Subgroups — C₅×#19890 #11942610

Order 1280.

718 conjugacy classes of subgroups.

The subgroup lattice has 630 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×#3335	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×D₄×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#3272	C₂	1	1	yes	maximal, characteristic
5	C₅×#1705	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×#1671	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1665	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1654	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1651	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#1629	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#1622	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	C₂²×C₅×SD₁₆	—	2	1	no	—
18	C₅×#554	C₂²	1	1	yes	characteristic, complemented
19	C₅×D₄×Q₈	C₂²	1	1	yes	characteristic
20	C₅×#547	C₂²	1	1	yes	characteristic
21	C₅×D₄²	C₂²	1	1	yes	characteristic
22	C₅×#501	—	2	1	no	—
23	C₅×#498	C₂²	1	1	yes	characteristic, complemented
24	C₅×#498	C₂²	1	1	yes	characteristic, complemented
25	C₅×#498	C₂²	1	1	yes	characteristic, complemented
26	C₅×#492	C₂²	1	1	yes	characteristic
27	C₅×#492	C₂²	1	1	yes	characteristic
28	C₅×#492	C₂²	1	1	yes	characteristic
29	C₅×#483	—	2	1	no	—
30	C₅×#481	—	2	1	no	—
31	C₅×#478	—	2	1	no	—
32	C₅×#476	—	2	1	no	—
33	C₅×#476	C₂²	1	1	yes	characteristic
34	C₅×#476	C₂²	1	1	yes	characteristic
35	C₅×#475	C₂²	1	1	yes	characteristic, complemented
36	C₅×#474	C₂²	1	1	yes	characteristic, complemented
37	C₅×#468	—	2	1	no	—
38	C₅×#465	—	2	1	no	—
39	C₅×#465	—	2	1	no	—
40	C₅×#461	C₂²	1	1	yes	characteristic
41	C₅×#461	C₂²	1	1	yes	characteristic
42	C₅×#460	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×#449	—	2	1	no	—
47	C₅×#448	—	2	1	no	—
48	C₅×#446	C₂²	1	1	yes	characteristic, complemented
49	C₅×#442	—	2	1	no	—
50	C₄×C₅×SD₁₆	C₂²	1	1	yes	characteristic
51	C₄×C₅×D₈	C₂²	1	1	yes	characteristic
52	C₅×#436	C₂²	1	1	yes	characteristic
53	C₅×C₈×D₄	C₂²	1	1	yes	characteristic
54	C₅×C₈×D₄	C₂²	1	1	yes	characteristic, complemented
55	C₂×C₅×#106	—	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	#19890	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	—	4	1	no	—
81	C₂×C₅×SD₁₆	—	4	4	no	—
82	C₂×C₅×SD₁₆	D₄	1	1	yes	characteristic
83	C₂×C₅×D₈	—	2	1	no	—
84	C₂×C₅×D₈	D₄	1	1	yes	characteristic
85	C₂×C₅×M₁₆	—	2	1	no	—
86	C₂²×C₅×C₈	—	2	1	no	—
87	C₂²×C₅×C₈	—	2	1	no	—
88	C₅×C₄⋊Q₈	—	2	1	no	—
89	C₅×C₄⋊Q₈	C₂³	1	1	yes	characteristic
90	C₅×C₄⋊Q₈	C₂³	1	1	yes	characteristic
91	C₅×C₄⋊Q₈	C₂³	1	1	yes	characteristic
92	C₅×#127	C₂³	1	1	yes	characteristic
93	C₅×#125	—	2	1	no	—
94	C₅×#123	—	4	1	no	—
95	C₅×C₂²⋊Q₈	—	2	1	no	—
96	C₅×C₂²⋊Q₈	—	2	1	no	—
97	C₅×C₂²⋊Q₈	—	2	1	no	—
