Subgroups — C₅×#19343 #11942063

Order 1280.

590 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3255	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#3254	C₂	1	1	yes	maximal, characteristic
3	C₅×#3167	C₂	1	1	yes	maximal, characteristic
4	C₅×#2960	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#1704	C₂	1	2	yes	maximal, complemented
6	C₅×#1702	C₂	1	2	yes	maximal, complemented
7	C₅×#1672	C₂	1	2	yes	maximal, complemented
8	C₅×#1666	C₂	1	2	yes	maximal, complemented
9	C₅×#1566	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1561	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1560	C₂	1	1	yes	maximal, characteristic
12	C₅×#533	C₂²	1	1	yes	characteristic
13	C₅×#533	C₂²	1	1	yes	characteristic
14	C₅×#532	C₂²	1	1	yes	characteristic
15	C₅×#498	C₂²	1	1	yes	characteristic
16	C₅×#492	C₂²	1	1	yes	characteristic
17	C₅×#487	C₂²	1	1	yes	characteristic
18	C₅×#486	C₂²	1	1	yes	characteristic
19	C₅×#477	C₂²	1	2	yes	—
20	C₅×#475	—	2	1	no	—
21	C₅×#475	C₂²	1	2	yes	—
22	C₅×#474	—	2	1	no	—
23	C₅×#470	—	2	2	no	—
24	C₅×#468	—	2	2	no	—
25	C₅×#465	—	2	1	no	—
26	C₅×#465	—	2	1	no	—
27	C₅×#462	—	2	1	no	—
28	C₅×#462	C₂²	1	2	yes	—
29	C₅×#461	—	2	1	no	—
30	C₅×#460	C₂²	1	2	yes	—
31	C₅×#446	—	2	1	no	—
32	C₅×#446	C₂²	1	2	yes	—
33	C₅×C₈×Q₈	—	2	1	no	—
34	C₅×C₈×Q₈	C₂²	1	2	yes	—
35	C₄×C₅×SD₁₆	—	2	1	no	—
36	C₄×C₅×SD₁₆	—	2	1	no	—
37	C₅×#424	—	2	1	no	—
38	C₅×#423	C₂²	1	1	yes	characteristic
39	C₅×#423	C₂²	1	1	yes	characteristic
40	C₅×#423	C₂²	1	1	yes	characteristic
41	C₅×#405	—	2	1	no	—
42	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
43	C₅×#334	C₂²	1	2	yes	—
44	C₅×#334	C₂²	1	2	yes	—
45	C₅×#333	C₂²	1	2	yes	—
46	C₅×#332	C₂²	1	2	yes	—
47	C₅×#332	C₂²	1	2	yes	—
48	C₅×#331	C₂²	1	2	yes	—
49	#19343	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
50	C₂×C₅×#41	—	2	1	no	—
51	C₂×C₅×Q₁₆	—	2	2	no	—
52	C₂×C₅×SD₁₆	—	2	2	no	—
53	C₂×C₅×SD₁₆	—	2	1	no	—
54	C₂×C₅×SD₁₆	—	2	1	no	—
55	C₂×C₅×M₁₆	—	2	1	no	—
56	C₂×C₅×M₁₆	—	2	1	no	—
57	C₂×C₅×M₁₆	—	2	1	no	—
58	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
59	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
60	C₅×C₄⋊Q₈	D₄	1	1	yes	characteristic
61	C₅×C₄⋊Q₈	D₄	1	1	yes	characteristic
62	C₅×C₄⋊Q₈	C₂³	1	1	yes	characteristic
