×D₄	—	2	1	no	—
72	C₅×AGL(1,ℤ/8)	—	4	4	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	D₄	1	1	yes	characteristic
79	C₂×C₅×D₈	—	2	1	no	—
80	C₂×C₅×D₈	D₄	1	1	yes	characteristic
81	C₂×C₅×M₁₆	—	2	1	no	—
82	C₂²×C₅×C₈	—	2	1	no	—
83	C₂²×C₅×C₈	—	2	1	no	—
84	C₅×C₄⋊Q₈	—	2	1	no	—
85	C₅×C₄⋊Q₈	C₂³	1	1	yes	characteristic
86	C₅×C₄⋊Q₈	C₂³	1	1	yes	characteristic
87	C₅×C₄⋊Q₈	C₂³	1	1	yes	characteristic
88	C₅×#127	C₂³	1	1	yes	characteristic
89	C₅×#125	—	2	1	no	—
90	C₅×#123	—	4	1	no	—
91	C₅×C₂²⋊Q₈	—	2	1	no	—
92	C₅×C₂²⋊Q₈	—	2	1	no	—
93	C₅×C₂²⋊Q₈	—	2	1	no	—
94	C₅×C₂²⋊Q₈	—	4	1	no	—
95	C₅×C₂²⋊Q₈	—	4	1	no	—
96	C₅×#121	—	2	1	no	—
97	C₅×#121	—	2	1	no	—
98	C₅×#121	—	2	1	no	—
99	C₅×#120	—	4	1	no	—
100	C₄×C₅×Q₈	C₂³	1	1	yes	characteristic
101	C₄×C₅×D₄	—	2	1	no	—
102	C₄×C₅×D₄	—	2	1	no	—
103	C₄×C₅×D₄	C₂³	1	1	yes	characteristic
104	C₄×C₅×D₄	C₂³	1	1	yes	characteristic
105	C₄×C₅×D₄	C₂³	1	1	yes	characteristic
106	C₂×C₅×C₄⋊C₄	—	2	1	no	—
107	C₂×C₅×C₄⋊C₄	—	2	1	no	—
108	C₅×#107	—	2	1	no	—
109	C₅×#107	D₄	1	1	yes	characteristic
110	C₅×#106	—	2	1	no	—
111	C₅×#106	—	2	1	no	—
112	C₅×#106	—	2	1	no	—
113	C₅×#106	—	2	1	no	—
114	C₅×#106	—	2	1	no	—
115	C₅×#106	D₄	1	1	yes	characteristic
116	C₅×C₄⋊C₈	—	2	1	no	—
117	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
118	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
119	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
120	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
121	C₅×#103	—	2	1	no	—
122	C₅×#103	—	2	1	no	—
123	C₅×#103	—	2	1	no	—
124	C₅×#103	—	2	1	no	—
125	C₅×#103	—	2	1	no	—
126	C₅×#103	—	4	1	no	—
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	—	4	1	no	—
136	C₅×#102	D₄	1	1	yes	characteristic
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×C₂²⋊C₈	—	2	1	no	—
142	C₅×#97	—	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	#3384	C₂×C₅	1	1	yes	characteristic, complemented
147	#3298	C₂×C₅	1	1	yes	characteristic, complemented
148	#3295	C₂×C₅	1	1	yes	characteristic, complemented
149	#3272	C₂×C₅	1	1	yes	characteristic
150	#1708	C₂×C₅	1	1	yes	characteristic, complemented
151	#1691	C₂×C₅	1	1	yes	characteristic, complemented
152	#1686	C₂×C₅	1	1	yes	characteristic, complemented
153	#1679	C₂×C₅	1	1	yes	characteristic, complemented
154	#1677	C₂×C₅	1	1	yes	characteristic, complemented
155	#1643	C₂×C₅	1	1	yes	characteristic, complemented