98	C₅×C₂²⋊Q₈	—	4	1	no	—
99	C₅×C₂²⋊Q₈	—	4	1	no	—
100	C₅×#121	—	2	1	no	—
101	C₅×#121	—	2	1	no	—
102	C₅×#121	—	2	1	no	—
103	C₅×#120	—	4	1	no	—
104	C₄×C₅×Q₈	C₂³	1	1	yes	characteristic
105	C₄×C₅×D₄	—	2	1	no	—
106	C₄×C₅×D₄	—	2	1	no	—
107	C₄×C₅×D₄	C₂³	1	1	yes	characteristic
108	C₄×C₅×D₄	C₂³	1	1	yes	characteristic
109	C₄×C₅×D₄	C₂³	1	1	yes	characteristic
110	C₂×C₅×C₄⋊C₄	—	2	1	no	—
111	C₂×C₅×C₄⋊C₄	—	2	1	no	—
112	C₅×#107	—	2	1	no	—
113	C₅×#107	D₄	1	1	yes	characteristic
114	C₅×#106	—	2	1	no	—
115	C₅×#106	—	2	1	no	—
116	C₅×#106	—	2	1	no	—
117	C₅×#106	—	2	1	no	—
118	C₅×#106	—	2	1	no	—
119	C₅×#106	—	2	1	no	—
120	C₅×#106	—	2	1	no	—
121	C₅×#106	—	4	1	no	—
122	C₅×#106	D₄	1	1	yes	characteristic
123	C₅×C₄⋊C₈	—	2	1	no	—
124	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
125	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
126	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
127	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
128	C₅×#103	—	2	1	no	—
129	C₅×#103	—	2	1	no	—
130	C₅×#103	—	2	1	no	—
131	C₅×#103	D₄	1	1	yes	characteristic
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×#102	D₄	1	1	yes	characteristic
140	C₅×C₂²⋊C₈	—	2	1	no	—
141	C₅×C₂²⋊C₈	—	2	1	no	—
142	C₅×C₂²⋊C₈	—	2	1	no	—
143	C₅×#97	—	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	#3384	C₂×C₅	1	1	yes	characteristic, complemented
148	#3335	C₂×C₅	1	1	yes	characteristic, complemented
149	D₄×SD₁₆	C₂×C₅	1	1	yes	characteristic, complemented
150	#3272	C₂×C₅	1	1	yes	characteristic
151	#1705	C₂×C₅	1	1	yes	characteristic, complemented
152	#1691	C₂×C₅	1	1	yes	characteristic, complemented
153	#1686	C₂×C₅	1	1	yes	characteristic, complemented
154	#1671	C₂×C₅	1	1	yes	characteristic, complemented
155	#1665	C₂×C₅	1	1	yes	characteristic, complemented
156	#1654	C₂×C₅	1	1	yes	characteristic, complemented
157	#1651	C₂×C₅	1	1	yes	characteristic, complemented
158	#1629	C₂×C₅	1	1	yes	characteristic, complemented
159	#1622	C₂×C₅	1	1	yes	characteristic, complemented
160	#1590	C₂×C₅	1	1	yes	characteristic, complemented
161	C₈×D₈	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	—	2	1	no	—
168	C₂×C₅×Q₈	—	4	1	no	—
169	C₂×C₅×Q₈	—	4	2	no	—
170	C₂×C₅×Q₈	—	8	1	no	—
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	—	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	—	4	1	no	—
180	C₂×C₅×D₄	—	8	1	no	—
181	C₂×C₅×D₄	—	8	1	no	—
182	C₂×C₅×D₄	C₂×D₄	1	1	yes	characteristic
183	C₂×C₅×D₄	C₂×D₄	1	1	yes	characteristic
184	C₂×C₅×D₄	C₂×D₄	1	1	yes	characteristic
185	C₂²×C₄×C₅	—	2	1	no	—
186	C₂²×C₄×C₅	—	2	1	no	—
187	C₂²×C₄×C₅	—	2	1	no	—
188	C₂²×C₄×C₅	—	4	1	no	—
189	C₂²×C₄×C₅	—	4	1	no	—
190	C₂²×C₄×C₅	—	4	1	no	—
191	C₅×SD₁₆	—	2	2	no	—
192	C₅×SD₁₆	—	4	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	—	8	1	no	—