63	C₅×C₄⋊Q₈	C₂³	1	1	yes	characteristic
64	C₅×C₄⋊Q₈	C₂³	1	1	yes	characteristic
65	C₅×#127	C₂³	1	1	yes	characteristic
66	C₅×#125	—	2	1	no	—
67	C₅×#125	—	2	1	no	—
68	C₅×#124	—	2	1	no	—
69	C₅×C₂²⋊Q₈	—	2	1	no	—
70	C₅×C₂²⋊Q₈	—	2	1	no	—
71	C₅×C₂²⋊Q₈	—	2	1	no	—
72	C₅×C₂²⋊Q₈	D₄	1	2	yes	—
73	C₅×#121	—	2	1	no	—
74	C₅×#121	—	2	1	no	—
75	C₄×C₅×Q₈	—	2	1	no	—
76	C₄×C₅×Q₈	—	2	1	no	—
77	C₄×C₅×Q₈	—	2	1	no	—
78	C₄×C₅×Q₈	C₂³	1	2	yes	—
79	C₄×C₅×D₄	—	2	1	no	—
80	C₄×C₅×D₄	—	2	1	no	—
81	C₅×#117	—	2	1	no	—
82	C₅×#117	—	2	1	no	—
83	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
84	C₅×#107	—	2	2	no	—
85	C₅×#106	—	2	1	no	—
86	C₅×#106	—	2	1	no	—
87	C₅×#106	—	2	2	no	—
88	C₅×C₄⋊C₈	—	2	2	no	—
89	C₅×C₄⋊C₈	—	2	2	no	—
90	C₅×C₄⋊C₈	—	2	1	no	—
91	C₅×C₄⋊C₈	—	2	1	no	—
92	C₅×C₄⋊C₈	—	2	1	no	—
93	C₅×C₄⋊C₈	C₂³	1	2	yes	—
94	C₅×C₄⋊C₈	C₂³	1	2	yes	—
95	C₅×C₄⋊C₈	C₂³	1	2	yes	—
96	C₅×#103	—	2	2	no	—
97	C₅×#103	—	2	2	no	—
98	C₅×#103	—	2	1	no	—
99	C₅×#103	—	2	1	no	—
100	C₅×#103	—	2	2	no	—
101	C₅×#102	—	2	1	no	—
102	C₅×#102	—	2	1	no	—
103	C₅×#102	—	2	2	no	—
104	C₅×#97	—	2	2	no	—
105	C₄×C₅×C₈	—	2	2	no	—
106	C₄×C₅×C₈	D₄	1	1	yes	characteristic
107	C₄×C₅×C₈	D₄	1	1	yes	characteristic
108	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
109	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
110	#3255	C₂×C₅	1	1	yes	characteristic, complemented
111	#3254	C₂×C₅	1	1	yes	characteristic
112	#3167	C₂×C₅	1	1	yes	characteristic
113	#2960	C₂×C₅	1	1	yes	characteristic, complemented
114	#1704	C₂×C₅	1	2	yes	complemented
115	#1702	C₂×C₅	1	2	yes	complemented
116	#1672	C₂×C₅	1	2	yes	complemented
117	#1666	C₂×C₅	1	2	yes	complemented
118	#1566	C₂×C₅	1	1	yes	characteristic, complemented
119	#1561	C₂×C₅	1	1	yes	characteristic, complemented
120	#1560	C₂×C₅	1	1	yes	characteristic
121	C₅×#41	—	8	2	no	—
122	C₂×C₅×Q₈	—	2	1	no	—
123	C₂×C₅×Q₈	—	2	1	no	—
124	C₂×C₅×Q₈	—	2	1	no	—
125	C₂×C₅×Q₈	—	2	1	no	—
126	C₂×C₅×Q₈	C₂×D₄	1	2	yes	—
127	C₂×C₅×D₄	—	2	1	no	—
128	C₂×C₅×D₄	—	2	1	no	—
129	C₂×C₅×D₄	—	2	1	no	—
130	C₂×C₅×D₄	—	4	1	no	—
131	C₂²×C₄×C₅	—	4	1	no	—
132	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₄×C₅	#41	1	1	yes	characteristic
135	C₅×Q₁₆	—	8	2	no	—
136	C₅×SD₁₆	—	4	2	no	—
137	C₅×SD₁₆	—	4	2	no	—