156	#1639	C₂×C₅	1	1	yes	characteristic, complemented
157	#1635	C₂×C₅	1	1	yes	characteristic, complemented
158	#1627	C₂×C₅	1	1	yes	characteristic, complemented
159	#1590	C₂×C₅	1	1	yes	characteristic, complemented
160	C₈×D₈	C₂×C₅	1	1	yes	characteristic, complemented
161	C₂⁴×C₅	—	4	1	no	—
162	C₅×#41	—	4	2	no	—
163	C₅×#41	—	8	1	no	—
164	C₂×C₅×Q₈	—	2	1	no	—
165	C₂×C₅×Q₈	—	2	1	no	—
166	C₂×C₅×Q₈	—	2	1	no	—
167	C₂×C₅×Q₈	—	4	1	no	—
168	C₂×C₅×Q₈	—	4	2	no	—
169	C₂×C₅×Q₈	—	8	1	no	—
170	C₂×C₅×Q₈	C₂×D₄	1	1	yes	characteristic
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	—	4	1	no	—
175	C₂×C₅×D₄	—	4	1	no	—
176	C₂×C₅×D₄	—	4	2	no	—
177	C₂×C₅×D₄	—	4	2	no	—
178	C₂×C₅×D₄	—	4	1	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	C₂×C₅×D₄	C₂×D₄	1	1	yes	characteristic
184	C₂²×C₄×C₅	—	2	1	no	—
185	C₂²×C₄×C₅	—	2	1	no	—
186	C₂²×C₄×C₅	—	2	1	no	—
187	C₂²×C₄×C₅	—	4	1	no	—
188	C₂²×C₄×C₅	—	4	1	no	—
189	C₂²×C₄×C₅	—	4	1	no	—
190	C₅×SD₁₆	—	4	1	no	—
191	C₅×SD₁₆	—	4	2	no	—
192	C₅×SD₁₆	—	4	2	no	—
193	C₅×SD₁₆	—	8	1	no	—
194	C₅×SD₁₆	—	8	1	no	—
195	C₅×SD₁₆	—	8	1	no	—
196	C₅×D₈	—	4	2	no	—
197	C₅×D₈	SD₁₆	1	4	yes	complemented
198	C₅×M₁₆	—	4	2	no	—
199	C₂×C₅×C₈	—	2	1	no	—
200	C₂×C₅×C₈	—	2	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	—	8	1	no	—
205	C₂×C₅×C₈	—	8	1	no	—
206	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
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	C₅×C₄⋊C₄	—	2	1	no	—
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	—	4	1	no	—
220	C₅×C₄⋊C₄	—	4	1	no	—
221	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
222	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
223	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
224	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
225	C₅×C₂²⋊C₄	—	2	1	no	—
226	C₅×C₂²⋊C₄	—	2	1	no	—
227	C₅×C₂²⋊C₄	—	2	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	C₂⁴	1	1	yes	characteristic
234	C₂×AGL(1,ℤ/8)	—	2	1	no	—
235	#554	C₂²×C₅	1	1	yes	characteristic
236	D₄×Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
237	#547	C₂²×C₅	1	1	yes	characteristic
238	D₄²	C₂²×C₅	1	1	yes	characteristic
239	#501	—	2	1	no	—
240	#498	C₂²×C₅	1	1	yes	characteristic, complemented
241	#492	C₂²×C₅	1	1	yes	characteristic
242	#487	C₂²×C₅	1	1	yes	characteristic, complemented
243	#487	C₂²×C₅	1	1	yes	characteristic, complemented
244	#486	C₂²×C₅	1	1	yes	characteristic
245	#486	C₂²×C₅	1	1	yes	characteristic