198	C₅×SD₁₆	—	8	1	no	—
199	C₅×SD₁₆	—	8	2	no	—
200	C₅×D₈	—	4	2	no	—
201	C₅×D₈	SD₁₆	1	4	yes	complemented
202	C₅×M₁₆	—	4	2	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	—	2	1	no	—
207	C₂×C₅×C₈	—	2	1	no	—
208	C₂×C₅×C₈	—	4	2	no	—
209	C₂×C₅×C₈	—	4	2	no	—
210	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
211	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
212	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
213	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
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	—	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	—	4	1	no	—
222	C₅×C₄⋊C₄	—	4	1	no	—
223	C₅×C₄⋊C₄	—	4	1	no	—
224	C₅×C₄⋊C₄	—	4	1	no	—
225	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
226	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
227	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
228	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
229	C₅×C₂²⋊C₄	—	2	1	no	—
230	C₅×C₂²⋊C₄	—	2	1	no	—
231	C₅×C₂²⋊C₄	—	2	1	no	—
232	C₅×C₂²⋊C₄	—	4	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	C₂⁴	1	1	yes	characteristic
238	C₂×AGL(1,ℤ/8)	—	2	1	no	—
239	C₂²×SD₁₆	—	2	1	no	—
240	#554	C₂²×C₅	1	1	yes	characteristic, complemented
241	D₄×Q₈	C₂²×C₅	1	1	yes	characteristic
242	#547	C₂²×C₅	1	1	yes	characteristic
243	D₄²	C₂²×C₅	1	1	yes	characteristic
244	#501	—	2	1	no	—
245	#498	C₂²×C₅	1	1	yes	characteristic, complemented
246	#498	C₂²×C₅	1	1	yes	characteristic, complemented
247	#498	C₂²×C₅	1	1	yes	characteristic, complemented
248	#492	C₂²×C₅	1	1	yes	characteristic
249	#492	C₂²×C₅	1	1	yes	characteristic
250	#492	C₂²×C₅	1	1	yes	characteristic
251	#483	—	2	1	no	—
252	#481	—	2	1	no	—
253	#478	—	2	1	no	—
254	#476	—	2	1	no	—
255	#476	C₂²×C₅	1	1	yes	characteristic
256	#476	C₂²×C₅	1	1	yes	characteristic
257	#475	C₂²×C₅	1	1	yes	characteristic, complemented
258	#474	C₂²×C₅	1	1	yes	characteristic, complemented
259	#468	—	2	1	no	—
260	#465	—	2	1	no	—
261	#465	—	2	1	no	—
262	#461	C₂²×C₅	1	1	yes	characteristic
263	#461	C₂²×C₅	1	1	yes	characteristic
264	#460	C₂²×C₅	1	1	yes	characteristic
265	#459	C₂²×C₅	1	1	yes	characteristic
266	#450	—	2	1	no	—
267	#450	—	2	1	no	—
268	#449	—	2	1	no	—
269	#448	—	2	1	no	—
270	#446	C₂²×C₅	1	1	yes	characteristic, complemented
271	#442	—	2	1	no	—
272	C₄×SD₁₆	C₂²×C₅	1	1	yes	characteristic
273	C₄×D₈	C₂²×C₅	1	1	yes	characteristic
274	#436	C₂²×C₅	1	1	yes	characteristic
275	C₈×D₄	C₂²×C₅	1	1	yes	characteristic
276	C₈×D₄	C₂²×C₅	1	1	yes	characteristic, complemented
277	C₂×#106	—	2	1	no	—
278	#335	C₂²×C₅	1	1	yes	characteristic, complemented
279	#334	C₂²×C₅	1	1	yes	characteristic, complemented
280	#333	C₂²×C₅	1	1	yes	characteristic, complemented
