Subgroups — C₅×#19310 #11942030

Order 1280.

654 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3184	C₂	1	1	yes	maximal, characteristic
2	C₅×#3112	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#3037	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×Q₈×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#1702	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#1698	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#1692	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1688	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1682	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1678	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1672	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#1668	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#1569	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#1560	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#1557	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₅×#137	—	2	1	no	—
17	C₅×#532	C₂²	1	1	yes	characteristic
18	C₅×#532	C₂²	1	1	yes	characteristic
19	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
20	C₅×#498	C₂²	1	1	yes	characteristic
21	C₅×#493	C₂²	1	1	yes	characteristic
22	C₅×#486	C₂²	1	1	yes	characteristic
23	C₅×#486	C₂²	1	1	yes	characteristic
24	C₅×#480	—	2	1	no	—
25	C₅×#477	C₂²	1	1	yes	characteristic
26	C₅×#477	C₂²	1	1	yes	characteristic
27	C₅×#469	—	2	1	no	—
28	C₅×#469	—	2	1	no	—
29	C₅×#464	—	2	1	no	—
30	C₅×#464	—	2	1	no	—
31	C₅×#462	C₂²	1	1	yes	characteristic
32	C₅×#462	C₂²	1	1	yes	characteristic
33	C₅×#460	C₂²	1	1	yes	characteristic
34	C₅×#460	C₂²	1	1	yes	characteristic
35	C₅×#460	C₂²	1	1	yes	characteristic
36	C₅×#460	C₂²	1	1	yes	characteristic
37	C₅×#448	—	2	1	no	—
38	C₅×#446	—	2	1	no	—
39	C₅×#446	—	2	1	no	—
40	C₅×#446	C₂²	1	1	yes	characteristic
41	C₅×#446	C₂²	1	1	yes	characteristic
42	C₅×C₈×Q₈	C₂²	1	1	yes	characteristic
43	C₅×C₈×Q₈	C₂²	1	1	yes	characteristic
44	C₅×#442	—	2	1	no	—
45	C₅×#442	—	2	1	no	—
46	C₅×#440	—	2	1	no	—
47	C₅×#440	—	2	1	no	—
48	C₅×#432	C₂²	1	1	yes	characteristic
49	C₅×#423	—	2	1	no	—
50	C₅×#423	C₂²	1	1	yes	characteristic
51	C₅×#423	C₂²	1	1	yes	characteristic
52	C₅×#417	—	2	1	no	—
53	C₄×C₅×M₁₆	—	2	1	no	—
54	C₄×C₅×M₁₆	C₂²	1	1	yes	characteristic
55	C₅×#335	C₂²	1	1	yes	characteristic
56	C₅×#335	C₂²	1	1	yes	characteristic
57	C₅×#334	C₂²	1	1	yes	characteristic
58	C₅×#334	C₂²	1	1	yes	characteristic
59	C₅×#333	C₂²	1	1	yes	characteristic
60	C₅×#333	C₂²	1	1	yes	characteristic
61	C₅×#332	C₂²	1	1	yes	characteristic
62	C₅×#332	C₂²	1	1	yes	characteristic
63	C₅×#331	C₂²	1	1	yes	characteristic
64	C₅×#331	C₂²	1	1	yes	characteristic
65	C₅×#331	C₂²	1	1	yes	characteristic
66	C₅×#331	C₂²	1	1	yes	characteristic
