Subgroups — C₅×#19892 #11942612

Order 1280.

720 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3392	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#3386	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×D₄×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#3274	C₂	1	1	yes	maximal, characteristic
5	C₅×#1706	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#1693	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#1688	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×#1642	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1639	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#1627	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#1626	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#1590	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×C₈×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₅×AGL(1,ℤ/8)	—	2	1	no	—
17	C₂²×C₅×SD₁₆	—	2	1	no	—
18	C₅×#557	C₂²	1	1	yes	characteristic, complemented
19	C₅×#550	C₂²	1	1	yes	characteristic
20	C₅×D₄×Q₈	C₂²	1	1	yes	characteristic
21	C₅×D₄²	C₂²	1	1	yes	characteristic
22	C₅×#501	—	2	1	no	—
23	C₅×#500	C₂²	1	1	yes	characteristic, complemented
24	C₅×#493	C₂²	1	1	yes	characteristic
25	C₅×#492	—	2	1	no	—
26	C₅×#492	C₂²	1	1	yes	characteristic
27	C₅×#492	C₂²	1	1	yes	characteristic, complemented
28	C₅×#486	C₂²	1	1	yes	characteristic
29	C₅×#486	C₂²	1	1	yes	characteristic, complemented
30	C₅×#478	—	2	1	no	—
31	C₅×#477	—	2	1	no	—
32	C₅×#475	C₂²	1	1	yes	characteristic, complemented
33	C₅×#474	C₂²	1	1	yes	characteristic
34	C₅×#469	—	2	1	no	—
35	C₅×#465	—	2	1	no	—
36	C₅×#461	—	2	1	no	—
37	C₅×#461	C₂²	1	1	yes	characteristic
38	C₅×#461	C₂²	1	1	yes	characteristic
39	C₅×#460	—	2	1	no	—
40	C₅×#460	C₂²	1	1	yes	characteristic
41	C₅×#460	C₂²	1	1	yes	characteristic
42	C₅×#460	C₂²	1	1	yes	characteristic, complemented
43	C₅×#459	C₂²	1	1	yes	characteristic
44	C₅×#450	—	2	1	no	—
45	C₅×#449	—	2	1	no	—
46	C₅×#448	—	2	1	no	—
47	C₅×#447	—	2	1	no	—
48	C₅×#446	C₂²	1	1	yes	characteristic, complemented
49	C₅×C₈×Q₈	C₂²	1	1	yes	characteristic, complemented
50	C₅×#440	—	2	1	no	—
51	C₄×C₅×SD₁₆	—	2	1	no	—
52	C₄×C₅×SD₁₆	C₂²	1	1	yes	characteristic
53	C₄×C₅×SD₁₆	C₂²	1	1	yes	characteristic
54	C₅×#436	C₂²	1	1	yes	characteristic
55	C₅×C₈×D₄	C₂²	1	1	yes	characteristic
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	#19892	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	—	2	1	no	—
79	C₂×C₅×SD₁₆	—	2	1	no	—
80	C₂×C₅×SD₁₆	—	2	1	no	—
81	C₂×C₅×SD₁₆	—	2	1	no	—
82	C₂×C₅×SD₁₆	—	4	4	no	—
83	C₂×C₅×SD₁₆	D₄	1	1	yes	characteristic
84	C₂×C₅×SD₁₆	D₄	1	1	yes	characteristic