246	#483	—	2	1	no	—
247	#481	—	2	1	no	—
248	#478	—	2	1	no	—
249	#476	—	2	1	no	—
250	#476	C₂²×C₅	1	1	yes	characteristic
251	#476	C₂²×C₅	1	1	yes	characteristic, complemented
252	#475	C₂²×C₅	1	1	yes	characteristic, complemented
253	#474	C₂²×C₅	1	1	yes	characteristic
254	#468	—	2	1	no	—
255	#465	—	2	1	no	—
256	#465	—	2	1	no	—
257	#461	C₂²×C₅	1	1	yes	characteristic
258	#461	C₂²×C₅	1	1	yes	characteristic
259	#460	C₂²×C₅	1	1	yes	characteristic
260	#459	C₂²×C₅	1	1	yes	characteristic
261	#450	—	2	1	no	—
262	#450	—	2	1	no	—
263	#449	—	2	1	no	—
264	#448	—	2	1	no	—
265	#446	C₂²×C₅	1	1	yes	characteristic, complemented
266	#442	—	2	1	no	—
267	C₄×SD₁₆	C₂²×C₅	1	1	yes	characteristic
268	C₄×D₈	C₂²×C₅	1	1	yes	characteristic
269	#436	C₂²×C₅	1	1	yes	characteristic
270	C₈×D₄	C₂²×C₅	1	1	yes	characteristic
271	C₈×D₄	C₂²×C₅	1	1	yes	characteristic, complemented
272	C₂×#103	—	2	1	no	—
273	C₂×#102	—	2	1	no	—
274	#335	C₂²×C₅	1	1	yes	characteristic, complemented
275	#334	C₂²×C₅	1	1	yes	characteristic, complemented
276	#333	C₂²×C₅	1	1	yes	characteristic, complemented
277	#332	C₂²×C₅	1	1	yes	characteristic, complemented
278	#332	C₂²×C₅	1	1	yes	characteristic, complemented
279	#331	C₂²×C₅	1	1	yes	characteristic
280	Q₈⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
281	D₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
282	D₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
283	D₄⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
284	C₈²	C₂²×C₅	1	1	yes	characteristic, complemented
285	C₂³×C₅	—	2	1	no	—
286	C₂³×C₅	—	2	1	no	—
287	C₂³×C₅	—	2	1	no	—
288	C₂³×C₅	—	4	1	no	—
289	C₂³×C₅	—	8	2	no	—
290	C₂³×C₅	—	8	2	no	—
291	C₂³×C₅	—	16	1	no	—
292	C₅×Q₈	—	2	1	no	—
293	C₅×Q₈	—	2	1	no	—
294	C₅×Q₈	—	4	1	no	—
295	C₅×Q₈	—	4	1	no	—
296	C₅×Q₈	—	4	1	no	—
297	C₅×Q₈	—	4	1	no	—
298	C₅×Q₈	—	8	1	no	—
299	C₅×Q₈	—	8	2	no	—
300	C₅×D₄	—	2	1	no	—
301	C₅×D₄	—	2	1	no	—
302	C₅×D₄	—	2	1	no	—
303	C₅×D₄	—	2	1	no	—
304	C₅×D₄	—	4	1	no	—
305	C₅×D₄	—	4	1	no	—
306	C₅×D₄	—	4	1	no	—
307	C₅×D₄	—	4	1	no	—
308	C₅×D₄	—	8	1	no	—
309	C₅×D₄	—	8	2	no	—
310	C₅×D₄	—	8	2	no	—
311	C₅×D₄	—	8	2	no	—
312	C₅×D₄	C₂×SD₁₆	1	2	yes	—
313	C₅×D₄	C₂×SD₁₆	1	2	yes	—
314	C₂×C₄×C₅	—	2	1	no	—
315	C₂×C₄×C₅	—	2	1	no	—
316	C₂×C₄×C₅	—	2	1	no	—
317	C₂×C₄×C₅	—	2	1	no	—
318	C₂×C₄×C₅	—	2	1	no	—
319	C₂×C₄×C₅	—	4	1	no	—
320	C₂×C₄×C₅	—	4	1	no	—
321	C₂×C₄×C₅	—	4	1	no	—