67	#19310	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
68	C₂×C₅×#41	—	2	1	no	—
69	C₂×C₅×#41	—	2	1	no	—
70	C₂²×C₅×Q₈	D₄	1	1	yes	characteristic
71	C₅×#137	—	4	4	no	—
72	C₂×C₅×Q₁₆	—	2	1	no	—
73	C₂×C₅×Q₁₆	—	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×D₈	—	2	1	no	—
79	C₂×C₅×D₈	—	2	1	no	—
80	C₂×C₅×M₁₆	—	2	1	no	—
81	C₂×C₅×M₁₆	—	2	1	no	—
82	C₂×C₅×M₁₆	D₄	1	1	yes	characteristic
83	C₂×C₅×M₁₆	D₄	1	1	yes	characteristic
84	C₅×C₄⋊Q₈	C₂³	1	1	yes	characteristic
85	C₅×C₄⋊Q₈	C₂³	1	1	yes	characteristic
86	C₅×#127	C₂³	1	1	yes	characteristic
87	C₅×#127	C₂³	1	1	yes	characteristic
88	C₅×#124	—	2	1	no	—
89	C₅×#124	—	2	1	no	—
90	C₅×#121	—	2	1	no	—
91	C₅×#121	—	2	1	no	—
92	C₅×#121	—	2	1	no	—
93	C₅×#121	—	2	1	no	—
94	C₄×C₅×Q₈	—	2	1	no	—
95	C₄×C₅×Q₈	—	2	1	no	—
96	C₄×C₅×Q₈	D₄	1	1	yes	characteristic
97	C₄×C₅×Q₈	D₄	1	1	yes	characteristic
98	C₄×C₅×Q₈	C₂³	1	1	yes	characteristic
99	C₄×C₅×Q₈	C₂³	1	1	yes	characteristic
100	C₄×C₅×D₄	—	2	1	no	—
101	C₄×C₅×D₄	—	2	1	no	—
102	C₄×C₅×D₄	—	2	1	no	—
103	C₄×C₅×D₄	—	2	1	no	—
104	C₂×C₅×C₄⋊C₄	—	2	1	no	—
105	C₂×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
106	C₂×C₄²×C₅	—	2	1	no	—
107	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
108	C₅×#107	—	2	1	no	—
109	C₅×#107	—	2	1	no	—
110	C₅×#106	—	2	1	no	—
111	C₅×#106	—	2	1	no	—
112	C₅×C₄⋊C₈	—	2	1	no	—
113	C₅×C₄⋊C₈	—	2	1	no	—
114	C₅×C₄⋊C₈	—	2	1	no	—
115	C₅×C₄⋊C₈	—	2	1	no	—
116	C₅×C₄⋊C₈	—	2	1	no	—
117	C₅×C₄⋊C₈	—	2	1	no	—
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×C₄⋊C₈	C₂³	1	1	yes	characteristic
122	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
123	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
124	C₅×#103	—	2	1	no	—
125	C₅×#103	—	2	1	no	—
126	C₅×#103	—	2	1	no	—
127	C₅×#103	—	2	1	no	—
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×C₂²⋊C₈	—	2	1	no	—
137	C₅×#97	—	2	1	no	—
138	C₅×#97	—	2	1	no	—
139	C₅×#97	—	2	1	no	—
140	C₅×#97	D₄	1	1	yes	characteristic
141	C₅×#97	D₄	1	1	yes	characteristic
142	C₄×C₅×C₈	—	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	#3184	C₂×C₅	1	1	yes	characteristic
147	#3112	C₂×C₅	1	1	yes	characteristic, complemented
148	#3037	C₂×C₅	1	1	yes	characteristic, complemented
149	Q₈×M₁₆	C₂×C₅	1	1	yes	characteristic, complemented
150	#1702	C₂×C₅	1	1	yes	characteristic, complemented
151	#1698	C₂×C₅	1	1	yes	characteristic, complemented
152	#1692	C₂×C₅	1	1	yes	characteristic, complemented
153	#1688	C₂×C₅	1	1	yes	characteristic, complemented
154	#1682	C₂×C₅	1	1	yes	characteristic, complemented
155	#1678	C₂×C₅	1	1	yes	characteristic, complemented
156	#1672	C₂×C₅	1	1	yes	characteristic, complemented
157	#1668	C₂×C₅	1	1	yes	characteristic, complemented
158	#1569	C₂×C₅	1	1	yes	characteristic, complemented
