Subgroups — C₅×#19580 #11942300

Order 1280.

602 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3247	C₂	1	1	yes	maximal, characteristic
2	C₅×#3239	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#3206	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#2994	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#1704	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#1703	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#1686	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1685	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1684	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1683	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1666	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#1665	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#1573	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#1551	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₅×#332	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#532	C₂²	1	1	yes	characteristic
17	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
18	C₅×#529	C₂²	1	1	yes	characteristic
19	C₅×#501	—	2	1	no	—
20	C₅×#492	C₂²	1	1	yes	characteristic
21	C₅×#492	C₂²	1	1	yes	characteristic
22	C₅×#489	—	2	1	no	—
23	C₅×#487	C₂²	1	1	yes	characteristic
24	C₅×#487	C₂²	1	1	yes	characteristic
25	C₅×#484	—	2	1	no	—
26	C₅×#481	—	2	1	no	—
27	C₅×#478	—	2	1	no	—
28	C₅×#477	C₂²	1	1	yes	characteristic
29	C₅×#476	C₂²	1	1	yes	characteristic
30	C₅×#475	C₂²	1	1	yes	characteristic
31	C₅×#475	C₂²	1	1	yes	characteristic
32	C₅×#474	C₂²	1	1	yes	characteristic
33	C₅×#474	C₂²	1	1	yes	characteristic
34	C₅×#466	—	2	1	no	—
35	C₅×#465	—	2	1	no	—
36	C₅×#463	—	2	1	no	—
37	C₅×#461	—	2	1	no	—
38	C₅×#461	—	2	1	no	—
39	C₅×#460	C₂²	1	1	yes	characteristic
40	C₅×#459	C₂²	1	1	yes	characteristic
41	C₅×#448	—	2	1	no	—
42	C₅×#448	—	2	1	no	—
43	C₅×#446	C₂²	1	1	yes	characteristic
44	C₅×C₈×Q₈	C₂²	1	1	yes	characteristic
45	C₅×#436	C₂²	1	1	yes	characteristic
46	C₅×#435	—	2	1	no	—
47	C₅×C₈×D₄	—	2	1	no	—
48	C₅×C₈×D₄	C₂²	1	1	yes	characteristic
49	C₅×#433	—	2	1	no	—
50	C₅×#432	C₂²	1	1	yes	characteristic
51	C₅×#431	C₂²	1	1	yes	characteristic
52	C₅×#424	—	2	1	no	—
53	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
54	C₂×C₅×C₄⋊C₈	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×#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	#19580	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	C₂×C₅×SD₁₆	—	2	1	no	—
71	C₂×C₅×SD₁₆	—	2	1	no	—
72	C₂×C₅×SD₁₆	—	2	1	no	—
73	C₂×C₅×SD₁₆	—	2	1	no	—
74	C₂×C₅×SD₁₆	—	2	1	no	—
75	C₂×C₅×D₈	—	2	1	no	—
76	C₂×C₅×M₁₆	—	2	1	no	—