85	C₂×C₅×D₈	—	2	1	no	—
86	C₂×C₅×D₈	—	2	1	no	—
87	C₂×C₅×D₈	—	2	1	no	—
88	C₂×C₅×M₁₆	—	2	1	no	—
89	C₂²×C₅×C₈	—	2	1	no	—
90	C₅×C₄⋊Q₈	—	2	1	no	—
91	C₅×C₄⋊Q₈	—	2	1	no	—
92	C₅×C₄⋊Q₈	C₂³	1	1	yes	characteristic
93	C₅×C₄⋊Q₈	C₂³	1	1	yes	characteristic
94	C₅×#127	—	2	1	no	—
95	C₅×#127	C₂³	1	1	yes	characteristic
96	C₅×#127	C₂³	1	1	yes	characteristic
97	C₅×#125	—	2	1	no	—
98	C₅×#125	—	4	1	no	—
99	C₅×C₂²⋊Q₈	—	2	1	no	—
100	C₅×C₂²⋊Q₈	—	4	1	no	—
101	C₅×#121	—	2	1	no	—
102	C₅×#121	—	2	1	no	—
103	C₅×#121	—	2	1	no	—
104	C₅×#121	—	4	1	no	—
105	C₅×#120	—	4	1	no	—
106	C₄×C₅×Q₈	—	2	1	no	—
107	C₄×C₅×Q₈	—	2	1	no	—
108	C₄×C₅×Q₈	C₂³	1	1	yes	characteristic
109	C₄×C₅×Q₈	C₂³	1	1	yes	characteristic
110	C₄×C₅×D₄	—	2	1	no	—
111	C₄×C₅×D₄	—	2	1	no	—
112	C₄×C₅×D₄	C₂³	1	1	yes	characteristic
113	C₄×C₅×D₄	C₂³	1	1	yes	characteristic
114	C₅×#107	—	2	1	no	—
115	C₅×#107	—	2	1	no	—
116	C₅×#107	—	2	1	no	—
117	C₅×#106	—	2	1	no	—
118	C₅×#106	D₄	1	1	yes	characteristic
119	C₅×#106	D₄	1	1	yes	characteristic
120	C₅×C₄⋊C₈	—	2	1	no	—
121	C₅×C₄⋊C₈	—	2	1	no	—
122	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
123	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
124	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
125	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
126	C₅×#103	—	2	1	no	—
127	C₅×#103	—	2	1	no	—
128	C₅×#103	—	2	1	no	—
129	C₅×#103	D₄	1	1	yes	characteristic
130	C₅×#103	D₄	1	1	yes	characteristic
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	—	4	1	no	—
137	C₅×#102	—	4	1	no	—
138	C₅×#102	D₄	1	1	yes	characteristic
139	C₅×#102	D₄	1	1	yes	characteristic
140	C₅×C₂²⋊C₈	—	2	1	no	—
141	C₅×C₂²⋊C₈	—	2	1	no	—
142	C₅×#97	—	2	1	no	—
143	C₄×C₅×C₈	—	2	1	no	—
144	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
145	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
146	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
147	#3392	C₂×C₅	1	1	yes	characteristic, complemented
148	#3386	C₂×C₅	1	1	yes	characteristic, complemented
149	D₄×SD₁₆	C₂×C₅	1	1	yes	characteristic, complemented
150	#3274	C₂×C₅	1	1	yes	characteristic
151	#1706	C₂×C₅	1	1	yes	characteristic, complemented
152	#1693	C₂×C₅	1	1	yes	characteristic, complemented
153	#1688	C₂×C₅	1	1	yes	characteristic, complemented
154	#1666	C₂×C₅	1	1	yes	characteristic, complemented
155	#1665	C₂×C₅	1	1	yes	characteristic, complemented
156	#1642	C₂×C₅	1	1	yes	characteristic, complemented
157	#1639	C₂×C₅	1	1	yes	characteristic, complemented
158	#1627	C₂×C₅	1	1	yes	characteristic, complemented
159	#1626	C₂×C₅	1	1	yes	characteristic, complemented