159	#1560	C₂×C₅	1	1	yes	characteristic, complemented
160	#1557	C₂×C₅	1	1	yes	characteristic, complemented
161	C₅×#41	—	4	2	no	—
162	C₅×#41	—	4	2	no	—
163	C₅×#41	—	8	2	no	—
164	C₂×C₅×Q₈	—	2	1	no	—
165	C₂×C₅×Q₈	—	2	2	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	C₂×D₄	1	1	yes	characteristic
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	—	2	1	no	—
175	C₂×C₅×D₄	—	2	1	no	—
176	C₂×C₅×D₄	—	2	1	no	—
177	C₂×C₅×D₄	—	4	1	no	—
178	C₂×C₅×D₄	—	4	1	no	—
179	C₂²×C₄×C₅	—	2	1	no	—
180	C₂²×C₄×C₅	—	2	1	no	—
181	C₂²×C₄×C₅	—	4	1	no	—
182	C₂²×C₄×C₅	—	4	1	no	—
183	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
184	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
185	C₂²×C₄×C₅	#41	1	1	yes	characteristic
186	C₅×Q₁₆	—	4	2	no	—
187	C₅×Q₁₆	—	4	2	no	—
188	C₅×SD₁₆	—	4	2	no	—
189	C₅×SD₁₆	—	4	2	no	—
190	C₅×SD₁₆	—	4	2	no	—
191	C₅×SD₁₆	—	4	2	no	—
192	C₅×D₈	—	4	2	no	—
193	C₅×D₈	—	4	2	no	—
194	C₅×M₁₆	—	2	2	no	—
195	C₅×M₁₆	—	4	1	no	—
196	C₅×M₁₆	—	4	2	no	—
197	C₅×M₁₆	—	4	2	no	—
198	C₂×C₅×C₈	—	2	1	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	C₂×D₄	1	1	yes	characteristic
205	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
206	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
207	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
208	C₅×C₄⋊C₄	—	2	1	no	—
209	C₅×C₄⋊C₄	—	2	1	no	—
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	C₂×D₄	1	1	yes	characteristic
218	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
219	C₅×C₂²⋊C₄	—	4	1	no	—
220	C₅×C₂²⋊C₄	—	4	1	no	—
221	C₅×C₂²⋊C₄	—	4	1	no	—
222	C₅×C₂²⋊C₄	—	4	1	no	—
223	C₄²×C₅	—	2	1	no	—
224	C₄²×C₅	—	2	1	no	—
225	C₄²×C₅	—	2	1	no	—
226	C₄²×C₅	—	2	1	no	—
227	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
228	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
229	C₄²×C₅	#41	1	1	yes	characteristic
230	C₄²×C₅	C₂⁴	1	1	yes	characteristic
231	C₂×#137	—	2	1	no	—
232	#532	C₂²×C₅	1	1	yes	characteristic
233	#532	C₂²×C₅	1	1	yes	characteristic
234	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
235	#498	C₂²×C₅	1	1	yes	characteristic
236	#493	C₂²×C₅	1	1	yes	characteristic
237	#486	C₂²×C₅	1	1	yes	characteristic
238	#486	C₂²×C₅	1	1	yes	characteristic
239	#480	—	2	1	no	—
240	#477	C₂²×C₅	1	1	yes	characteristic
241	#477	C₂²×C₅	1	1	yes	characteristic
242	#469	—	2	1	no	—
243	#469	—	2	1	no	—
244	#464	—	2	1	no	—
245	#464	—	2	1	no	—
246	#462	C₂²×C₅	1	1	yes	characteristic
247	#462	C₂²×C₅	1	1	yes	characteristic
248	#460	C₂²×C₅	1	1	yes	characteristic
249	#460	C₂²×C₅	1	1	yes	characteristic
250	#460	C₂²×C₅	1	1	yes	characteristic
251	#460	C₂²×C₅	1	1	yes	characteristic
252	#448	—	2	1	no	—
253	#446	—	2	1	no	—
254	#446	—	2	1	no	—
255	#446	C₂²×C₅	1	1	yes	characteristic
256	#446	C₂²×C₅	1	1	yes	characteristic