322	C₂×C₄×C₅	—	4	1	no	—
323	C₂×C₄×C₅	—	4	1	no	—
324	C₂×C₄×C₅	—	4	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	—	8	2	no	—
329	C₂×C₄×C₅	—	8	2	no	—
330	C₂×C₄×C₅	—	16	1	no	—
331	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
332	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
333	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
334	C₅×C₈	—	2	1	no	—
335	C₅×C₈	—	2	1	no	—
336	C₅×C₈	—	2	1	no	—
337	C₅×C₈	—	4	1	no	—
338	C₅×C₈	—	4	1	no	—
339	C₅×C₈	—	4	1	no	—
340	C₅×C₈	—	4	1	no	—
341	C₅×C₈	—	4	1	no	—
342	C₅×C₈	C₂×SD₁₆	1	2	yes	—
343	C₂×#41	—	2	1	no	—
344	C₂²×Q₈	—	2	1	no	—
345	C₂²×D₄	—	2	1	no	—
346	C₂²×D₄	—	2	1	no	—
347	AGL(1,ℤ/8)	—	4	4	no	—
348	C₂×SD₁₆	—	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	C₅×D₄	1	1	yes	characteristic
354	C₂×D₈	—	2	1	no	—
355	C₂×D₈	C₅×D₄	1	1	yes	characteristic
356	C₂×M₁₆	—	2	1	no	—
357	C₂²×C₈	—	2	1	no	—
358	C₂²×C₈	—	2	1	no	—
359	C₄⋊Q₈	—	2	1	no	—
360	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
361	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
362	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
363	#127	C₂³×C₅	1	1	yes	characteristic
364	#125	—	2	1	no	—
365	#123	—	4	1	no	—
366	C₂²⋊Q₈	—	2	1	no	—
367	C₂²⋊Q₈	—	2	1	no	—
368	C₂²⋊Q₈	—	2	1	no	—
369	C₂²⋊Q₈	—	4	1	no	—
370	C₂²⋊Q₈	—	4	1	no	—
371	#121	—	2	1	no	—
372	#121	—	2	1	no	—
373	#121	—	2	1	no	—
374	#120	—	4	1	no	—
375	C₄×Q₈	C₂³×C₅	1	1	yes	characteristic
376	C₄×D₄	—	2	1	no	—
377	C₄×D₄	—	2	1	no	—
378	C₄×D₄	C₂³×C₅	1	1	yes	characteristic
379	C₄×D₄	C₂³×C₅	1	1	yes	characteristic
380	C₄×D₄	C₂³×C₅	1	1	yes	characteristic
381	C₂×C₄⋊C₄	—	2	1	no	—
382	C₂×C₄⋊C₄	—	2	1	no	—
383	#107	—	2	1	no	—
384	#107	C₅×D₄	1	1	yes	characteristic
385	#106	—	2	1	no	—
386	#106	—	2	1	no	—
387	#106	—	2	1	no	—
388	#106	—	2	1	no	—
389	#106	—	2	1	no	—
390	#106	C₅×D₄	1	1	yes	characteristic
391	C₄⋊C₈	—	2	1	no	—
392	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
393	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
394	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
395	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
396	#103	—	2	1	no	—
397	#103	—	2	1	no	—
398	#103	—	2	1	no	—
399	#103	—	2	1	no	—
400	#103	—	2	1	no	—
401	#103	—	4	1	no	—
402	#103	C₅×D₄	1	1	yes	characteristic
403	#102	—	2	1	no	—
404	#102	—	2	1	no	—
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	—	4	1	no	—