77	C₂²×C₅×C₈	—	2	1	no	—
78	C₂²×C₅×C₈	—	2	1	no	—
79	C₂²×C₅×C₈	—	2	1	no	—
80	C₅×C₄⋊Q₈	—	2	1	no	—
81	C₅×C₄⋊Q₈	—	2	1	no	—
82	C₅×C₄⋊Q₈	—	2	1	no	—
83	C₅×C₄⋊Q₈	C₂³	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×#126	—	2	1	no	—
88	C₅×#125	D₄	1	1	yes	characteristic
89	C₅×#124	—	2	1	no	—
90	C₅×#124	D₄	1	1	yes	characteristic
91	C₅×#123	—	2	1	no	—
92	C₅×C₂²⋊Q₈	D₄	1	1	yes	characteristic
93	C₅×#121	—	2	1	no	—
94	C₅×#121	—	2	1	no	—
95	C₅×#121	D₄	1	1	yes	characteristic
96	C₄×C₅×Q₈	C₂³	1	1	yes	characteristic
97	C₄×C₅×D₄	—	2	1	no	—
98	C₄×C₅×D₄	—	2	1	no	—
99	C₄×C₅×D₄	—	2	1	no	—
100	C₄×C₅×D₄	C₂³	1	1	yes	characteristic
101	C₅×#117	—	2	1	no	—
102	C₂×C₅×C₄⋊C₄	—	2	1	no	—
103	C₂×C₅×C₄⋊C₄	—	2	1	no	—
104	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
105	C₅×#107	—	2	1	no	—
106	C₅×#107	—	2	1	no	—
107	C₅×#107	—	2	1	no	—
108	C₅×#106	—	2	1	no	—
109	C₅×#106	—	2	1	no	—
110	C₅×#106	—	2	1	no	—
111	C₅×C₄⋊C₈	—	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	D₄	1	1	yes	characteristic
116	C₅×C₄⋊C₈	D₄	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×C₄⋊C₈	C₂³	1	1	yes	characteristic
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×#103	—	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×C₂²⋊C₈	—	2	1	no	—
136	C₅×C₂²⋊C₈	—	2	1	no	—
137	C₅×C₂²⋊C₈	—	2	1	no	—
138	C₅×C₂²⋊C₈	D₄	1	1	yes	characteristic
139	C₅×C₂²⋊C₈	D₄	1	1	yes	characteristic
140	C₅×#97	—	2	1	no	—
141	C₅×#97	—	2	1	no	—
142	C₄×C₅×C₈	—	2	1	no	—
143	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
144	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
145	#3247	C₂×C₅	1	1	yes	characteristic
146	#3239	C₂×C₅	1	1	yes	characteristic, complemented
147	#3206	C₂×C₅	1	1	yes	characteristic, complemented
148	#2994	C₂×C₅	1	1	yes	characteristic, complemented
149	#1704	C₂×C₅	1	1	yes	characteristic, complemented
150	#1703	C₂×C₅	1	1	yes	characteristic, complemented
151	#1686	C₂×C₅	1	1	yes	characteristic, complemented
152	#1685	C₂×C₅	1	1	yes	characteristic, complemented
153	#1684	C₂×C₅	1	1	yes	characteristic, complemented
154	#1683	C₂×C₅	1	1	yes	characteristic, complemented
155	#1666	C₂×C₅	1	1	yes	characteristic, complemented
156	#1665	C₂×C₅	1	1	yes	characteristic, complemented
157	#1573	C₂×C₅	1	1	yes	characteristic, complemented
158	#1551	C₂×C₅	1	1	yes	characteristic, complemented
159	C₂×#332	C₂×C₅	1	1	yes	characteristic, complemented
160	C₅×#41	—	8	2	no	—
161	C₂×C₅×Q₈	—	2	1	no	—
162	C₂×C₅×Q₈	—	2	1	no	—
163	C₂×C₅×Q₈	—	2	1	no	—
164	C₂×C₅×Q₈	—	4	1	no	—
165	C₂×C₅×Q₈	—	8	1	no	—
166	C₂×C₅×Q₈	—	8	1	no	—
167	C₂×C₅×Q₈	C₂×D₄	1	1	yes	characteristic
168	C₂×C₅×D₄	—	2	1	no	—