257	C₈×Q₈	C₂²×C₅	1	1	yes	characteristic
258	C₈×Q₈	C₂²×C₅	1	1	yes	characteristic
259	#442	—	2	1	no	—
260	#442	—	2	1	no	—
261	#440	—	2	1	no	—
262	#440	—	2	1	no	—
263	#432	C₂²×C₅	1	1	yes	characteristic
264	#423	—	2	1	no	—
265	#423	C₂²×C₅	1	1	yes	characteristic
266	#423	C₂²×C₅	1	1	yes	characteristic
267	#417	—	2	1	no	—
268	C₄×M₁₆	—	2	1	no	—
269	C₄×M₁₆	C₂²×C₅	1	1	yes	characteristic
270	#335	C₂²×C₅	1	1	yes	characteristic
271	#335	C₂²×C₅	1	1	yes	characteristic
272	#334	C₂²×C₅	1	1	yes	characteristic
273	#334	C₂²×C₅	1	1	yes	characteristic
274	#333	C₂²×C₅	1	1	yes	characteristic
275	#333	C₂²×C₅	1	1	yes	characteristic
276	#332	C₂²×C₅	1	1	yes	characteristic
277	#332	C₂²×C₅	1	1	yes	characteristic
278	#331	C₂²×C₅	1	1	yes	characteristic
279	#331	C₂²×C₅	1	1	yes	characteristic
280	#331	C₂²×C₅	1	1	yes	characteristic
281	#331	C₂²×C₅	1	1	yes	characteristic
282	C₂³×C₅	—	4	1	no	—
283	C₂³×C₅	—	4	1	no	—
284	C₂³×C₅	#121	1	1	yes	characteristic
285	C₅×Q₈	—	2	1	no	—
286	C₅×Q₈	—	2	1	no	—
287	C₅×Q₈	—	2	1	no	—
288	C₅×Q₈	—	4	2	no	—
289	C₅×Q₈	—	4	1	no	—
290	C₅×Q₈	—	4	1	no	—
291	C₅×Q₈	—	8	1	no	—
292	C₅×Q₈	AGL(1,ℤ/8)	1	2	yes	—
293	C₅×D₄	—	4	1	no	—
294	C₅×D₄	—	4	1	no	—
295	C₅×D₄	—	4	1	no	—
296	C₅×D₄	—	4	1	no	—
297	C₅×D₄	—	4	1	no	—
298	C₅×D₄	—	4	1	no	—
299	C₅×D₄	—	4	1	no	—
300	C₅×D₄	—	4	1	no	—
301	C₅×D₄	—	8	1	no	—
302	C₅×D₄	—	8	1	no	—
303	C₅×D₄	—	8	2	no	—
304	C₅×D₄	—	8	2	no	—
305	C₂×C₄×C₅	—	2	1	no	—
306	C₂×C₄×C₅	—	2	1	no	—
307	C₂×C₄×C₅	—	2	1	no	—
308	C₂×C₄×C₅	—	2	1	no	—
309	C₂×C₄×C₅	—	2	1	no	—
310	C₂×C₄×C₅	—	2	1	no	—
311	C₂×C₄×C₅	—	2	1	no	—
312	C₂×C₄×C₅	—	2	1	no	—
313	C₂×C₄×C₅	—	4	1	no	—
314	C₂×C₄×C₅	—	4	2	no	—
315	C₂×C₄×C₅	—	4	1	no	—
316	C₂×C₄×C₅	—	4	1	no	—
317	C₂×C₄×C₅	—	8	2	no	—
318	C₂×C₄×C₅	—	8	2	no	—
319	C₂×C₄×C₅	—	8	1	no	—
320	C₂×C₄×C₅	#121	1	1	yes	characteristic
321	C₂×C₄×C₅	#121	1	1	yes	characteristic
322	C₂×C₄×C₅	#121	1	1	yes	characteristic
323	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
324	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
325	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
326	C₅×C₈	—	2	1	no	—
327	C₅×C₈	—	2	1	no	—
328	C₅×C₈	—	2	1	no	—
329	C₅×C₈	—	4	1	no	—
330	C₅×C₈	—	4	1	no	—
331	C₅×C₈	—	4	1	no	—
332	C₅×C₈	—	4	1	no	—
333	C₅×C₈	—	4	1	no	—
334	C₅×C₈	—	4	1	no	—
335	C₅×C₈	#137	1	2	yes	complemented
336	C₂×#41	—	2	1	no	—
337	C₂×#41	—	2	1	no	—
338	C₂²×Q₈	C₅×D₄	1	1	yes	characteristic
339	#137	—	4	4	no	—
340	C₂×Q₁₆	—	2	1	no	—
341	C₂×Q₁₆	—	2	1	no	—
342	C₂×SD₁₆	—	2	1	no	—
343	C₂×SD₁₆	—	2	1	no	—
344	C₂×SD₁₆	—	2	1	no	—
345	C₂×SD₁₆	—	2	1	no	—
346	C₂×D₈	—	2	1	no	—
347	C₂×D₈	—	2	1	no	—
348	C₂×M₁₆	—	2	1	no	—
349	C₂×M₁₆	—	2	1	no	—
350	C₂×M₁₆	C₅×D₄	1	1	yes	characteristic
351	C₂×M₁₆	C₅×D₄	1	1	yes	characteristic