160	#1590	C₂×C₅	1	1	yes	characteristic, complemented
161	C₈×SD₁₆	C₂×C₅	1	1	yes	characteristic, complemented
162	C₂⁴×C₅	—	4	1	no	—
163	C₅×#41	—	4	2	no	—
164	C₅×#41	—	8	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×Q₈	C₂×D₄	1	1	yes	characteristic
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	—	2	1	no	—
176	C₂×C₅×D₄	—	2	1	no	—
177	C₂×C₅×D₄	—	2	1	no	—
178	C₂×C₅×D₄	—	4	1	no	—
179	C₂×C₅×D₄	—	4	1	no	—
180	C₂×C₅×D₄	—	4	1	no	—
181	C₂×C₅×D₄	—	4	1	no	—
182	C₂×C₅×D₄	—	4	2	no	—
183	C₂×C₅×D₄	—	4	2	no	—
184	C₂×C₅×D₄	—	8	1	no	—
185	C₂×C₅×D₄	—	8	1	no	—
186	C₂×C₅×D₄	C₂×D₄	1	1	yes	characteristic
187	C₂×C₅×D₄	C₂×D₄	1	1	yes	characteristic
188	C₂²×C₄×C₅	—	2	1	no	—
189	C₂²×C₄×C₅	—	2	1	no	—
190	C₂²×C₄×C₅	—	4	1	no	—
191	C₂²×C₄×C₅	—	4	1	no	—
192	C₅×SD₁₆	—	2	2	no	—
193	C₅×SD₁₆	—	4	2	no	—
194	C₅×SD₁₆	—	4	2	no	—
195	C₅×SD₁₆	—	4	2	no	—
196	C₅×SD₁₆	—	4	2	no	—
197	C₅×SD₁₆	—	4	2	no	—
198	C₅×SD₁₆	—	8	1	no	—
199	C₅×SD₁₆	—	8	1	no	—
200	C₅×SD₁₆	—	8	1	no	—
201	C₅×SD₁₆	—	8	1	no	—
202	C₅×SD₁₆	SD₁₆	1	4	yes	complemented
203	C₅×D₈	—	4	2	no	—
204	C₅×D₈	—	4	2	no	—
205	C₅×D₈	—	8	1	no	—
206	C₅×M₁₆	—	4	2	no	—
207	C₂×C₅×C₈	—	2	1	no	—
208	C₂×C₅×C₈	—	2	1	no	—
209	C₂×C₅×C₈	—	2	1	no	—
210	C₂×C₅×C₈	—	2	1	no	—
211	C₂×C₅×C₈	—	2	1	no	—
212	C₂×C₅×C₈	—	4	2	no	—
213	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
214	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
215	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
216	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
217	C₅×C₄⋊C₄	—	2	1	no	—
218	C₅×C₄⋊C₄	—	2	1	no	—
219	C₅×C₄⋊C₄	—	2	1	no	—
220	C₅×C₄⋊C₄	—	2	1	no	—
221	C₅×C₄⋊C₄	—	2	1	no	—
222	C₅×C₄⋊C₄	—	2	1	no	—
223	C₅×C₄⋊C₄	—	4	1	no	—
224	C₅×C₄⋊C₄	—	4	1	no	—
225	C₅×C₄⋊C₄	—	4	1	no	—
226	C₅×C₄⋊C₄	—	4	1	no	—
227	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
228	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
229	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
230	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
231	C₅×C₂²⋊C₄	—	2	1	no	—
232	C₅×C₂²⋊C₄	—	2	1	no	—
233	C₅×C₂²⋊C₄	—	4	1	no	—
234	C₅×C₂²⋊C₄	—	4	1	no	—
235	C₅×C₂²⋊C₄	—	4	1	no	—
236	C₄²×C₅	—	2	1	no	—
237	C₄²×C₅	—	2	1	no	—
238	C₄²×C₅	—	4	1	no	—
239	C₄²×C₅	C₂⁴	1	1	yes	characteristic
240	C₂×AGL(1,ℤ/8)	—	2	1	no	—
241	C₂²×SD₁₆	—	2	1	no	—
242	#557	C₂²×C₅	1	1	yes	characteristic, complemented
243	#550	C₂²×C₅	1	1	yes	characteristic
244	D₄×Q₈	C₂²×C₅	1	1	yes	characteristic
245	D₄²	C₂²×C₅	1	1	yes	characteristic
246	#501	—	2	1	no	—
247	#500	C₂²×C₅	1	1	yes	characteristic, complemented
248	#493	C₂²×C₅	1	1	yes	characteristic
249	#492	—	2	1	no	—
250	#492	C₂²×C₅	1	1	yes	characteristic
