Subgroups — C₅×#19182 #11941902

Order 1280.

646 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3182	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#3107	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#3035	C₂	1	1	yes	maximal, characteristic
4	C₅×#2971	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#1701	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#1699	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#1693	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1685	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1682	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1680	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1674	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#1666	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#1565	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#1553	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#1552	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₅×#135	—	2	1	no	—
17	C₅×#533	C₂²	1	1	yes	characteristic
18	C₅×#532	C₂²	1	1	yes	characteristic
19	C₄×C₅×#41	C₂²	1	1	yes	characteristic
20	C₅×#500	C₂²	1	1	yes	characteristic
21	C₅×#492	C₂²	1	1	yes	characteristic
22	C₅×#487	C₂²	1	1	yes	characteristic
23	C₅×#486	C₂²	1	1	yes	characteristic
24	C₅×#485	—	2	1	no	—
25	C₅×#475	C₂²	1	1	yes	characteristic
26	C₅×#474	C₂²	1	1	yes	characteristic
27	C₅×#468	—	2	1	no	—
28	C₅×#468	—	2	1	no	—
29	C₅×#464	—	2	1	no	—
30	C₅×#463	—	2	1	no	—
31	C₅×#462	C₂²	1	1	yes	characteristic
32	C₅×#462	C₂²	1	1	yes	characteristic
33	C₅×#461	C₂²	1	1	yes	characteristic
34	C₅×#461	C₂²	1	1	yes	characteristic
35	C₅×#460	C₂²	1	1	yes	characteristic
36	C₅×#459	C₂²	1	1	yes	characteristic
37	C₅×#452	—	2	1	no	—
38	C₅×C₈×Q₈	C₂²	1	1	yes	characteristic
39	C₅×C₈×Q₈	C₂²	1	1	yes	characteristic
40	C₅×#440	—	2	1	no	—
41	C₅×#440	—	2	1	no	—
42	C₄×C₅×Q₁₆	—	2	1	no	—
43	C₄×C₅×SD₁₆	—	2	1	no	—
44	C₅×#436	—	2	1	no	—
45	C₅×#436	—	2	1	no	—
46	C₅×#436	C₂²	1	1	yes	characteristic
47	C₅×#436	C₂²	1	1	yes	characteristic
48	C₅×#432	—	2	1	no	—
49	C₅×#432	C₂²	1	1	yes	characteristic
50	C₅×#431	C₂²	1	1	yes	characteristic
51	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
52	C₅×#416	—	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×#332	C₂²	1	1	yes	characteristic
60	C₅×#332	C₂²	1	1	yes	characteristic
61	C₅×#332	C₂²	1	1	yes	characteristic
62	C₅×#332	C₂²	1	1	yes	characteristic
63	C₅×#332	C₂²	1	1	yes	characteristic
64	C₅×#332	C₂²	1	1	yes	characteristic
65	C₅×#331	C₂²	1	1	yes	characteristic
66	C₅×#331	C₂²	1	1	yes	characteristic