352	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
353	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
354	#127	C₂³×C₅	1	1	yes	characteristic
355	#127	C₂³×C₅	1	1	yes	characteristic
356	#124	—	2	1	no	—
357	#124	—	2	1	no	—
358	#121	—	2	1	no	—
359	#121	—	2	1	no	—
360	#121	—	2	1	no	—
361	#121	—	2	1	no	—
362	C₄×Q₈	—	2	1	no	—
363	C₄×Q₈	—	2	1	no	—
364	C₄×Q₈	C₅×D₄	1	1	yes	characteristic
365	C₄×Q₈	C₅×D₄	1	1	yes	characteristic
366	C₄×Q₈	C₂³×C₅	1	1	yes	characteristic
367	C₄×Q₈	C₂³×C₅	1	1	yes	characteristic
368	C₄×D₄	—	2	1	no	—
369	C₄×D₄	—	2	1	no	—
370	C₄×D₄	—	2	1	no	—
371	C₄×D₄	—	2	1	no	—
372	C₂×C₄⋊C₄	—	2	1	no	—
373	C₂×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
374	C₂×C₄²	—	2	1	no	—
375	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
376	#107	—	2	1	no	—
377	#107	—	2	1	no	—
378	#106	—	2	1	no	—
379	#106	—	2	1	no	—
380	C₄⋊C₈	—	2	1	no	—
381	C₄⋊C₈	—	2	1	no	—
382	C₄⋊C₈	—	2	1	no	—
383	C₄⋊C₈	—	2	1	no	—
384	C₄⋊C₈	—	2	1	no	—
385	C₄⋊C₈	—	2	1	no	—
386	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
387	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
388	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
389	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
390	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
391	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
392	#103	—	2	1	no	—
393	#103	—	2	1	no	—
394	#103	—	2	1	no	—
395	#103	—	2	1	no	—
396	#102	—	2	1	no	—
397	#102	—	2	1	no	—
398	#102	—	2	1	no	—
399	#102	—	2	1	no	—
400	#102	—	2	1	no	—
401	#102	—	2	1	no	—
402	#102	—	2	1	no	—
403	#102	—	2	1	no	—
404	C₂²⋊C₈	—	2	1	no	—
405	#97	—	2	1	no	—
406	#97	—	2	1	no	—
407	#97	—	2	1	no	—
408	#97	C₅×D₄	1	1	yes	characteristic
409	#97	C₅×D₄	1	1	yes	characteristic
410	C₄×C₈	—	2	1	no	—
411	C₄×C₈	—	2	1	no	—
412	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
413	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
414	C₂²×C₅	—	2	1	no	—
415	C₂²×C₅	—	2	1	no	—
416	C₂²×C₅	—	2	1	no	—
417	C₂²×C₅	—	8	1	no	—
418	C₂²×C₅	—	8	1	no	—
419	C₂²×C₅	—	8	1	no	—
420	C₂²×C₅	—	8	1	no	—
421	C₂²×C₅	—	8	1	no	—
422	C₂²×C₅	—	8	1	no	—
423	C₂²×C₅	C₂×#121	1	1	yes	characteristic
424	C₄×C₅	—	2	1	no	—
425	C₄×C₅	—	2	1	no	—
426	C₄×C₅	—	2	2	no	—
427	C₄×C₅	—	2	1	no	—
428	C₄×C₅	—	2	1	no	—
429	C₄×C₅	—	4	1	no	—
430	C₄×C₅	—	4	1	no	—
431	C₄×C₅	—	4	1	no	—
432	C₄×C₅	—	8	1	no	—
433	C₄×C₅	—	8	1	no	—
434	C₄×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
435	C₄×C₅	C₂×#137	1	1	yes	characteristic
436	C₄×C₅	#575	1	1	yes	characteristic
437	C₄×C₅	#575	1	1	yes	characteristic
438	#41	—	4	2	no	—
439	#41	—	4	2	no	—
440	#41	—	8	2	no	—
441	C₂×Q₈	—	2	1	no	—
442	C₂×Q₈	—	2	2	no	—
443	C₂×Q₈	—	2	1	no	—
444	C₂×Q₈	—	2	1	no	—
445	C₂×Q₈	—	4	1	no	—