411	#102	C₅×D₄	1	1	yes	characteristic
412	#102	C₅×D₄	1	1	yes	characteristic
413	#102	C₅×D₄	1	1	yes	characteristic
414	C₂²⋊C₈	—	2	1	no	—
415	C₂²⋊C₈	—	2	1	no	—
416	C₂²⋊C₈	—	2	1	no	—
417	#97	—	2	1	no	—
418	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
419	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
420	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
421	C₂²×C₅	—	2	2	no	—
422	C₂²×C₅	—	2	2	no	—
423	C₂²×C₅	—	4	1	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	—	4	1	no	—
430	C₂²×C₅	—	8	1	no	—
431	C₂²×C₅	—	8	1	no	—
432	C₂²×C₅	—	8	1	no	—
433	C₂²×C₅	—	16	4	no	—
434	C₂²×C₅	D₄²	1	1	yes	characteristic
435	C₄×C₅	—	2	1	no	—
436	C₄×C₅	—	4	1	no	—
437	C₄×C₅	—	4	1	no	—
438	C₄×C₅	—	4	1	no	—
439	C₄×C₅	—	4	1	no	—
440	C₄×C₅	—	4	1	no	—
441	C₄×C₅	—	8	1	no	—
442	C₄×C₅	—	8	1	no	—
443	C₄×C₅	—	8	1	no	—
444	C₄×C₅	C₂²×SD₁₆	1	1	yes	characteristic
445	C₄×C₅	#575	1	1	yes	characteristic
446	C₄×C₅	#576	1	1	yes	characteristic
447	C₄×C₅	#577	1	1	yes	characteristic
448	C₂⁴	—	4	1	no	—
449	#41	—	4	2	no	—
450	#41	—	8	1	no	—
451	C₂×Q₈	—	2	1	no	—
452	C₂×Q₈	—	2	1	no	—
453	C₂×Q₈	—	2	1	no	—
454	C₂×Q₈	—	4	1	no	—
455	C₂×Q₈	—	4	2	no	—
456	C₂×Q₈	—	8	1	no	—
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	—	4	1	no	—
462	C₂×D₄	—	4	1	no	—
463	C₂×D₄	—	4	2	no	—
464	C₂×D₄	—	4	2	no	—
465	C₂×D₄	—	4	1	no	—
466	C₂×D₄	—	8	1	no	—
467	C₂×D₄	—	8	1	no	—
468	C₂×D₄	C₂×C₅×D₄	1	1	yes	characteristic
469	C₂×D₄	C₂×C₅×D₄	1	1	yes	characteristic
470	C₂×D₄	C₂×C₅×D₄	1	1	yes	characteristic
471	C₂²×C₄	—	2	1	no	—
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	C₂²×C₄	—	4	1	no	—
477	SD₁₆	—	4	1	no	—
478	SD₁₆	—	4	2	no	—
479	SD₁₆	—	4	2	no	—
480	SD₁₆	—	8	1	no	—
481	SD₁₆	—	8	1	no	—
482	SD₁₆	—	8	1	no	—
483	D₈	—	4	2	no	—
484	D₈	C₅×SD₁₆	1	4	yes	complemented
485	M₁₆	—	4	2	no	—
486	C₂×C₈	—	2	1	no	—
487	C₂×C₈	—	2	1	no	—
488	C₂×C₈	—	2	1	no	—
489	C₂×C₈	—	2	1	no	—
490	C₂×C₈	—	2	1	no	—
491	C₂×C₈	—	8	1	no	—
492	C₂×C₈	—	8	1	no	—
493	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
494	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
495	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
496	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
497	C₄⋊C₄	—	2	1	no	—
498	C₄⋊C₄	—	2	1	no	—
499	C₄⋊C₄	—	2	1	no	—
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	—	4	1	no	—