281	#332	C₂²×C₅	1	1	yes	characteristic, complemented
282	#332	C₂²×C₅	1	1	yes	characteristic, complemented
283	#331	C₂²×C₅	1	1	yes	characteristic
284	Q₈⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
285	D₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
286	D₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
287	D₄⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
288	C₈²	C₂²×C₅	1	1	yes	characteristic, complemented
289	C₂³×C₅	—	2	1	no	—
290	C₂³×C₅	—	2	1	no	—
291	C₂³×C₅	—	2	1	no	—
292	C₂³×C₅	—	4	1	no	—
293	C₂³×C₅	—	8	2	no	—
294	C₂³×C₅	—	8	2	no	—
295	C₂³×C₅	—	16	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	1	no	—
303	C₅×Q₈	—	8	2	no	—
304	C₅×D₄	—	2	1	no	—
305	C₅×D₄	—	2	1	no	—
306	C₅×D₄	—	2	1	no	—
307	C₅×D₄	—	2	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	—	8	1	no	—
313	C₅×D₄	—	8	2	no	—
314	C₅×D₄	—	8	2	no	—
315	C₅×D₄	—	8	2	no	—
316	C₅×D₄	C₂×SD₁₆	1	2	yes	—
317	C₅×D₄	C₂×SD₁₆	1	2	yes	complemented
318	C₂×C₄×C₅	—	2	1	no	—
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	—	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	—	4	1	no	—
329	C₂×C₄×C₅	—	4	1	no	—
330	C₂×C₄×C₅	—	4	1	no	—
331	C₂×C₄×C₅	—	4	1	no	—
332	C₂×C₄×C₅	—	8	2	no	—
333	C₂×C₄×C₅	—	8	2	no	—
334	C₂×C₄×C₅	—	16	1	no	—
335	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
336	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
337	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
338	C₅×C₈	—	2	2	no	—
339	C₅×C₈	—	2	1	no	—
340	C₅×C₈	—	2	1	no	—
341	C₅×C₈	—	4	1	no	—
342	C₅×C₈	—	4	1	no	—
343	C₅×C₈	—	4	1	no	—
344	C₅×C₈	—	4	1	no	—
345	C₅×C₈	C₂×SD₁₆	1	2	yes	complemented
346	C₅×C₈	AGL(1,ℤ/8)	1	2	yes	complemented
347	C₂×#41	—	2	1	no	—
348	C₂²×Q₈	—	2	1	no	—
349	C₂²×D₄	—	2	1	no	—
350	C₂²×D₄	—	2	1	no	—
351	AGL(1,ℤ/8)	—	4	4	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	—	2	1	no	—
357	C₂×SD₁₆	—	2	1	no	—
358	C₂×SD₁₆	—	2	1	no	—
359	C₂×SD₁₆	—	4	1	no	—
360	C₂×SD₁₆	—	4	4	no	—
361	C₂×SD₁₆	C₅×D₄	1	1	yes	characteristic
362	C₂×D₈	—	2	1	no	—
363	C₂×D₈	C₅×D₄	1	1	yes	characteristic
364	C₂×M₁₆	—	2	1	no	—
365	C₂²×C₈	—	2	1	no	—
366	C₂²×C₈	—	2	1	no	—
367	C₄⋊Q₈	—	2	1	no	—
368	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
369	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
370	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
371	#127	C₂³×C₅	1	1	yes	characteristic
372	#125	—	2	1	no	—
373	#123	—	4	1	no	—
374	C₂²⋊Q₈	—	2	1	no	—
375	C₂²⋊Q₈	—	2	1	no	—
376	C₂²⋊Q₈	—	2	1	no	—
377	C₂²⋊Q₈	—	4	1	no	—
378	C₂²⋊Q₈	—	4	1	no	—
379	#121	—	2	1	no	—
380	#121	—	2	1	no	—
381	#121	—	2	1	no	—
382	#120	—	4	1	no	—
383	C₄×Q₈	C₂³×C₅	1	1	yes	characteristic
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	C₄×D₄	C₂³×C₅	1	1	yes	characteristic