67	#19182	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
68	C₂×C₅×#41	—	2	1	no	—
69	C₂×C₅×#41	D₄	1	1	yes	characteristic
70	C₅×#135	—	4	4	no	—
71	C₂×C₅×Q₁₆	—	2	1	no	—
72	C₂×C₅×Q₁₆	—	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×D₈	—	2	1	no	—
79	C₂×C₅×M₁₆	—	2	1	no	—
80	C₂×C₅×M₁₆	—	2	1	no	—
81	C₂×C₅×M₁₆	D₄	1	1	yes	characteristic
82	C₂×C₅×M₁₆	D₄	1	1	yes	characteristic
83	C₂²×C₅×C₈	—	2	1	no	—
84	C₅×C₄⋊Q₈	C₂³	1	1	yes	characteristic
85	C₅×C₄⋊Q₈	C₂³	1	1	yes	characteristic
86	C₅×C₄⋊Q₈	C₂³	1	1	yes	characteristic
87	C₅×#127	C₂³	1	1	yes	characteristic
88	C₅×#125	—	2	1	no	—
89	C₅×#124	—	2	1	no	—
90	C₅×C₂²⋊Q₈	—	2	1	no	—
91	C₅×C₂²⋊Q₈	—	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	C₂³	1	1	yes	characteristic
98	C₄×C₅×D₄	—	2	1	no	—
99	C₄×C₅×D₄	—	2	1	no	—
100	C₄×C₅×D₄	—	2	1	no	—
101	C₄×C₅×D₄	—	2	1	no	—
102	C₄×C₅×D₄	D₄	1	1	yes	characteristic
103	C₄×C₅×D₄	C₂³	1	1	yes	characteristic
104	C₅×#117	—	2	1	no	—
105	C₅×#117	—	2	1	no	—
106	C₅×#117	D₄	1	1	yes	characteristic
107	C₂×C₄²×C₅	—	2	1	no	—
108	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
109	C₅×#107	—	2	1	no	—
110	C₅×#107	—	2	1	no	—
111	C₅×#107	—	2	1	no	—
112	C₅×#106	—	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	C₂³	1	1	yes	characteristic
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×C₄⋊C₈	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
127	C₅×#103	—	2	1	no	—
128	C₅×#103	—	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×C₂²⋊C₈	—	2	1	no	—
135	C₅×C₂²⋊C₈	—	2	1	no	—
136	C₅×C₂²⋊C₈	—	2	1	no	—
137	C₅×C₂²⋊C₈	—	2	1	no	—
138	C₅×#97	—	2	1	no	—
139	C₅×#97	D₄	1	1	yes	characteristic
140	C₅×#97	D₄	1	1	yes	characteristic
141	C₄×C₅×C₈	—	2	1	no	—
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	#3182	C₂×C₅	1	1	yes	characteristic, complemented
147	#3107	C₂×C₅	1	1	yes	characteristic, complemented
148	#3035	C₂×C₅	1	1	yes	characteristic
149	#2971	C₂×C₅	1	1	yes	characteristic, complemented
150	#1701	C₂×C₅	1	1	yes	characteristic, complemented
151	#1699	C₂×C₅	1	1	yes	characteristic, complemented
152	#1693	C₂×C₅	1	1	yes	characteristic, complemented
153	#1685	C₂×C₅	1	1	yes	characteristic, complemented
154	#1682	C₂×C₅	1	1	yes	characteristic, complemented
155	#1680	C₂×C₅	1	1	yes	characteristic, complemented
156	#1674	C₂×C₅	1	1	yes	characteristic, complemented
157	#1666	C₂×C₅	1	1	yes	characteristic, complemented
158	#1565	C₂×C₅	1	1	yes	characteristic, complemented
159	#1553	C₂×C₅	1	1	yes	characteristic, complemented
160	#1552	C₂×C₅	1	1	yes	characteristic, complemented
161	C₅×#41	—	2	2	no	—
162	C₅×#41	—	4	1	no	—