505	C₄⋊C₄	—	4	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	—	2	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	C₄²	—	2	1	no	—
520	C₄²	C₂⁴×C₅	1	1	yes	characteristic
521	C₂×C₅	—	4	2	no	—
522	C₂×C₅	—	4	2	no	—
523	C₂×C₅	—	8	1	no	—
524	C₂×C₅	—	16	1	no	—
525	C₂×C₅	#3273	1	1	yes	characteristic
526	C₂×C₅	D₄×SD₁₆	1	1	yes	characteristic
527	C₂×C₅	#3290	1	1	yes	characteristic
528	C₂³	—	2	1	no	—
529	C₂³	—	2	1	no	—
530	C₂³	—	2	1	no	—
531	C₂³	—	4	1	no	—
532	C₂³	—	8	2	no	—
533	C₂³	—	8	2	no	—
534	C₂³	—	16	1	no	—
535	Q₈	—	2	1	no	—
536	Q₈	—	2	1	no	—
537	Q₈	—	4	1	no	—
538	Q₈	—	4	1	no	—
539	Q₈	—	4	1	no	—
540	Q₈	—	4	1	no	—
541	Q₈	—	8	1	no	—
542	Q₈	—	8	2	no	—
543	D₄	—	2	1	no	—
544	D₄	—	2	1	no	—
545	D₄	—	2	1	no	—
546	D₄	—	2	1	no	—
547	D₄	—	4	1	no	—
548	D₄	—	4	1	no	—
549	D₄	—	4	1	no	—
550	D₄	—	4	1	no	—
551	D₄	—	8	1	no	—
552	D₄	—	8	2	no	—
553	D₄	—	8	2	no	—
554	D₄	—	8	2	no	—
555	D₄	C₂×C₅×SD₁₆	1	2	yes	—
556	D₄	C₂×C₅×SD₁₆	1	2	yes	—
557	C₂×C₄	—	2	1	no	—
558	C₂×C₄	—	2	1	no	—
559	C₂×C₄	—	2	1	no	—
560	C₂×C₄	—	2	1	no	—
561	C₂×C₄	—	2	1	no	—
562	C₂×C₄	—	4	1	no	—
563	C₂×C₄	—	4	1	no	—
564	C₂×C₄	—	4	1	no	—
565	C₂×C₄	—	4	1	no	—
566	C₂×C₄	—	4	1	no	—
567	C₂×C₄	—	4	1	no	—
568	C₂×C₄	—	4	1	no	—
569	C₂×C₄	—	4	1	no	—
570	C₂×C₄	—	4	1	no	—
571	C₂×C₄	—	8	2	no	—
572	C₂×C₄	—	8	2	no	—
573	C₂×C₄	—	16	1	no	—
574	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
575	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
576	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
577	C₈	—	2	1	no	—
578	C₈	—	2	1	no	—
579	C₈	—	2	1	no	—
580	C₈	—	4	1	no	—
581	C₈	—	4	1	no	—
582	C₈	—	4	1	no	—
583	C₈	—	4	1	no	—
584	C₈	—	4	1	no	—
585	C₈	C₂×C₅×SD₁₆	1	2	yes	—
586	C₅	#19891	1	1	yes	characteristic, direct product factor, Sylow
587	C₂²	—	2	2	no	—
588	C₂²	—	2	2	no	—
589	C₂²	—	4	1	no	—
590	C₂²	—	4	1	no	—
591	C₂²	—	4	1	no	—
592	C₂²	—	4	1	no	—
593	C₂²	—	4	1	no	—
594	C₂²	—	4	1	no	—
595	C₂²	—	4	1	no	—
596	C₂²	—	8	1	no	—
597	C₂²	—	8	1	no	—
598	C₂²	—	8	1	no	—
599	C₂²	—	16	4	no	—
600	C₂²	C₅×D₄²	1	1	yes	characteristic
601	C₄	—	2	1	no	—
602	C₄	—	4	1	no	—
603	C₄	—	4	1	no	—
604	C₄	—	4	1	no	—
605	C₄	—	4	1	no	—
606	C₄	—	4	1	no	—
607	C₄	—	8	1	no	—
608	C₄	—	8	1	no	—
609	C₄	—	8	1	no	—
610	C₄	C₂²×C₅×SD₁₆	1	1	yes	characteristic
611	C₄	C₅×#575	1	1	yes	characteristic
612	C₄	C₅×#576	1	1	yes	characteristic
613	C₄	C₅×#577	1	1	yes	characteristic
614	C₂	—	4	2	no	—
615	C₂	—	4	2	no	—
616	C₂	—	8	1	no	—
617	C₂	—	16	1	no	—