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	—	4	1	no	—
173	C₂×C₅×D₄	C₂×D₄	1	1	yes	characteristic
174	C₂²×C₄×C₅	—	2	1	no	—
175	C₂²×C₄×C₅	—	4	1	no	—
176	C₂²×C₄×C₅	—	4	1	no	—
177	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
178	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
179	C₂²×C₄×C₅	#41	1	1	yes	characteristic
180	C₅×SD₁₆	—	8	1	no	—
181	C₅×SD₁₆	—	8	1	no	—
182	C₅×SD₁₆	—	8	1	no	—
183	C₅×SD₁₆	—	8	1	no	—
184	C₅×SD₁₆	—	8	1	no	—
185	C₅×D₈	—	8	1	no	—
186	C₅×M₁₆	—	8	1	no	—
187	C₂×C₅×C₈	—	2	1	no	—
188	C₂×C₅×C₈	—	2	1	no	—
189	C₂×C₅×C₈	—	2	1	no	—
190	C₂×C₅×C₈	—	2	1	no	—
191	C₂×C₅×C₈	—	2	1	no	—
192	C₂×C₅×C₈	—	2	1	no	—
193	C₂×C₅×C₈	—	8	1	no	—
194	C₂×C₅×C₈	—	8	1	no	—
195	C₂×C₅×C₈	—	8	1	no	—
196	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
197	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
198	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
199	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
200	C₅×C₄⋊C₄	—	2	1	no	—
201	C₅×C₄⋊C₄	—	2	1	no	—
202	C₅×C₄⋊C₄	—	2	1	no	—
203	C₅×C₄⋊C₄	—	2	1	no	—
204	C₅×C₄⋊C₄	—	2	1	no	—
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	—	4	1	no	—
211	C₅×C₄⋊C₄	—	4	1	no	—
212	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
213	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
214	C₅×C₂²⋊C₄	—	2	1	no	—
215	C₅×C₂²⋊C₄	—	2	1	no	—
216	C₅×C₂²⋊C₄	—	2	1	no	—
217	C₅×C₂²⋊C₄	—	2	1	no	—
218	C₅×C₂²⋊C₄	—	2	1	no	—
219	C₅×C₂²⋊C₄	—	4	1	no	—
220	C₅×C₂²⋊C₄	—	4	1	no	—
221	C₄²×C₅	—	2	1	no	—
222	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
223	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
224	C₄²×C₅	#41	1	1	yes	characteristic
225	C₄²×C₅	C₂⁴	1	1	yes	characteristic
226	#532	C₂²×C₅	1	1	yes	characteristic
227	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
228	#529	C₂²×C₅	1	1	yes	characteristic
229	#501	—	2	1	no	—
230	#492	C₂²×C₅	1	1	yes	characteristic
231	#492	C₂²×C₅	1	1	yes	characteristic
232	#489	—	2	1	no	—
233	#487	C₂²×C₅	1	1	yes	characteristic
234	#487	C₂²×C₅	1	1	yes	characteristic
235	#484	—	2	1	no	—
236	#481	—	2	1	no	—
237	#478	—	2	1	no	—
238	#477	C₂²×C₅	1	1	yes	characteristic
239	#476	C₂²×C₅	1	1	yes	characteristic
240	#475	C₂²×C₅	1	1	yes	characteristic
241	#475	C₂²×C₅	1	1	yes	characteristic
242	#474	C₂²×C₅	1	1	yes	characteristic
243	#474	C₂²×C₅	1	1	yes	characteristic
244	#466	—	2	1	no	—
245	#465	—	2	1	no	—
246	#463	—	2	1	no	—
247	#461	—	2	1	no	—
248	#461	—	2	1	no	—
249	#460	C₂²×C₅	1	1	yes	characteristic
250	#459	C₂²×C₅	1	1	yes	characteristic
251	#448	—	2	1	no	—
252	#448	—	2	1	no	—
253	#446	C₂²×C₅	1	1	yes	characteristic