251	#492	C₂²×C₅	1	1	yes	characteristic, complemented
252	#486	C₂²×C₅	1	1	yes	characteristic
253	#486	C₂²×C₅	1	1	yes	characteristic, complemented
254	#478	—	2	1	no	—
255	#477	—	2	1	no	—
256	#475	C₂²×C₅	1	1	yes	characteristic, complemented
257	#474	C₂²×C₅	1	1	yes	characteristic
258	#469	—	2	1	no	—
259	#465	—	2	1	no	—
260	#461	—	2	1	no	—
261	#461	C₂²×C₅	1	1	yes	characteristic
262	#461	C₂²×C₅	1	1	yes	characteristic
263	#460	—	2	1	no	—
264	#460	C₂²×C₅	1	1	yes	characteristic
265	#460	C₂²×C₅	1	1	yes	characteristic
266	#460	C₂²×C₅	1	1	yes	characteristic, complemented
267	#459	C₂²×C₅	1	1	yes	characteristic
268	#450	—	2	1	no	—
269	#449	—	2	1	no	—
270	#448	—	2	1	no	—
271	#447	—	2	1	no	—
272	#446	C₂²×C₅	1	1	yes	characteristic, complemented
273	C₈×Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
274	#440	—	2	1	no	—
275	C₄×SD₁₆	—	2	1	no	—
276	C₄×SD₁₆	C₂²×C₅	1	1	yes	characteristic
277	C₄×SD₁₆	C₂²×C₅	1	1	yes	characteristic
278	#436	C₂²×C₅	1	1	yes	characteristic
279	C₈×D₄	C₂²×C₅	1	1	yes	characteristic
280	#334	C₂²×C₅	1	1	yes	characteristic, complemented
281	#334	C₂²×C₅	1	1	yes	characteristic, complemented
282	#332	C₂²×C₅	1	1	yes	characteristic, complemented
283	#332	C₂²×C₅	1	1	yes	characteristic, complemented
284	#331	C₂²×C₅	1	1	yes	characteristic
285	#331	C₂²×C₅	1	1	yes	characteristic, complemented
286	Q₈⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
287	Q₈⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
288	D₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
289	D₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
290	C₈²	C₂²×C₅	1	1	yes	characteristic, complemented
291	C₂³×C₅	—	2	1	no	—
292	C₂³×C₅	—	2	1	no	—
293	C₂³×C₅	—	4	1	no	—
294	C₂³×C₅	—	4	1	no	—
295	C₂³×C₅	—	8	2	no	—
296	C₂³×C₅	—	8	2	no	—
297	C₂³×C₅	—	16	1	no	—
298	C₅×Q₈	—	2	1	no	—
299	C₅×Q₈	—	2	1	no	—
300	C₅×Q₈	—	2	1	no	—
301	C₅×Q₈	—	4	1	no	—
302	C₅×Q₈	—	4	1	no	—
303	C₅×Q₈	—	4	1	no	—
304	C₅×Q₈	—	4	1	no	—
305	C₅×Q₈	—	8	2	no	—
306	C₅×Q₈	C₂×SD₁₆	1	2	yes	complemented
307	C₅×D₄	—	2	1	no	—
308	C₅×D₄	—	2	1	no	—
309	C₅×D₄	—	2	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	—	4	1	no	—
315	C₅×D₄	—	4	1	no	—
316	C₅×D₄	—	4	1	no	—
317	C₅×D₄	—	4	1	no	—
318	C₅×D₄	—	8	2	no	—
319	C₅×D₄	—	8	1	no	—
320	C₅×D₄	—	8	1	no	—
321	C₅×D₄	—	8	2	no	—
322	C₅×D₄	—	8	2	no	—
323	C₅×D₄	—	16	1	no	—
324	C₅×D₄	C₂×SD₁₆	1	2	yes	—
325	C₂×C₄×C₅	—	2	1	no	—
326	C₂×C₄×C₅	—	2	1	no	—
327	C₂×C₄×C₅	—	2	1	no	—
328	C₂×C₄×C₅	—	2	1	no	—
329	C₂×C₄×C₅	—	2	1	no	—
330	C₂×C₄×C₅	—	2	1	no	—
331	C₂×C₄×C₅	—	4	1	no	—
332	C₂×C₄×C₅	—	4	1	no	—
333	C₂×C₄×C₅	—	4	1	no	—