446	C₂×Q₈	C₂×C₅×D₄	1	1	yes	characteristic
447	C₂×Q₈	C₂×C₅×D₄	1	1	yes	characteristic
448	C₂×D₄	—	2	1	no	—
449	C₂×D₄	—	2	1	no	—
450	C₂×D₄	—	2	1	no	—
451	C₂×D₄	—	2	1	no	—
452	C₂×D₄	—	2	1	no	—
453	C₂×D₄	—	2	1	no	—
454	C₂×D₄	—	4	1	no	—
455	C₂×D₄	—	4	1	no	—
456	C₂²×C₄	—	2	1	no	—
457	C₂²×C₄	—	2	1	no	—
458	C₂²×C₄	—	4	1	no	—
459	C₂²×C₄	—	4	1	no	—
460	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
461	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
462	C₂²×C₄	C₅×#41	1	1	yes	characteristic
463	Q₁₆	—	4	2	no	—
464	Q₁₆	—	4	2	no	—
465	SD₁₆	—	4	2	no	—
466	SD₁₆	—	4	2	no	—
467	SD₁₆	—	4	2	no	—
468	SD₁₆	—	4	2	no	—
469	D₈	—	4	2	no	—
470	D₈	—	4	2	no	—
471	M₁₆	—	2	2	no	—
472	M₁₆	—	4	1	no	—
473	M₁₆	—	4	2	no	—
474	M₁₆	—	4	2	no	—
475	C₂×C₈	—	2	1	no	—
476	C₂×C₈	—	2	1	no	—
477	C₂×C₈	—	2	1	no	—
478	C₂×C₈	—	2	1	no	—
479	C₂×C₈	—	2	1	no	—
480	C₂×C₈	—	2	1	no	—
481	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
482	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
483	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
484	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
485	C₄⋊C₄	—	2	1	no	—
486	C₄⋊C₄	—	2	1	no	—
487	C₄⋊C₄	—	2	1	no	—
488	C₄⋊C₄	—	2	1	no	—
489	C₄⋊C₄	—	2	1	no	—
490	C₄⋊C₄	—	2	1	no	—
491	C₄⋊C₄	—	2	1	no	—
492	C₄⋊C₄	—	2	1	no	—
493	C₄⋊C₄	—	2	1	no	—
494	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
495	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
496	C₂²⋊C₄	—	4	1	no	—
497	C₂²⋊C₄	—	4	1	no	—
498	C₂²⋊C₄	—	4	1	no	—
499	C₂²⋊C₄	—	4	1	no	—
500	C₄²	—	2	1	no	—
501	C₄²	—	2	1	no	—
502	C₄²	—	2	1	no	—
503	C₄²	—	2	1	no	—
504	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
505	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
506	C₄²	C₅×#41	1	1	yes	characteristic
507	C₄²	C₂⁴×C₅	1	1	yes	characteristic
508	C₂×C₅	—	4	1	no	—
509	C₂×C₅	—	16	1	no	—
510	C₂×C₅	—	16	1	no	—
511	C₂×C₅	#3037	1	1	yes	characteristic
512	C₂×C₅	#3055	1	1	yes	characteristic
513	C₂×C₅	#3068	1	1	yes	characteristic
514	C₂³	—	4	1	no	—
515	C₂³	—	4	1	no	—
516	C₂³	C₅×#121	1	1	yes	characteristic
517	Q₈	—	2	1	no	—
518	Q₈	—	2	1	no	—
519	Q₈	—	2	1	no	—
520	Q₈	—	4	2	no	—
521	Q₈	—	4	1	no	—
522	Q₈	—	4	1	no	—
523	Q₈	—	8	1	no	—
524	Q₈	C₅×AGL(1,ℤ/8)	1	2	yes	—
525	D₄	—	4	1	no	—
526	D₄	—	4	1	no	—
527	D₄	—	4	1	no	—
528	D₄	—	4	1	no	—
529	D₄	—	4	1	no	—
530	D₄	—	4	1	no	—
531	D₄	—	4	1	no	—
532	D₄	—	4	1	no	—
533	D₄	—	8	1	no	—
534	D₄	—	8	1	no	—
535	D₄	—	8	2	no	—
536	D₄	—	8	2	no	—
537	C₂×C₄	—	2	1	no	—
538	C₂×C₄	—	2	1	no	—
539	C₂×C₄	—	2	1	no	—
540	C₂×C₄	—	2	1	no	—
541	C₂×C₄	—	2	1	no	—
542	C₂×C₄	—	2	1	no	—
543	C₂×C₄	—	2	1	no	—
544	C₂×C₄	—	2	1	no	—
545	C₂×C₄	—	4	1	no	—
546	C₂×C₄	—	4	2	no	—
547	C₂×C₄	—	4	1	no	—
548	C₂×C₄	—	4	1	no	—
549	C₂×C₄	—	8	2	no	—
550	C₂×C₄	—	8	2	no	—
551	C₂×C₄	—	8	1	no	—