254	C₈×Q₈	C₂²×C₅	1	1	yes	characteristic
255	#436	C₂²×C₅	1	1	yes	characteristic
256	#435	—	2	1	no	—
257	C₈×D₄	—	2	1	no	—
258	C₈×D₄	C₂²×C₅	1	1	yes	characteristic
259	#433	—	2	1	no	—
260	#432	C₂²×C₅	1	1	yes	characteristic
261	#431	C₂²×C₅	1	1	yes	characteristic
262	#424	—	2	1	no	—
263	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
264	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
265	#335	C₂²×C₅	1	1	yes	characteristic
266	#335	C₂²×C₅	1	1	yes	characteristic
267	#334	C₂²×C₅	1	1	yes	characteristic
268	#334	C₂²×C₅	1	1	yes	characteristic
269	#333	C₂²×C₅	1	1	yes	characteristic
270	#333	C₂²×C₅	1	1	yes	characteristic
271	#332	C₂²×C₅	1	1	yes	characteristic
272	#332	C₂²×C₅	1	1	yes	characteristic
273	#332	C₂²×C₅	1	1	yes	characteristic
274	#332	C₂²×C₅	1	1	yes	characteristic
275	#331	C₂²×C₅	1	1	yes	characteristic
276	#331	C₂²×C₅	1	1	yes	characteristic
277	C₂³×C₅	—	2	1	no	—
278	C₂³×C₅	—	4	1	no	—
279	C₂³×C₅	#121	1	1	yes	characteristic
280	C₅×Q₈	—	2	1	no	—
281	C₅×Q₈	—	2	1	no	—
282	C₅×Q₈	—	4	1	no	—
283	C₅×Q₈	—	4	1	no	—
284	C₅×Q₈	—	4	1	no	—
285	C₅×Q₈	—	4	1	no	—
286	C₅×Q₈	—	8	1	no	—
287	C₅×Q₈	—	8	2	no	—
288	C₅×D₄	—	2	1	no	—
289	C₅×D₄	—	2	1	no	—
290	C₅×D₄	—	4	2	no	—
291	C₅×D₄	—	4	1	no	—
292	C₅×D₄	—	4	1	no	—
293	C₅×D₄	—	4	1	no	—
294	C₅×D₄	—	4	1	no	—
295	C₅×D₄	—	8	1	no	—
296	C₅×D₄	—	8	2	no	—
297	C₂×C₄×C₅	—	2	2	no	—
298	C₂×C₄×C₅	—	2	1	no	—
299	C₂×C₄×C₅	—	2	1	no	—
300	C₂×C₄×C₅	—	2	1	no	—
301	C₂×C₄×C₅	—	2	1	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	—	4	1	no	—
306	C₂×C₄×C₅	—	4	1	no	—
307	C₂×C₄×C₅	—	4	1	no	—
308	C₂×C₄×C₅	—	4	1	no	—
309	C₂×C₄×C₅	—	4	1	no	—
310	C₂×C₄×C₅	—	8	2	no	—
311	C₂×C₄×C₅	—	8	2	no	—
312	C₂×C₄×C₅	#121	1	1	yes	characteristic
313	C₂×C₄×C₅	#121	1	1	yes	characteristic
314	C₂×C₄×C₅	#121	1	1	yes	characteristic
315	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
316	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
317	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
318	C₅×C₈	—	2	1	no	—
319	C₅×C₈	—	2	1	no	—
320	C₅×C₈	—	2	1	no	—
321	C₅×C₈	—	2	1	no	—
322	C₅×C₈	—	4	1	no	—
323	C₅×C₈	—	4	1	no	—
324	C₅×C₈	—	4	1	no	—
325	C₅×C₈	—	4	1	no	—
326	C₅×C₈	—	4	1	no	—
327	C₅×C₈	—	4	1	no	—
328	C₂×#41	—	2	1	no	—
329	C₂²×Q₈	—	2	1	no	—
330	C₂×SD₁₆	—	2	1	no	—
331	C₂×SD₁₆	—	2	1	no	—
332	C₂×SD₁₆	—	2	1	no	—
333	C₂×SD₁₆	—	2	1	no	—
334	C₂×SD₁₆	—	2	1	no	—
335	C₂×D₈	—	2	1	no	—
336	C₂×M₁₆	—	2	1	no	—
337	C₂²×C₈	—	2	1	no	—
338	C₂²×C₈	—	2	1	no	—
339	C₂²×C₈	—	2	1	no	—
340	C₄⋊Q₈	—	2	1	no	—
341	C₄⋊Q₈	—	2	1	no	—
342	C₄⋊Q₈	—	2	1	no	—
343	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