334	C₂×C₄×C₅	—	4	1	no	—
335	C₂×C₄×C₅	—	4	1	no	—
336	C₂×C₄×C₅	—	4	1	no	—
337	C₂×C₄×C₅	—	8	2	no	—
338	C₂×C₄×C₅	—	8	2	no	—
339	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
340	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
341	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
342	C₅×C₈	—	2	1	no	—
343	C₅×C₈	—	2	1	no	—
344	C₅×C₈	—	4	1	no	—
345	C₅×C₈	—	4	1	no	—
346	C₅×C₈	—	4	1	no	—
347	C₅×C₈	—	4	1	no	—
348	C₅×C₈	—	4	1	no	—
349	C₅×C₈	C₂×SD₁₆	1	2	yes	complemented
350	C₅×C₈	AGL(1,ℤ/8)	1	2	yes	complemented
351	C₂×#41	—	2	1	no	—
352	C₂²×Q₈	—	2	1	no	—
353	C₂²×D₄	—	2	1	no	—
354	C₂²×D₄	—	2	1	no	—
355	AGL(1,ℤ/8)	—	4	4	no	—
356	C₂×SD₁₆	—	2	1	no	—
357	C₂×SD₁₆	—	2	1	no	—
358	C₂×SD₁₆	—	2	1	no	—
359	C₂×SD₁₆	—	2	1	no	—
360	C₂×SD₁₆	—	2	1	no	—
361	C₂×SD₁₆	—	2	1	no	—
362	C₂×SD₁₆	—	2	1	no	—
363	C₂×SD₁₆	—	2	1	no	—
364	C₂×SD₁₆	—	2	1	no	—
365	C₂×SD₁₆	—	4	4	no	—
366	C₂×SD₁₆	C₅×D₄	1	1	yes	characteristic
367	C₂×SD₁₆	C₅×D₄	1	1	yes	characteristic
368	C₂×D₈	—	2	1	no	—
369	C₂×D₈	—	2	1	no	—
370	C₂×D₈	—	2	1	no	—
371	C₂×M₁₆	—	2	1	no	—
372	C₂²×C₈	—	2	1	no	—
373	C₄⋊Q₈	—	2	1	no	—
374	C₄⋊Q₈	—	2	1	no	—
375	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
376	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
377	#127	—	2	1	no	—
378	#127	C₂³×C₅	1	1	yes	characteristic
379	#127	C₂³×C₅	1	1	yes	characteristic
380	#125	—	2	1	no	—
381	#125	—	4	1	no	—
382	C₂²⋊Q₈	—	2	1	no	—
383	C₂²⋊Q₈	—	4	1	no	—
384	#121	—	2	1	no	—
385	#121	—	2	1	no	—
386	#121	—	2	1	no	—
387	#121	—	4	1	no	—
388	#120	—	4	1	no	—
389	C₄×Q₈	—	2	1	no	—
390	C₄×Q₈	—	2	1	no	—
391	C₄×Q₈	C₂³×C₅	1	1	yes	characteristic
392	C₄×Q₈	C₂³×C₅	1	1	yes	characteristic
393	C₄×D₄	—	2	1	no	—
394	C₄×D₄	—	2	1	no	—
395	C₄×D₄	C₂³×C₅	1	1	yes	characteristic
396	C₄×D₄	C₂³×C₅	1	1	yes	characteristic
397	#107	—	2	1	no	—
398	#107	—	2	1	no	—
399	#107	—	2	1	no	—
400	#106	—	2	1	no	—
401	#106	C₅×D₄	1	1	yes	characteristic
402	#106	C₅×D₄	1	1	yes	characteristic
403	C₄⋊C₈	—	2	1	no	—
404	C₄⋊C₈	—	2	1	no	—
405	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
406	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
407	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
408	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
409	#103	—	2	1	no	—
410	#103	—	2	1	no	—
411	#103	—	2	1	no	—
412	#103	C₅×D₄	1	1	yes	characteristic
413	#103	C₅×D₄	1	1	yes	characteristic
414	#102	—	2	1	no	—
415	#102	—	2	1	no	—
416	#102	—	2	1	no	—
417	#102	—	2	1	no	—
418	#102	—	2	1	no	—
419	#102	—	4	1	no	—
420	#102	—	4	1	no	—
421	#102	C₅×D₄	1	1	yes	characteristic
422	#102	C₅×D₄	1	1	yes	characteristic
423	C₂²⋊C₈	—	2	1	no	—