163	C₅×#41	—	4	2	no	—
164	C₅×#41	—	4	2	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	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	—	4	1	no	—
174	C₂×C₅×D₄	C₂×D₄	1	1	yes	characteristic
175	C₂²×C₄×C₅	—	2	1	no	—
176	C₂²×C₄×C₅	—	2	1	no	—
177	C₂²×C₄×C₅	—	2	1	no	—
178	C₂²×C₄×C₅	—	4	1	no	—
179	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
180	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
181	C₂²×C₄×C₅	#41	1	1	yes	characteristic
182	C₅×Q₁₆	—	4	2	no	—
183	C₅×Q₁₆	—	4	2	no	—
184	C₅×SD₁₆	—	4	2	no	—
185	C₅×SD₁₆	—	4	2	no	—
186	C₅×SD₁₆	—	4	2	no	—
187	C₅×SD₁₆	—	4	2	no	—
188	C₅×SD₁₆	—	4	2	no	—
189	C₅×D₈	—	4	2	no	—
190	C₅×M₁₆	—	2	2	no	—
191	C₅×M₁₆	—	4	1	no	—
192	C₅×M₁₆	—	4	2	no	—
193	C₅×M₁₆	—	4	2	no	—
194	C₂×C₅×C₈	—	2	1	no	—
195	C₂×C₅×C₈	—	2	1	no	—
196	C₂×C₅×C₈	—	2	1	no	—
197	C₂×C₅×C₈	—	2	1	no	—
198	C₂×C₅×C₈	—	2	1	no	—
199	C₂×C₅×C₈	—	2	1	no	—
200	C₂×C₅×C₈	—	4	2	no	—
201	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
202	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
203	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
204	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
205	C₅×C₄⋊C₄	—	2	1	no	—
206	C₅×C₄⋊C₄	—	2	1	no	—
207	C₅×C₄⋊C₄	—	2	1	no	—
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	—	4	1	no	—
214	C₅×C₄⋊C₄	—	4	1	no	—
215	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
216	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
217	C₅×C₂²⋊C₄	—	2	1	no	—
218	C₅×C₂²⋊C₄	—	2	1	no	—
219	C₅×C₂²⋊C₄	—	2	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	—	4	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×#135	—	2	1	no	—
232	#533	C₂²×C₅	1	1	yes	characteristic
233	#532	C₂²×C₅	1	1	yes	characteristic
234	C₄×#41	C₂²×C₅	1	1	yes	characteristic
235	#500	C₂²×C₅	1	1	yes	characteristic
236	#492	C₂²×C₅	1	1	yes	characteristic
237	#487	C₂²×C₅	1	1	yes	characteristic
238	#486	C₂²×C₅	1	1	yes	characteristic
239	#485	—	2	1	no	—
240	#475	C₂²×C₅	1	1	yes	characteristic
241	#474	C₂²×C₅	1	1	yes	characteristic
242	#468	—	2	1	no	—
243	#468	—	2	1	no	—
244	#464	—	2	1	no	—
245	#463	—	2	1	no	—
246	#462	C₂²×C₅	1	1	yes	characteristic
247	#462	C₂²×C₅	1	1	yes	characteristic
248	#461	C₂²×C₅	1	1	yes	characteristic
249	#461	C₂²×C₅	1	1	yes	characteristic
250	#460	C₂²×C₅	1	1	yes	characteristic
251	#459	C₂²×C₅	1	1	yes	characteristic
252	#452	—	2	1	no	—
253	C₈×Q₈	C₂²×C₅	1	1	yes	characteristic
254	C₈×Q₈	C₂²×C₅	1	1	yes	characteristic
255	#440	—	2	1	no	—
256	#440	—	2	1	no	—
257	C₄×Q₁₆	—	2	1	no	—
258	C₄×SD₁₆	—	2	1	no	—
259	#436	—	2	1	no	—
260	#436	—	2	1	no	—