344	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
345	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
346	#127	C₂³×C₅	1	1	yes	characteristic
347	#126	—	2	1	no	—
348	#125	C₅×D₄	1	1	yes	characteristic
349	#124	—	2	1	no	—
350	#124	C₅×D₄	1	1	yes	characteristic
351	#123	—	2	1	no	—
352	C₂²⋊Q₈	C₅×D₄	1	1	yes	characteristic
353	#121	—	2	1	no	—
354	#121	—	2	1	no	—
355	#121	C₅×D₄	1	1	yes	characteristic
356	C₄×Q₈	C₂³×C₅	1	1	yes	characteristic
357	C₄×D₄	—	2	1	no	—
358	C₄×D₄	—	2	1	no	—
359	C₄×D₄	—	2	1	no	—
360	C₄×D₄	C₂³×C₅	1	1	yes	characteristic
361	#117	—	2	1	no	—
362	C₂×C₄⋊C₄	—	2	1	no	—
363	C₂×C₄⋊C₄	—	2	1	no	—
364	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
365	#107	—	2	1	no	—
366	#107	—	2	1	no	—
367	#107	—	2	1	no	—
368	#106	—	2	1	no	—
369	#106	—	2	1	no	—
370	#106	—	2	1	no	—
371	C₄⋊C₈	—	2	1	no	—
372	C₄⋊C₈	—	2	1	no	—
373	C₄⋊C₈	—	2	1	no	—
374	C₄⋊C₈	—	2	1	no	—
375	C₄⋊C₈	C₅×D₄	1	1	yes	characteristic
376	C₄⋊C₈	C₅×D₄	1	1	yes	characteristic
377	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
378	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
379	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
380	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
381	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
382	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
383	#103	—	2	1	no	—
384	#103	—	2	1	no	—
385	#103	—	2	1	no	—
386	#103	—	2	1	no	—
387	#103	—	2	1	no	—
388	#103	—	2	1	no	—
389	#103	—	2	1	no	—
390	#102	—	2	1	no	—
391	#102	—	2	1	no	—
392	#102	—	2	1	no	—
393	#102	—	2	1	no	—
394	#102	—	2	1	no	—
395	C₂²⋊C₈	—	2	1	no	—
396	C₂²⋊C₈	—	2	1	no	—
397	C₂²⋊C₈	—	2	1	no	—
398	C₂²⋊C₈	C₅×D₄	1	1	yes	characteristic
399	C₂²⋊C₈	C₅×D₄	1	1	yes	characteristic
400	#97	—	2	1	no	—
401	#97	—	2	1	no	—
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	C₂²×C₅	—	2	1	no	—
406	C₂²×C₅	—	2	1	no	—
407	C₂²×C₅	—	4	1	no	—
408	C₂²×C₅	—	4	1	no	—
409	C₂²×C₅	—	4	1	no	—
410	C₂²×C₅	—	8	1	no	—
411	C₂²×C₅	—	8	1	no	—
412	C₂²×C₅	—	8	1	no	—
413	C₂²×C₅	#471	1	2	yes	—
414	C₂²×C₅	C₂×#121	1	1	yes	characteristic
415	C₄×C₅	—	2	1	no	—
416	C₄×C₅	—	2	1	no	—
417	C₄×C₅	—	2	1	no	—
418	C₄×C₅	—	2	1	no	—
419	C₄×C₅	—	4	1	no	—
420	C₄×C₅	—	4	1	no	—
421	C₄×C₅	—	4	1	no	—
422	C₄×C₅	—	8	1	no	—
423	C₄×C₅	—	8	1	no	—
424	C₄×C₅	—	8	1	no	—
425	C₄×C₅	#576	1	1	yes	characteristic
426	C₄×C₅	#577	1	1	yes	characteristic
427	C₄×C₅	#577	1	1	yes	characteristic
428	C₄×C₅	#578	1	1	yes	characteristic
429	#41	—	8	2	no	—
430	C₂×Q₈	—	2	1	no	—
431	C₂×Q₈	—	2	1	no	—
432	C₂×Q₈	—	2	1	no	—
433	C₂×Q₈	—	4	1	no	—
434	C₂×Q₈	—	8	1	no	—
435	C₂×Q₈	—	8	1	no	—