389	C₂×C₄⋊C₄	—	2	1	no	—
390	C₂×C₄⋊C₄	—	2	1	no	—
391	#107	—	2	1	no	—
392	#107	C₅×D₄	1	1	yes	characteristic
393	#106	—	2	1	no	—
394	#106	—	2	1	no	—
395	#106	—	2	1	no	—
396	#106	—	2	1	no	—
397	#106	—	2	1	no	—
398	#106	—	2	1	no	—
399	#106	—	2	1	no	—
400	#106	—	4	1	no	—
401	#106	C₅×D₄	1	1	yes	characteristic
402	C₄⋊C₈	—	2	1	no	—
403	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
404	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
405	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
406	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
407	#103	—	2	1	no	—
408	#103	—	2	1	no	—
409	#103	—	2	1	no	—
410	#103	C₅×D₄	1	1	yes	characteristic
411	#102	—	2	1	no	—
412	#102	—	2	1	no	—
413	#102	—	2	1	no	—
414	#102	—	2	1	no	—
415	#102	—	2	1	no	—
416	#102	C₅×D₄	1	1	yes	characteristic
417	#102	C₅×D₄	1	1	yes	characteristic
418	#102	C₅×D₄	1	1	yes	characteristic
419	C₂²⋊C₈	—	2	1	no	—
420	C₂²⋊C₈	—	2	1	no	—
421	C₂²⋊C₈	—	2	1	no	—
422	#97	—	2	1	no	—
423	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
424	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
425	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
426	C₂²×C₅	—	2	2	no	—
427	C₂²×C₅	—	2	2	no	—
428	C₂²×C₅	—	4	1	no	—
429	C₂²×C₅	—	4	1	no	—
430	C₂²×C₅	—	4	1	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	—	8	1	no	—
436	C₂²×C₅	—	8	1	no	—
437	C₂²×C₅	—	8	1	no	—
438	C₂²×C₅	—	16	4	no	—
439	C₂²×C₅	D₄²	1	1	yes	characteristic
440	C₄×C₅	—	2	1	no	—
441	C₄×C₅	—	4	1	no	—
442	C₄×C₅	—	4	1	no	—
443	C₄×C₅	—	4	1	no	—
444	C₄×C₅	—	4	1	no	—
445	C₄×C₅	—	4	1	no	—
446	C₄×C₅	—	8	1	no	—
447	C₄×C₅	—	8	1	no	—
448	C₄×C₅	—	8	1	no	—
449	C₄×C₅	C₂²×SD₁₆	1	1	yes	characteristic
450	C₄×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
451	C₄×C₅	#577	1	1	yes	characteristic
452	C₄×C₅	#577	1	1	yes	characteristic
453	C₂⁴	—	4	1	no	—
454	#41	—	4	2	no	—
455	#41	—	8	1	no	—
456	C₂×Q₈	—	2	1	no	—
457	C₂×Q₈	—	2	1	no	—
458	C₂×Q₈	—	2	1	no	—
459	C₂×Q₈	—	4	1	no	—
460	C₂×Q₈	—	4	2	no	—
461	C₂×Q₈	—	8	1	no	—
462	C₂×Q₈	C₂×C₅×D₄	1	1	yes	characteristic
463	C₂×D₄	—	2	1	no	—
464	C₂×D₄	—	2	1	no	—
465	C₂×D₄	—	2	1	no	—
466	C₂×D₄	—	4	1	no	—
467	C₂×D₄	—	4	1	no	—
468	C₂×D₄	—	4	2	no	—
469	C₂×D₄	—	4	2	no	—
470	C₂×D₄	—	4	1	no	—
471	C₂×D₄	—	8	1	no	—
472	C₂×D₄	—	8	1	no	—
473	C₂×D₄	C₂×C₅×D₄	1	1	yes	characteristic
474	C₂×D₄	C₂×C₅×D₄	1	1	yes	characteristic
475	C₂×D₄	C₂×C₅×D₄	1	1	yes	characteristic
476	C₂²×C₄	—	2	1	no	—
477	C₂²×C₄	—	2	1	no	—
478	C₂²×C₄	—	2	1	no	—
479	C₂²×C₄	—	4	1	no	—
480	C₂²×C₄	—	4	1	no	—
481	C₂²×C₄	—	4	1	no	—
482	SD₁₆	—	2	2	no	—
483	SD₁₆	—	4	2	no	—
484	SD₁₆	—	4	2	no	—
485	SD₁₆	—	4	2	no	—
486	SD₁₆	—	4	2	no	—
487	SD₁₆	—	4	2	no	—
488	SD₁₆	—	8	1	no	—
489	SD₁₆	—	8	1	no	—
490	SD₁₆	—	8	2	no	—
491	D₈	—	4	2	no	—