261	#436	C₂²×C₅	1	1	yes	characteristic
262	#436	C₂²×C₅	1	1	yes	characteristic
263	#432	—	2	1	no	—
264	#432	C₂²×C₅	1	1	yes	characteristic
265	#431	C₂²×C₅	1	1	yes	characteristic
266	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
267	#416	—	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	#332	C₂²×C₅	1	1	yes	characteristic
275	#332	C₂²×C₅	1	1	yes	characteristic
276	#332	C₂²×C₅	1	1	yes	characteristic
277	#332	C₂²×C₅	1	1	yes	characteristic
278	#332	C₂²×C₅	1	1	yes	characteristic
279	#332	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	—	2	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	—	4	1	no	—
287	C₅×Q₈	—	4	1	no	—
288	C₅×Q₈	—	4	1	no	—
289	C₅×Q₈	—	4	1	no	—
290	C₅×Q₈	—	4	1	no	—
291	C₅×Q₈	—	4	1	no	—
292	C₅×Q₈	AGL(1,ℤ/8)	1	2	yes	—
293	C₅×D₄	—	2	1	no	—
294	C₅×D₄	—	2	1	no	—
295	C₅×D₄	—	4	2	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	—	8	1	no	—
301	C₅×D₄	—	8	2	no	—
302	C₂×C₄×C₅	—	2	1	no	—
303	C₂×C₄×C₅	—	2	1	no	—
304	C₂×C₄×C₅	—	2	1	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	—	4	1	no	—
310	C₂×C₄×C₅	—	4	2	no	—
311	C₂×C₄×C₅	—	4	1	no	—
312	C₂×C₄×C₅	—	4	1	no	—
313	C₂×C₄×C₅	—	4	1	no	—
314	C₂×C₄×C₅	—	4	1	no	—
315	C₂×C₄×C₅	—	4	1	no	—
316	C₂×C₄×C₅	—	8	1	no	—
317	C₂×C₄×C₅	—	8	2	no	—
318	C₂×C₄×C₅	#121	1	1	yes	characteristic
319	C₂×C₄×C₅	#121	1	1	yes	characteristic
320	C₂×C₄×C₅	#121	1	1	yes	characteristic
321	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
322	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
323	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
324	C₅×C₈	—	2	1	no	—
325	C₅×C₈	—	2	1	no	—
326	C₅×C₈	—	2	1	no	—
327	C₅×C₈	—	4	1	no	—
328	C₅×C₈	—	4	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	#135	1	2	yes	complemented
334	C₂×#41	—	2	1	no	—
335	C₂×#41	C₅×D₄	1	1	yes	characteristic
336	#135	—	4	4	no	—
337	C₂×Q₁₆	—	2	1	no	—
338	C₂×Q₁₆	—	2	1	no	—
339	C₂×SD₁₆	—	2	1	no	—
340	C₂×SD₁₆	—	2	1	no	—
341	C₂×SD₁₆	—	2	1	no	—
342	C₂×SD₁₆	—	2	1	no	—
343	C₂×SD₁₆	—	2	1	no	—
344	C₂×D₈	—	2	1	no	—
345	C₂×M₁₆	—	2	1	no	—
346	C₂×M₁₆	—	2	1	no	—
347	C₂×M₁₆	C₅×D₄	1	1	yes	characteristic
348	C₂×M₁₆	C₅×D₄	1	1	yes	characteristic
349	C₂²×C₈	—	2	1	no	—
350	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
351	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
352	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
353	#127	C₂³×C₅	1	1	yes	characteristic
354	#125	—	2	1	no	—
355	#124	—	2	1	no	—
356	C₂²⋊Q₈	—	2	1	no	—
357	C₂²⋊Q₈	—	2	1	no	—
358	#121	—	2	1	no	—
359	#121	—	2	1	no	—
360	C₄×Q₈	—	2	1	no	—
361	C₄×Q₈	—	2	1	no	—