436	C₂×Q₈	C₂×C₅×D₄	1	1	yes	characteristic
437	C₂×D₄	—	2	1	no	—
438	C₂×D₄	—	2	1	no	—
439	C₂×D₄	—	2	1	no	—
440	C₂×D₄	—	2	1	no	—
441	C₂×D₄	—	4	1	no	—
442	C₂×D₄	C₂×C₅×D₄	1	1	yes	characteristic
443	C₂²×C₄	—	2	1	no	—
444	C₂²×C₄	—	4	1	no	—
445	C₂²×C₄	—	4	1	no	—
446	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
447	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
448	C₂²×C₄	C₅×#41	1	1	yes	characteristic
449	SD₁₆	—	8	1	no	—
450	SD₁₆	—	8	1	no	—
451	SD₁₆	—	8	1	no	—
452	SD₁₆	—	8	1	no	—
453	SD₁₆	—	8	1	no	—
454	D₈	—	8	1	no	—
455	M₁₆	—	8	1	no	—
456	C₂×C₈	—	2	1	no	—
457	C₂×C₈	—	2	1	no	—
458	C₂×C₈	—	2	1	no	—
459	C₂×C₈	—	2	1	no	—
460	C₂×C₈	—	2	1	no	—
461	C₂×C₈	—	2	1	no	—
462	C₂×C₈	—	8	1	no	—
463	C₂×C₈	—	8	1	no	—
464	C₂×C₈	—	8	1	no	—
465	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
466	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
467	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
468	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
469	C₄⋊C₄	—	2	1	no	—
470	C₄⋊C₄	—	2	1	no	—
471	C₄⋊C₄	—	2	1	no	—
472	C₄⋊C₄	—	2	1	no	—
473	C₄⋊C₄	—	2	1	no	—
474	C₄⋊C₄	—	2	1	no	—
475	C₄⋊C₄	—	2	1	no	—
476	C₄⋊C₄	—	2	1	no	—
477	C₄⋊C₄	—	2	1	no	—
478	C₄⋊C₄	—	2	1	no	—
479	C₄⋊C₄	—	4	1	no	—
480	C₄⋊C₄	—	4	1	no	—
481	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
482	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
483	C₂²⋊C₄	—	2	1	no	—
484	C₂²⋊C₄	—	2	1	no	—
485	C₂²⋊C₄	—	2	1	no	—
486	C₂²⋊C₄	—	2	1	no	—
487	C₂²⋊C₄	—	2	1	no	—
488	C₂²⋊C₄	—	4	1	no	—
489	C₂²⋊C₄	—	4	1	no	—
490	C₄²	—	2	1	no	—
491	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
492	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
493	C₄²	C₅×#41	1	1	yes	characteristic
494	C₄²	C₂⁴×C₅	1	1	yes	characteristic
495	C₂×C₅	—	2	2	no	—
496	C₂×C₅	—	8	1	no	—
497	C₂×C₅	—	16	1	no	—
498	C₂×C₅	#3045	1	1	yes	characteristic
499	C₂×C₅	#3063	1	1	yes	characteristic
500	C₂×C₅	C₂×#471	1	1	yes	characteristic
501	C₂³	—	2	1	no	—
502	C₂³	—	4	1	no	—
503	C₂³	C₅×#121	1	1	yes	characteristic
504	Q₈	—	2	1	no	—
505	Q₈	—	2	1	no	—
506	Q₈	—	4	1	no	—
507	Q₈	—	4	1	no	—
508	Q₈	—	4	1	no	—
509	Q₈	—	4	1	no	—
510	Q₈	—	8	1	no	—
511	Q₈	—	8	2	no	—
512	D₄	—	2	1	no	—
513	D₄	—	2	1	no	—
514	D₄	—	4	2	no	—
515	D₄	—	4	1	no	—
516	D₄	—	4	1	no	—
517	D₄	—	4	1	no	—
518	D₄	—	4	1	no	—
519	D₄	—	8	1	no	—
520	D₄	—	8	2	no	—
521	C₂×C₄	—	2	2	no	—
522	C₂×C₄	—	2	1	no	—
523	C₂×C₄	—	2	1	no	—
524	C₂×C₄	—	2	1	no	—
525	C₂×C₄	—	2	1	no	—
526	C₂×C₄	—	2	1	no	—
527	C₂×C₄	—	2	1	no	—
528	C₂×C₄	—	2	1	no	—
529	C₂×C₄	—	4	1	no	—
530	C₂×C₄	—	4	1	no	—
531	C₂×C₄	—	4	1	no	—
532	C₂×C₄	—	4	1	no	—
533	C₂×C₄	—	4	1	no	—
534	C₂×C₄	—	8	2	no	—