492	D₈	C₅×SD₁₆	1	4	yes	complemented
493	M₁₆	—	4	2	no	—
494	C₂×C₈	—	2	1	no	—
495	C₂×C₈	—	2	1	no	—
496	C₂×C₈	—	2	1	no	—
497	C₂×C₈	—	2	1	no	—
498	C₂×C₈	—	2	1	no	—
499	C₂×C₈	—	4	2	no	—
500	C₂×C₈	—	4	2	no	—
501	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
502	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
503	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
504	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
505	C₄⋊C₄	—	2	1	no	—
506	C₄⋊C₄	—	2	1	no	—
507	C₄⋊C₄	—	2	1	no	—
508	C₄⋊C₄	—	2	1	no	—
509	C₄⋊C₄	—	2	1	no	—
510	C₄⋊C₄	—	2	1	no	—
511	C₄⋊C₄	—	2	1	no	—
512	C₄⋊C₄	—	4	1	no	—
513	C₄⋊C₄	—	4	1	no	—
514	C₄⋊C₄	—	4	1	no	—
515	C₄⋊C₄	—	4	1	no	—
516	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
517	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
518	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
519	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
520	C₂²⋊C₄	—	2	1	no	—
521	C₂²⋊C₄	—	2	1	no	—
522	C₂²⋊C₄	—	2	1	no	—
523	C₂²⋊C₄	—	4	1	no	—
524	C₂²⋊C₄	—	4	1	no	—
525	C₂²⋊C₄	—	4	1	no	—
526	C₂²⋊C₄	—	4	1	no	—
527	C₄²	—	2	1	no	—
528	C₄²	C₂⁴×C₅	1	1	yes	characteristic
529	C₂×C₅	—	4	2	no	—
530	C₂×C₅	—	4	2	no	—
531	C₂×C₅	—	8	1	no	—
532	C₂×C₅	—	16	1	no	—
533	C₂×C₅	#3272	1	1	yes	characteristic
534	C₂×C₅	D₄×SD₁₆	1	1	yes	characteristic
535	C₂×C₅	#3291	1	1	yes	characteristic
536	C₂³	—	2	1	no	—
537	C₂³	—	2	1	no	—
538	C₂³	—	2	1	no	—
539	C₂³	—	4	1	no	—
540	C₂³	—	8	2	no	—
541	C₂³	—	8	2	no	—
542	C₂³	—	16	1	no	—
543	Q₈	—	2	1	no	—
544	Q₈	—	2	1	no	—
545	Q₈	—	4	1	no	—
546	Q₈	—	4	1	no	—
547	Q₈	—	4	1	no	—
548	Q₈	—	4	1	no	—
549	Q₈	—	8	1	no	—
550	Q₈	—	8	2	no	—
551	D₄	—	2	1	no	—
552	D₄	—	2	1	no	—
553	D₄	—	2	1	no	—
554	D₄	—	2	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	2	no	—
561	D₄	—	8	2	no	—
562	D₄	—	8	2	no	—
563	D₄	C₂×C₅×SD₁₆	1	2	yes	—
564	D₄	C₂×C₅×SD₁₆	1	2	yes	complemented
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	—	4	1	no	—
577	C₂×C₄	—	4	1	no	—
578	C₂×C₄	—	4	1	no	—
579	C₂×C₄	—	8	2	no	—
580	C₂×C₄	—	8	2	no	—
581	C₂×C₄	—	16	1	no	—
582	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
583	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
584	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
585	C₈	—	2	2	no	—
586	C₈	—	2	1	no	—
587	C₈	—	2	1	no	—
588	C₈	—	4	1	no	—
589	C₈	—	4	1	no	—
590	C₈	—	4	1	no	—
591	C₈	—	4	1	no	—
592	C₈	C₂×C₅×SD₁₆	1	2	yes	complemented
593	C₈	C₅×AGL(1,ℤ/8)	1	2	yes	complemented
594	C₅	#19890	1	1	yes	characteristic, direct product factor, Sylow
595	C₂²	—	2	2	no	—
596	C₂²	—	2	2	no	—
597	C₂²	—	4	1	no	—
598	C₂²	—	4	1	no	—
599	C₂²	—	4	1	no	—
600	C₂²	—	4	1	no	—
601	C₂²	—	4	1	no	—
602	C₂²	—	4	1	no	—
603	C₂²	—	4	1	no	—
604	C₂²	—	8	1	no	—
605	C₂²	—	8	1	no	—
606	C₂²	—	8	1	no	—