362	C₄×Q₈	C₅×D₄	1	1	yes	characteristic
363	C₄×Q₈	C₂³×C₅	1	1	yes	characteristic
364	C₄×D₄	—	2	1	no	—
365	C₄×D₄	—	2	1	no	—
366	C₄×D₄	—	2	1	no	—
367	C₄×D₄	—	2	1	no	—
368	C₄×D₄	C₅×D₄	1	1	yes	characteristic
369	C₄×D₄	C₂³×C₅	1	1	yes	characteristic
370	#117	—	2	1	no	—
371	#117	—	2	1	no	—
372	#117	C₅×D₄	1	1	yes	characteristic
373	C₂×C₄²	—	2	1	no	—
374	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
375	#107	—	2	1	no	—
376	#107	—	2	1	no	—
377	#107	—	2	1	no	—
378	#106	—	2	1	no	—
379	C₄⋊C₈	—	2	1	no	—
380	C₄⋊C₈	—	2	1	no	—
381	C₄⋊C₈	—	2	1	no	—
382	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
383	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
384	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
385	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
386	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
387	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
388	#103	—	2	1	no	—
389	#103	—	2	1	no	—
390	#103	—	2	1	no	—
391	#103	—	2	1	no	—
392	#103	—	2	1	no	—
393	#103	—	2	1	no	—
394	#103	—	2	1	no	—
395	#102	—	2	1	no	—
396	#102	—	2	1	no	—
397	#102	—	2	1	no	—
398	#102	—	2	1	no	—
399	#102	—	2	1	no	—
400	C₂²⋊C₈	—	2	1	no	—
401	C₂²⋊C₈	—	2	1	no	—
402	C₂²⋊C₈	—	2	1	no	—
403	C₂²⋊C₈	—	2	1	no	—
404	#97	—	2	1	no	—
405	#97	C₅×D₄	1	1	yes	characteristic
406	#97	C₅×D₄	1	1	yes	characteristic
407	C₄×C₈	—	2	1	no	—
408	C₄×C₈	—	2	1	no	—
409	C₄×C₈	—	2	1	no	—
410	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
411	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
412	C₂²×C₅	—	2	1	no	—
413	C₂²×C₅	—	2	1	no	—
414	C₂²×C₅	—	2	1	no	—
415	C₂²×C₅	—	4	1	no	—
416	C₂²×C₅	—	4	1	no	—
417	C₂²×C₅	—	4	1	no	—
418	C₂²×C₅	—	8	1	no	—
419	C₂²×C₅	—	8	1	no	—
420	C₂²×C₅	—	8	1	no	—
421	C₂²×C₅	C₂×#121	1	1	yes	characteristic
422	C₄×C₅	—	2	1	no	—
423	C₄×C₅	—	2	1	no	—
424	C₄×C₅	—	2	2	no	—
425	C₄×C₅	—	2	1	no	—
426	C₄×C₅	—	2	1	no	—
427	C₄×C₅	—	4	1	no	—
428	C₄×C₅	—	4	1	no	—
429	C₄×C₅	—	8	1	no	—
430	C₄×C₅	—	8	1	no	—
431	C₄×C₅	—	8	1	no	—
432	C₄×C₅	C₂×#135	1	1	yes	characteristic
433	C₄×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
434	C₄×C₅	#575	1	1	yes	characteristic
435	C₄×C₅	#575	1	1	yes	characteristic
436	#41	—	2	2	no	—
437	#41	—	4	1	no	—
438	#41	—	4	2	no	—
439	#41	—	4	2	no	—
440	C₂×Q₈	—	2	1	no	—
441	C₂×Q₈	—	2	1	no	—
442	C₂×Q₈	—	2	1	no	—
443	C₂×Q₈	C₂×C₅×D₄	1	1	yes	characteristic
444	C₂×D₄	—	2	1	no	—
445	C₂×D₄	—	2	1	no	—
446	C₂×D₄	—	2	1	no	—
447	C₂×D₄	—	2	1	no	—
448	C₂×D₄	—	4	1	no	—
449	C₂×D₄	C₂×C₅×D₄	1	1	yes	characteristic
450	C₂²×C₄	—	2	1	no	—
451	C₂²×C₄	—	2	1	no	—
452	C₂²×C₄	—	2	1	no	—
453	C₂²×C₄	—	4	1	no	—