535	C₂×C₄	—	8	2	no	—
536	C₂×C₄	C₅×#121	1	1	yes	characteristic
537	C₂×C₄	C₅×#121	1	1	yes	characteristic
538	C₂×C₄	C₅×#121	1	1	yes	characteristic
539	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
540	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
541	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
542	C₈	—	2	1	no	—
543	C₈	—	2	1	no	—
544	C₈	—	2	1	no	—
545	C₈	—	2	1	no	—
546	C₈	—	4	1	no	—
547	C₈	—	4	1	no	—
548	C₈	—	4	1	no	—
549	C₈	—	4	1	no	—
550	C₈	—	4	1	no	—
551	C₈	—	4	1	no	—
552	C₅	#19580	1	1	yes	characteristic, direct product factor, Sylow
553	C₂²	—	2	1	no	—
554	C₂²	—	2	1	no	—
555	C₂²	—	4	1	no	—
556	C₂²	—	4	1	no	—
557	C₂²	—	4	1	no	—
558	C₂²	—	8	1	no	—
559	C₂²	—	8	1	no	—
560	C₂²	—	8	1	no	—
561	C₂²	C₅×#471	1	2	yes	—
562	C₂²	C₂×C₅×#121	1	1	yes	characteristic
563	C₄	—	2	1	no	—
564	C₄	—	2	1	no	—
565	C₄	—	2	1	no	—
566	C₄	—	2	1	no	—
567	C₄	—	4	1	no	—
568	C₄	—	4	1	no	—
569	C₄	—	4	1	no	—
570	C₄	—	8	1	no	—
571	C₄	—	8	1	no	—
572	C₄	—	8	1	no	—
573	C₄	C₅×#576	1	1	yes	characteristic
574	C₄	C₅×#577	1	1	yes	characteristic
575	C₄	C₅×#577	1	1	yes	characteristic
576	C₄	C₅×#578	1	1	yes	characteristic
577	C₂	—	2	2	no	—
578	C₂	—	8	1	no	—
579	C₂	—	16	1	no	—
580	C₂	C₅×#3045	1	1	yes	characteristic
581	C₂	C₅×#3063	1	1	yes	characteristic
582	C₂	C₂×C₅×#471	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₅
prime radical	C₅×#3247	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×#3239	C₂	semidirect
3. C₅×#3206	C₂	semidirect
4. C₅×#2994	C₂	semidirect
5. C₅×#1704	C₂	semidirect
6. C₅×#1703	C₂	semidirect
7. C₅×#1686	C₂	semidirect
8. C₅×#1685	C₂	semidirect
9. C₅×#1684	C₂	semidirect
10. C₅×#1683	C₂	semidirect
11. C₅×#1666	C₂	semidirect
12. C₅×#1665	C₂	semidirect
13. C₅×#1573	C₂	semidirect
14. C₅×#1551	C₂	semidirect
15. C₂×C₅×#332	C₂	semidirect
67. #19580	C₅	direct (N × H)
146. #3239	C₂×C₅	semidirect
147. #3206	C₂×C₅	semidirect
148. #2994	C₂×C₅	semidirect
149. #1704	C₂×C₅	semidirect
150. #1703	C₂×C₅	semidirect
151. #1686	C₂×C₅	semidirect
152. #1685	C₂×C₅	semidirect
153. #1684	C₂×C₅	semidirect
154. #1683	C₂×C₅	semidirect
155. #1666	C₂×C₅	semidirect
156. #1665	C₂×C₅	semidirect
157. #1573	C₂×C₅	semidirect
158. #1551	C₂×C₅	semidirect
159. C₂×#332	C₂×C₅	semidirect
552. C₅	#19580	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×#3247	2
C₅×#3239	2
C₅×#3206	2
C₅×#2994	2
C₅×#1704	2
C₅×#1703	2
C₅×#1686	2
C₅×#1685	2
C₅×#1684	2
C₅×#1683	2
C₅×#1666	2
C₅×#1665	2
C₅×#1573	2
C₅×#1551	2
C₂×C₅×#332	2
#19580	5

Subgroups — C5×#19580 #11942300

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#19580 #11942300