607	C₂²	—	16	4	no	—
608	C₂²	C₅×D₄²	1	1	yes	characteristic
609	C₄	—	2	1	no	—
610	C₄	—	4	1	no	—
611	C₄	—	4	1	no	—
612	C₄	—	4	1	no	—
613	C₄	—	4	1	no	—
614	C₄	—	4	1	no	—
615	C₄	—	8	1	no	—
616	C₄	—	8	1	no	—
617	C₄	—	8	1	no	—
618	C₄	C₂²×C₅×SD₁₆	1	1	yes	characteristic
619	C₄	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
620	C₄	C₅×#577	1	1	yes	characteristic
621	C₄	C₅×#577	1	1	yes	characteristic
622	C₂	—	4	2	no	—
623	C₂	—	4	2	no	—
624	C₂	—	8	1	no	—
625	C₂	—	16	1	no	—
626	C₂	C₅×#3272	1	1	yes	characteristic
627	C₂	C₅×D₄×SD₁₆	1	1	yes	characteristic
628	C₂	C₅×#3291	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×#3335	C₂	semidirect
3. C₅×D₄×SD₁₆	C₂	semidirect
5. C₅×#1705	C₂	semidirect
6. C₅×#1691	C₂	semidirect
7. C₅×#1686	C₂	semidirect
8. C₅×#1671	C₂	semidirect
9. C₅×#1665	C₂	semidirect
10. C₅×#1654	C₂	semidirect
11. C₅×#1651	C₂	semidirect
12. C₅×#1629	C₂	semidirect
13. C₅×#1622	C₂	semidirect
14. C₅×#1590	C₂	semidirect
15. C₅×C₈×D₈	C₂	semidirect
18. C₅×#554	C₂²	semidirect
23. C₅×#498	C₂²	semidirect
24. C₅×#498	C₂²	semidirect
25. C₅×#498	C₂²	semidirect
35. C₅×#475	C₂²	semidirect
36. C₅×#474	C₂²	semidirect
48. C₅×#446	C₂²	semidirect
54. 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. #19890	C₅	direct (N × H)
147. #3384	C₂×C₅	semidirect
148. #3335	C₂×C₅	semidirect
149. D₄×SD₁₆	C₂×C₅	semidirect
151. #1705	C₂×C₅	semidirect
152. #1691	C₂×C₅	semidirect
153. #1686	C₂×C₅	semidirect
154. #1671	C₂×C₅	semidirect
155. #1665	C₂×C₅	semidirect
156. #1654	C₂×C₅	semidirect
157. #1651	C₂×C₅	semidirect
158. #1629	C₂×C₅	semidirect
159. #1622	C₂×C₅	semidirect
160. #1590	C₂×C₅	semidirect
161. C₈×D₈	C₂×C₅	semidirect
201. C₅×D₈	SD₁₆	semidirect
240. #554	C₂²×C₅	semidirect
245. #498	C₂²×C₅	semidirect
246. #498	C₂²×C₅	semidirect
247. #498	C₂²×C₅	semidirect
257. #475	C₂²×C₅	semidirect
258. #474	C₂²×C₅	semidirect
270. #446	C₂²×C₅	semidirect
276. C₈×D₄	C₂²×C₅	semidirect
278. #335	C₂²×C₅	semidirect
279. #334	C₂²×C₅	semidirect
280. #333	C₂²×C₅	semidirect
281. #332	C₂²×C₅	semidirect
282. #332	C₂²×C₅	semidirect
284. Q₈⋊C₈	C₂²×C₅	semidirect
287. D₄⋊C₈	C₂²×C₅	semidirect
288. C₈²	C₂²×C₅	semidirect
317. C₅×D₄	C₂×SD₁₆	semidirect
345. C₅×C₈	C₂×SD₁₆	semidirect
346. C₅×C₈	AGL(1,ℤ/8)	semidirect
492. D₈	C₅×SD₁₆	semidirect
564. D₄	C₂×C₅×SD₁₆	semidirect
592. C₈	C₂×C₅×SD₁₆	semidirect
593. C₈	C₅×AGL(1,ℤ/8)	semidirect
594. C₅	#19890	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×#3335	2
C₅×D₄×SD₁₆	2
C₅×#3272	2
C₅×#1705	2
C₅×#1691	2
C₅×#1686	2
C₅×#1671	2
C₅×#1665	2
C₅×#1654	2
C₅×#1651	2
C₅×#1629	2
C₅×#1622	2
C₅×#1590	2
C₅×C₈×D₈	2
#19890	5

Subgroups — C5×#19890 #11942610

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#19890 #11942610