424	C₂²⋊C₈	—	2	1	no	—
425	#97	—	2	1	no	—
426	C₄×C₈	—	2	1	no	—
427	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
428	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
429	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
430	C₂²×C₅	—	2	2	no	—
431	C₂²×C₅	—	4	1	no	—
432	C₂²×C₅	—	4	1	no	—
433	C₂²×C₅	—	4	1	no	—
434	C₂²×C₅	—	4	1	no	—
435	C₂²×C₅	—	4	1	no	—
436	C₂²×C₅	—	8	1	no	—
437	C₂²×C₅	—	8	1	no	—
438	C₂²×C₅	—	8	1	no	—
439	C₂²×C₅	—	8	1	no	—
440	C₂²×C₅	—	8	1	no	—
441	C₂²×C₅	—	8	1	no	—
442	C₂²×C₅	—	16	4	no	—
443	C₂²×C₅	D₄²	1	1	yes	characteristic
444	C₄×C₅	—	2	2	no	—
445	C₄×C₅	—	2	1	no	—
446	C₄×C₅	—	4	1	no	—
447	C₄×C₅	—	4	1	no	—
448	C₄×C₅	—	4	1	no	—
449	C₄×C₅	—	4	1	no	—
450	C₄×C₅	—	4	1	no	—
451	C₄×C₅	—	8	1	no	—
452	C₄×C₅	—	8	1	no	—
453	C₄×C₅	C₂²×SD₁₆	1	1	yes	characteristic
454	C₄×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
455	C₄×C₅	#576	1	1	yes	characteristic
456	C₄×C₅	#577	1	1	yes	characteristic
457	C₂⁴	—	4	1	no	—
458	#41	—	4	2	no	—
459	#41	—	8	1	no	—
460	C₂×Q₈	—	2	1	no	—
461	C₂×Q₈	—	2	1	no	—
462	C₂×Q₈	—	4	1	no	—
463	C₂×Q₈	—	4	2	no	—
464	C₂×Q₈	—	8	1	no	—
465	C₂×Q₈	C₂×C₅×D₄	1	1	yes	characteristic
466	C₂×Q₈	C₂×C₅×D₄	1	1	yes	characteristic
467	C₂×D₄	—	2	1	no	—
468	C₂×D₄	—	2	1	no	—
469	C₂×D₄	—	2	1	no	—
470	C₂×D₄	—	2	1	no	—
471	C₂×D₄	—	2	1	no	—
472	C₂×D₄	—	2	1	no	—
473	C₂×D₄	—	4	1	no	—
474	C₂×D₄	—	4	1	no	—
475	C₂×D₄	—	4	1	no	—
476	C₂×D₄	—	4	1	no	—
477	C₂×D₄	—	4	2	no	—
478	C₂×D₄	—	4	2	no	—
479	C₂×D₄	—	8	1	no	—
480	C₂×D₄	—	8	1	no	—
481	C₂×D₄	C₂×C₅×D₄	1	1	yes	characteristic
482	C₂×D₄	C₂×C₅×D₄	1	1	yes	characteristic
483	C₂²×C₄	—	2	1	no	—
484	C₂²×C₄	—	2	1	no	—
485	C₂²×C₄	—	4	1	no	—
486	C₂²×C₄	—	4	1	no	—
487	SD₁₆	—	2	2	no	—
488	SD₁₆	—	4	2	no	—
489	SD₁₆	—	4	2	no	—
490	SD₁₆	—	4	2	no	—
491	SD₁₆	—	4	2	no	—
492	SD₁₆	—	4	2	no	—
493	SD₁₆	—	8	1	no	—
494	SD₁₆	—	8	1	no	—
495	SD₁₆	—	8	1	no	—
496	SD₁₆	—	8	1	no	—
497	SD₁₆	C₅×SD₁₆	1	4	yes	complemented
498	D₈	—	4	2	no	—
499	D₈	—	4	2	no	—
500	D₈	—	8	1	no	—
501	M₁₆	—	4	2	no	—
502	C₂×C₈	—	2	1	no	—
503	C₂×C₈	—	2	1	no	—
504	C₂×C₈	—	2	1	no	—
505	C₂×C₈	—	2	1	no	—
506	C₂×C₈	—	2	1	no	—
507	C₂×C₈	—	4	2	no	—
508	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
509	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
510	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
511	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
512	C₄⋊C₄	—	2	1	no	—
513	C₄⋊C₄	—	2	1	no	—
514	C₄⋊C₄	—	2	1	no	—
515	C₄⋊C₄	—	2	1	no	—
516	C₄⋊C₄	—	2	1	no	—
517	C₄⋊C₄	—	2	1	no	—
518	C₄⋊C₄	—	4	1	no	—
519	C₄⋊C₄	—	4	1	no	—
520	C₄⋊C₄	—	4	1	no	—
521	C₄⋊C₄	—	4	1	no	—