454	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
455	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
456	C₂²×C₄	C₅×#41	1	1	yes	characteristic
457	Q₁₆	—	4	2	no	—
458	Q₁₆	—	4	2	no	—
459	SD₁₆	—	4	2	no	—
460	SD₁₆	—	4	2	no	—
461	SD₁₆	—	4	2	no	—
462	SD₁₆	—	4	2	no	—
463	SD₁₆	—	4	2	no	—
464	D₈	—	4	2	no	—
465	M₁₆	—	2	2	no	—
466	M₁₆	—	4	1	no	—
467	M₁₆	—	4	2	no	—
468	M₁₆	—	4	2	no	—
469	C₂×C₈	—	2	1	no	—
470	C₂×C₈	—	2	1	no	—
471	C₂×C₈	—	2	1	no	—
472	C₂×C₈	—	2	1	no	—
473	C₂×C₈	—	2	1	no	—
474	C₂×C₈	—	2	1	no	—
475	C₂×C₈	—	4	2	no	—
476	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
477	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
478	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
479	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
480	C₄⋊C₄	—	2	1	no	—
481	C₄⋊C₄	—	2	1	no	—
482	C₄⋊C₄	—	2	1	no	—
483	C₄⋊C₄	—	2	1	no	—
484	C₄⋊C₄	—	2	1	no	—
485	C₄⋊C₄	—	2	1	no	—
486	C₄⋊C₄	—	2	1	no	—
487	C₄⋊C₄	—	2	1	no	—
488	C₄⋊C₄	—	4	1	no	—
489	C₄⋊C₄	—	4	1	no	—
490	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
491	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
492	C₂²⋊C₄	—	2	1	no	—
493	C₂²⋊C₄	—	2	1	no	—
494	C₂²⋊C₄	—	2	1	no	—
495	C₂²⋊C₄	—	4	1	no	—
496	C₂²⋊C₄	—	4	1	no	—
497	C₂²⋊C₄	—	4	1	no	—
498	C₄²	—	2	1	no	—
499	C₄²	—	2	1	no	—
500	C₄²	—	2	1	no	—
501	C₄²	—	4	1	no	—
502	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
503	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
504	C₄²	C₅×#41	1	1	yes	characteristic
505	C₄²	C₂⁴×C₅	1	1	yes	characteristic
506	C₂×C₅	—	4	1	no	—
507	C₂×C₅	—	8	1	no	—
508	C₂×C₅	—	16	1	no	—
509	C₂×C₅	#3035	1	1	yes	characteristic
510	C₂×C₅	#3055	1	1	yes	characteristic
511	C₂×C₅	#3069	1	1	yes	characteristic
512	C₂³	—	2	1	no	—
513	C₂³	—	4	1	no	—
514	C₂³	C₅×#121	1	1	yes	characteristic
515	Q₈	—	2	1	no	—
516	Q₈	—	4	1	no	—
517	Q₈	—	4	1	no	—
518	Q₈	—	4	1	no	—
519	Q₈	—	4	1	no	—
520	Q₈	—	4	1	no	—
521	Q₈	—	4	1	no	—
522	Q₈	C₅×AGL(1,ℤ/8)	1	2	yes	—
523	D₄	—	2	1	no	—
524	D₄	—	2	1	no	—
525	D₄	—	4	2	no	—
526	D₄	—	4	1	no	—
527	D₄	—	4	1	no	—
528	D₄	—	4	1	no	—
529	D₄	—	4	1	no	—
530	D₄	—	8	1	no	—
531	D₄	—	8	2	no	—
532	C₂×C₄	—	2	1	no	—
533	C₂×C₄	—	2	1	no	—
534	C₂×C₄	—	2	1	no	—
535	C₂×C₄	—	2	1	no	—
536	C₂×C₄	—	2	1	no	—
537	C₂×C₄	—	2	1	no	—
538	C₂×C₄	—	2	1	no	—
539	C₂×C₄	—	4	1	no	—
540	C₂×C₄	—	4	2	no	—
541	C₂×C₄	—	4	1	no	—
542	C₂×C₄	—	4	1	no	—
543	C₂×C₄	—	4	1	no	—
544	C₂×C₄	—	4	1	no	—
545	C₂×C₄	—	4	1	no	—
546	C₂×C₄	—	8	1	no	—
547	C₂×C₄	—	8	2	no	—
548	C₂×C₄	C₅×#121	1	1	yes	characteristic
549	C₂×C₄	C₅×#121	1	1	yes	characteristic