552	C₂×C₄	C₅×#121	1	1	yes	characteristic
553	C₂×C₄	C₅×#121	1	1	yes	characteristic
554	C₂×C₄	C₅×#121	1	1	yes	characteristic
555	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
556	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
557	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
558	C₈	—	2	1	no	—
559	C₈	—	2	1	no	—
560	C₈	—	2	1	no	—
561	C₈	—	4	1	no	—
562	C₈	—	4	1	no	—
563	C₈	—	4	1	no	—
564	C₈	—	4	1	no	—
565	C₈	—	4	1	no	—
566	C₈	—	4	1	no	—
567	C₈	C₅×#137	1	2	yes	complemented
568	C₅	#19310	1	1	yes	characteristic, direct product factor, Sylow
569	C₂²	—	2	1	no	—
570	C₂²	—	2	1	no	—
571	C₂²	—	2	1	no	—
572	C₂²	—	8	1	no	—
573	C₂²	—	8	1	no	—
574	C₂²	—	8	1	no	—
575	C₂²	—	8	1	no	—
576	C₂²	—	8	1	no	—
577	C₂²	—	8	1	no	—
578	C₂²	C₂×C₅×#121	1	1	yes	characteristic
579	C₄	—	2	1	no	—
580	C₄	—	2	1	no	—
581	C₄	—	2	2	no	—
582	C₄	—	2	1	no	—
583	C₄	—	2	1	no	—
584	C₄	—	4	1	no	—
585	C₄	—	4	1	no	—
586	C₄	—	4	1	no	—
587	C₄	—	8	1	no	—
588	C₄	—	8	1	no	—
589	C₄	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
590	C₄	C₂×C₅×#137	1	1	yes	characteristic
591	C₄	C₅×#575	1	1	yes	characteristic
592	C₄	C₅×#575	1	1	yes	characteristic
593	C₂	—	4	1	no	—
594	C₂	—	16	1	no	—
595	C₂	—	16	1	no	—
596	C₂	C₅×#3037	1	1	yes	characteristic
597	C₂	C₅×#3055	1	1	yes	characteristic
598	C₂	C₅×#3068	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₅
prime radical	C₅×#3184	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₅ ◁ C₂×C₄²×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₅×#3112	C₂	semidirect
3. C₅×#3037	C₂	semidirect
4. C₅×Q₈×M₁₆	C₂	semidirect
5. C₅×#1702	C₂	semidirect
6. C₅×#1698	C₂	semidirect
7. C₅×#1692	C₂	semidirect
8. C₅×#1688	C₂	semidirect
9. C₅×#1682	C₂	semidirect
10. C₅×#1678	C₂	semidirect
11. C₅×#1672	C₂	semidirect
12. C₅×#1668	C₂	semidirect
13. C₅×#1569	C₂	semidirect
14. C₅×#1560	C₂	semidirect
15. C₅×#1557	C₂	semidirect
67. #19310	C₅	direct (N × H)
147. #3112	C₂×C₅	semidirect
148. #3037	C₂×C₅	semidirect
149. Q₈×M₁₆	C₂×C₅	semidirect
150. #1702	C₂×C₅	semidirect
151. #1698	C₂×C₅	semidirect
152. #1692	C₂×C₅	semidirect
153. #1688	C₂×C₅	semidirect
154. #1682	C₂×C₅	semidirect
155. #1678	C₂×C₅	semidirect
156. #1672	C₂×C₅	semidirect
157. #1668	C₂×C₅	semidirect
158. #1569	C₂×C₅	semidirect
159. #1560	C₂×C₅	semidirect
160. #1557	C₂×C₅	semidirect
335. C₅×C₈	#137	semidirect
567. C₈	C₅×#137	semidirect
568. C₅	#19310	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×#3184	2
C₅×#3112	2
C₅×#3037	2
C₅×Q₈×M₁₆	2
C₅×#1702	2
C₅×#1698	2
C₅×#1692	2
C₅×#1688	2
C₅×#1682	2
C₅×#1678	2
C₅×#1672	2
C₅×#1668	2
C₅×#1569	2
C₅×#1560	2
C₅×#1557	2
#19310	5

Subgroups — C5×#19310 #11942030

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#19310 #11942030