522	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
523	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
524	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
525	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
526	C₂²⋊C₄	—	2	1	no	—
527	C₂²⋊C₄	—	2	1	no	—
528	C₂²⋊C₄	—	4	1	no	—
529	C₂²⋊C₄	—	4	1	no	—
530	C₂²⋊C₄	—	4	1	no	—
531	C₄²	—	2	1	no	—
532	C₄²	—	2	1	no	—
533	C₄²	—	4	1	no	—
534	C₄²	C₂⁴×C₅	1	1	yes	characteristic
535	C₂×C₅	—	4	2	no	—
536	C₂×C₅	—	8	1	no	—
537	C₂×C₅	—	16	1	no	—
538	C₂×C₅	—	16	1	no	—
539	C₂×C₅	#3274	1	1	yes	characteristic
540	C₂×C₅	D₄×SD₁₆	1	1	yes	characteristic
541	C₂×C₅	#3290	1	1	yes	characteristic
542	C₂³	—	2	1	no	—
543	C₂³	—	2	1	no	—
544	C₂³	—	4	1	no	—
545	C₂³	—	4	1	no	—
546	C₂³	—	8	2	no	—
547	C₂³	—	8	2	no	—
548	C₂³	—	16	1	no	—
549	Q₈	—	2	1	no	—
550	Q₈	—	2	1	no	—
551	Q₈	—	2	1	no	—
552	Q₈	—	4	1	no	—
553	Q₈	—	4	1	no	—
554	Q₈	—	4	1	no	—
555	Q₈	—	4	1	no	—
556	Q₈	—	8	2	no	—
557	Q₈	C₂×C₅×SD₁₆	1	2	yes	complemented
558	D₄	—	2	1	no	—
559	D₄	—	2	1	no	—
560	D₄	—	2	1	no	—
561	D₄	—	4	1	no	—
562	D₄	—	4	1	no	—
563	D₄	—	4	1	no	—
564	D₄	—	4	1	no	—
565	D₄	—	4	1	no	—
566	D₄	—	4	1	no	—
567	D₄	—	4	1	no	—
568	D₄	—	4	1	no	—
569	D₄	—	8	2	no	—
570	D₄	—	8	1	no	—
571	D₄	—	8	1	no	—
572	D₄	—	8	2	no	—
573	D₄	—	8	2	no	—
574	D₄	—	16	1	no	—
575	D₄	C₂×C₅×SD₁₆	1	2	yes	—
576	C₂×C₄	—	2	1	no	—
577	C₂×C₄	—	2	1	no	—
578	C₂×C₄	—	2	1	no	—
579	C₂×C₄	—	2	1	no	—
580	C₂×C₄	—	2	1	no	—
581	C₂×C₄	—	2	1	no	—
582	C₂×C₄	—	4	1	no	—
583	C₂×C₄	—	4	1	no	—
584	C₂×C₄	—	4	1	no	—
585	C₂×C₄	—	4	1	no	—
586	C₂×C₄	—	4	1	no	—
587	C₂×C₄	—	4	1	no	—
588	C₂×C₄	—	8	2	no	—
589	C₂×C₄	—	8	2	no	—
590	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
591	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
592	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
593	C₈	—	2	1	no	—
594	C₈	—	2	1	no	—
595	C₈	—	4	1	no	—
596	C₈	—	4	1	no	—
597	C₈	—	4	1	no	—
598	C₈	—	4	1	no	—
599	C₈	—	4	1	no	—
600	C₈	C₂×C₅×SD₁₆	1	2	yes	complemented
601	C₈	C₅×AGL(1,ℤ/8)	1	2	yes	complemented
602	C₅	#19892	1	1	yes	characteristic, direct product factor, Sylow
603	C₂²	—	2	2	no	—
604	C₂²	—	4	1	no	—
605	C₂²	—	4	1	no	—
606	C₂²	—	4	1	no	—
607	C₂²	—	4	1	no	—
608	C₂²	—	4	1	no	—
609	C₂²	—	8	1	no	—
610	C₂²	—	8	1	no	—
611	C₂²	—	8	1	no	—
612	C₂²	—	8	1	no	—
613	C₂²	—	8	1	no	—
614	C₂²	—	8	1	no	—
615	C₂²	—	16	4	no	—
616	C₂²	C₅×D₄²	1	1	yes	characteristic
617	C₄	—	2	2	no	—
618	C₄	—	2	1	no	—
619	C₄	—	4	1	no	—
620	C₄	—	4	1	no	—
621	C₄	—	4	1	no	—
622	C₄	—	4	1	no	—
623	C₄	—	4	1	no	—
624	C₄	—	8	1	no	—
625	C₄	—	8	1	no	—
626	C₄	C₂²×C₅×SD₁₆	1	1	yes	characteristic