550	C₂×C₄	C₅×#121	1	1	yes	characteristic
551	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
552	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
553	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
554	C₈	—	2	1	no	—
555	C₈	—	2	1	no	—
556	C₈	—	2	1	no	—
557	C₈	—	4	1	no	—
558	C₈	—	4	1	no	—
559	C₈	—	4	1	no	—
560	C₈	—	4	1	no	—
561	C₈	—	4	1	no	—
562	C₈	—	4	1	no	—
563	C₈	C₅×#135	1	2	yes	complemented
564	C₅	#19182	1	1	yes	characteristic, direct product factor, Sylow
565	C₂²	—	2	1	no	—
566	C₂²	—	2	1	no	—
567	C₂²	—	2	1	no	—
568	C₂²	—	4	1	no	—
569	C₂²	—	4	1	no	—
570	C₂²	—	4	1	no	—
571	C₂²	—	8	1	no	—
572	C₂²	—	8	1	no	—
573	C₂²	—	8	1	no	—
574	C₂²	C₂×C₅×#121	1	1	yes	characteristic
575	C₄	—	2	1	no	—
576	C₄	—	2	1	no	—
577	C₄	—	2	2	no	—
578	C₄	—	2	1	no	—
579	C₄	—	2	1	no	—
580	C₄	—	4	1	no	—
581	C₄	—	4	1	no	—
582	C₄	—	8	1	no	—
583	C₄	—	8	1	no	—
584	C₄	—	8	1	no	—
585	C₄	C₂×C₅×#135	1	1	yes	characteristic
586	C₄	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
587	C₄	C₅×#575	1	1	yes	characteristic
588	C₄	C₅×#575	1	1	yes	characteristic
589	C₂	—	4	1	no	—
590	C₂	—	8	1	no	—
591	C₂	—	16	1	no	—
592	C₂	C₅×#3035	1	1	yes	characteristic
593	C₂	C₅×#3055	1	1	yes	characteristic
594	C₂	C₅×#3069	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₅
prime radical	C₅×#3035	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
1. C₅×#3182	C₂	semidirect
2. C₅×#3107	C₂	semidirect
4. C₅×#2971	C₂	semidirect
5. C₅×#1701	C₂	semidirect
6. C₅×#1699	C₂	semidirect
7. C₅×#1693	C₂	semidirect
8. C₅×#1685	C₂	semidirect
9. C₅×#1682	C₂	semidirect
10. C₅×#1680	C₂	semidirect
11. C₅×#1674	C₂	semidirect
12. C₅×#1666	C₂	semidirect
13. C₅×#1565	C₂	semidirect
14. C₅×#1553	C₂	semidirect
15. C₅×#1552	C₂	semidirect
67. #19182	C₅	direct (N × H)
146. #3182	C₂×C₅	semidirect
147. #3107	C₂×C₅	semidirect
149. #2971	C₂×C₅	semidirect
150. #1701	C₂×C₅	semidirect
151. #1699	C₂×C₅	semidirect
152. #1693	C₂×C₅	semidirect
153. #1685	C₂×C₅	semidirect
154. #1682	C₂×C₅	semidirect
155. #1680	C₂×C₅	semidirect
156. #1674	C₂×C₅	semidirect
157. #1666	C₂×C₅	semidirect
158. #1565	C₂×C₅	semidirect
159. #1553	C₂×C₅	semidirect
160. #1552	C₂×C₅	semidirect
333. C₅×C₈	#135	semidirect
563. C₈	C₅×#135	semidirect
564. C₅	#19182	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×#3182	2
C₅×#3107	2
C₅×#3035	2
C₅×#2971	2
C₅×#1701	2
C₅×#1699	2
C₅×#1693	2
C₅×#1685	2
C₅×#1682	2
C₅×#1680	2
C₅×#1674	2
C₅×#1666	2
C₅×#1565	2
C₅×#1553	2
C₅×#1552	2
#19182	5

Subgroups — C5×#19182 #11941902

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#19182 #11941902