618	C₂	C₅×#3273	1	1	yes	characteristic
619	C₂	C₅×D₄×SD₁₆	1	1	yes	characteristic
620	C₂	C₅×#3290	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅	D₄²
commutator, Frattini, cosocle	C₄²	C₂⁴×C₅
prime radical	C₅×#3272	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×#3384	C₂	semidirect
2. C₅×#3298	C₂	semidirect
3. C₅×#3295	C₂	semidirect
5. C₅×#1708	C₂	semidirect
6. C₅×#1691	C₂	semidirect
7. C₅×#1686	C₂	semidirect
8. C₅×#1679	C₂	semidirect
9. C₅×#1677	C₂	semidirect
10. C₅×#1643	C₂	semidirect
11. C₅×#1639	C₂	semidirect
12. C₅×#1635	C₂	semidirect
13. C₅×#1627	C₂	semidirect
14. C₅×#1590	C₂	semidirect
15. C₅×C₈×D₈	C₂	semidirect
18. C₅×D₄×Q₈	C₂²	semidirect
22. C₅×#498	C₂²	semidirect
24. C₅×#487	C₂²	semidirect
25. C₅×#487	C₂²	semidirect
33. C₅×#476	C₂²	semidirect
34. C₅×#475	C₂²	semidirect
47. C₅×#446	C₂²	semidirect
53. C₅×C₈×D₄	C₂²	semidirect
56. C₅×#335	C₂²	semidirect
57. C₅×#334	C₂²	semidirect
58. C₅×#333	C₂²	semidirect
59. C₅×#332	C₂²	semidirect
60. C₅×#332	C₂²	semidirect
62. C₅×Q₈⋊C₈	C₂²	semidirect
65. C₅×D₄⋊C₈	C₂²	semidirect
66. C₅×C₈²	C₂²	semidirect
67. #19891	C₅	direct (N × H)
146. #3384	C₂×C₅	semidirect
147. #3298	C₂×C₅	semidirect
148. #3295	C₂×C₅	semidirect
150. #1708	C₂×C₅	semidirect
151. #1691	C₂×C₅	semidirect
152. #1686	C₂×C₅	semidirect
153. #1679	C₂×C₅	semidirect
154. #1677	C₂×C₅	semidirect
155. #1643	C₂×C₅	semidirect
156. #1639	C₂×C₅	semidirect
157. #1635	C₂×C₅	semidirect
158. #1627	C₂×C₅	semidirect
159. #1590	C₂×C₅	semidirect
160. C₈×D₈	C₂×C₅	semidirect
197. C₅×D₈	SD₁₆	semidirect
236. D₄×Q₈	C₂²×C₅	semidirect
240. #498	C₂²×C₅	semidirect
242. #487	C₂²×C₅	semidirect
243. #487	C₂²×C₅	semidirect
251. #476	C₂²×C₅	semidirect
252. #475	C₂²×C₅	semidirect
265. #446	C₂²×C₅	semidirect
271. C₈×D₄	C₂²×C₅	semidirect
274. #335	C₂²×C₅	semidirect
275. #334	C₂²×C₅	semidirect
276. #333	C₂²×C₅	semidirect
277. #332	C₂²×C₅	semidirect
278. #332	C₂²×C₅	semidirect
280. Q₈⋊C₈	C₂²×C₅	semidirect
283. D₄⋊C₈	C₂²×C₅	semidirect
284. C₈²	C₂²×C₅	semidirect
484. D₈	C₅×SD₁₆	semidirect
586. C₅	#19891	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×#3384	2
C₅×#3298	2
C₅×#3295	2
C₅×#3272	2
C₅×#1708	2
C₅×#1691	2
C₅×#1686	2
C₅×#1679	2
C₅×#1677	2
C₅×#1643	2
C₅×#1639	2
C₅×#1635	2
C₅×#1627	2
C₅×#1590	2
C₅×C₈×D₈	2
#19891	5

Subgroups — C5×#19891 #11942611

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#19891 #11942611