627	C₄	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
628	C₄	C₅×#576	1	1	yes	characteristic
629	C₄	C₅×#577	1	1	yes	characteristic
630	C₂	—	4	2	no	—
631	C₂	—	8	1	no	—
632	C₂	—	16	1	no	—
633	C₂	—	16	1	no	—
634	C₂	C₅×#3274	1	1	yes	characteristic
635	C₂	C₅×D₄×SD₁₆	1	1	yes	characteristic
636	C₂	C₅×#3290	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅	D₄²
commutator, Frattini, cosocle	C₄²	C₂⁴×C₅
prime radical	C₅×#3274	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×#3392	C₂	semidirect
2. C₅×#3386	C₂	semidirect
3. C₅×D₄×SD₁₆	C₂	semidirect
5. C₅×#1706	C₂	semidirect
6. C₅×#1693	C₂	semidirect
7. C₅×#1688	C₂	semidirect
8. C₅×#1666	C₂	semidirect
9. C₅×#1665	C₂	semidirect
10. C₅×#1642	C₂	semidirect
11. C₅×#1639	C₂	semidirect
12. C₅×#1627	C₂	semidirect
13. C₅×#1626	C₂	semidirect
14. C₅×#1590	C₂	semidirect
15. C₅×C₈×SD₁₆	C₂	semidirect
18. C₅×#557	C₂²	semidirect
23. C₅×#500	C₂²	semidirect
27. C₅×#492	C₂²	semidirect
29. C₅×#486	C₂²	semidirect
32. C₅×#475	C₂²	semidirect
42. C₅×#460	C₂²	semidirect
48. C₅×#446	C₂²	semidirect
49. 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. #19892	C₅	direct (N × H)
147. #3392	C₂×C₅	semidirect
148. #3386	C₂×C₅	semidirect
149. D₄×SD₁₆	C₂×C₅	semidirect
151. #1706	C₂×C₅	semidirect
152. #1693	C₂×C₅	semidirect
153. #1688	C₂×C₅	semidirect
154. #1666	C₂×C₅	semidirect
155. #1665	C₂×C₅	semidirect
156. #1642	C₂×C₅	semidirect
157. #1639	C₂×C₅	semidirect
158. #1627	C₂×C₅	semidirect
159. #1626	C₂×C₅	semidirect
160. #1590	C₂×C₅	semidirect
161. C₈×SD₁₆	C₂×C₅	semidirect
202. C₅×SD₁₆	SD₁₆	semidirect
242. #557	C₂²×C₅	semidirect
247. #500	C₂²×C₅	semidirect
251. #492	C₂²×C₅	semidirect
253. #486	C₂²×C₅	semidirect
256. #475	C₂²×C₅	semidirect
266. #460	C₂²×C₅	semidirect
272. #446	C₂²×C₅	semidirect
273. C₈×Q₈	C₂²×C₅	semidirect
280. #334	C₂²×C₅	semidirect
281. #334	C₂²×C₅	semidirect
282. #332	C₂²×C₅	semidirect
283. #332	C₂²×C₅	semidirect
285. #331	C₂²×C₅	semidirect
286. Q₈⋊C₈	C₂²×C₅	semidirect
287. Q₈⋊C₈	C₂²×C₅	semidirect
290. C₈²	C₂²×C₅	semidirect
306. C₅×Q₈	C₂×SD₁₆	semidirect
349. C₅×C₈	C₂×SD₁₆	semidirect
350. C₅×C₈	AGL(1,ℤ/8)	semidirect
497. SD₁₆	C₅×SD₁₆	semidirect
557. Q₈	C₂×C₅×SD₁₆	semidirect
600. C₈	C₂×C₅×SD₁₆	semidirect
601. C₈	C₅×AGL(1,ℤ/8)	semidirect
602. C₅	#19892	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×#3392	2
C₅×#3386	2
C₅×D₄×SD₁₆	2
C₅×#3274	2
C₅×#1706	2
C₅×#1693	2
C₅×#1688	2
C₅×#1666	2
C₅×#1665	2
C₅×#1642	2
C₅×#1639	2
C₅×#1627	2
C₅×#1626	2
C₅×#1590	2
C₅×C₈×SD₁₆	2
#19892	5

Subgroups — C5×#19892 #11942612

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#19892 #11942612