138	C₅×SD₁₆	—	8	2	no	—
139	C₅×M₁₆	—	4	2	no	—
140	C₅×M₁₆	—	8	1	no	—
141	C₅×M₁₆	—	8	1	no	—
142	C₂×C₅×C₈	—	2	2	no	—
143	C₂×C₅×C₈	—	2	2	no	—
144	C₂×C₅×C₈	—	2	2	no	—
145	C₂×C₅×C₈	—	2	2	no	—
146	C₂×C₅×C₈	—	4	1	no	—
147	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
148	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
149	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
150	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
151	C₅×C₄⋊C₄	—	2	1	no	—
152	C₅×C₄⋊C₄	—	2	1	no	—
153	C₅×C₄⋊C₄	—	2	1	no	—
154	C₅×C₄⋊C₄	—	2	2	no	—
155	C₅×C₄⋊C₄	—	2	2	no	—
156	C₅×C₄⋊C₄	—	2	1	no	—
157	C₅×C₄⋊C₄	—	2	1	no	—
158	C₅×C₄⋊C₄	—	2	1	no	—
159	C₅×C₄⋊C₄	—	2	1	no	—
160	C₅×C₄⋊C₄	—	2	1	no	—
161	C₅×C₄⋊C₄	—	2	1	no	—
162	C₅×C₄⋊C₄	—	4	1	no	—
163	C₅×C₄⋊C₄	—	4	1	no	—
164	C₅×C₄⋊C₄	C₂×D₄	1	2	yes	—
165	C₅×C₂²⋊C₄	—	2	2	no	—
166	C₅×C₂²⋊C₄	—	4	1	no	—
167	C₅×C₂²⋊C₄	—	4	1	no	—
168	C₅×C₂²⋊C₄	—	4	1	no	—
169	C₄²×C₅	—	2	2	no	—
170	C₄²×C₅	—	4	1	no	—
171	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
172	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
173	C₄²×C₅	#41	1	1	yes	characteristic
174	C₄²×C₅	C₂⁴	1	1	yes	characteristic
175	#533	C₂²×C₅	1	1	yes	characteristic
176	#533	C₂²×C₅	1	1	yes	characteristic
177	#532	C₂²×C₅	1	1	yes	characteristic
178	#498	C₂²×C₅	1	1	yes	characteristic
179	#492	C₂²×C₅	1	1	yes	characteristic
180	#487	C₂²×C₅	1	1	yes	characteristic
181	#486	C₂²×C₅	1	1	yes	characteristic
182	#477	C₂²×C₅	1	2	yes	—
183	#475	—	2	1	no	—
184	#475	C₂²×C₅	1	2	yes	—
185	#474	—	2	1	no	—
186	#470	—	2	2	no	—
187	#468	—	2	2	no	—
188	#465	—	2	1	no	—
189	#465	—	2	1	no	—
190	#462	—	2	1	no	—
191	#462	C₂²×C₅	1	2	yes	—
192	#461	—	2	1	no	—
193	#460	C₂²×C₅	1	2	yes	—
194	#446	—	2	1	no	—
195	#446	C₂²×C₅	1	2	yes	—
196	C₈×Q₈	—	2	1	no	—
197	C₈×Q₈	C₂²×C₅	1	2	yes	—
198	C₄×SD₁₆	—	2	1	no	—
199	C₄×SD₁₆	—	2	1	no	—
200	#424	—	2	1	no	—
201	#423	C₂²×C₅	1	1	yes	characteristic
202	#423	C₂²×C₅	1	1	yes	characteristic
203	#423	C₂²×C₅	1	1	yes	characteristic
204	#405	—	2	1	no	—
205	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
206	#334	C₂²×C₅	1	2	yes	—
207	#334	C₂²×C₅	1	2	yes	—
208	#333	C₂²×C₅	1	2	yes	—
209	#332	C₂²×C₅	1	2	yes	—
210	#332	C₂²×C₅	1	2	yes	—
211	#331	C₂²×C₅	1	2	yes	—
212	C₂³×C₅	—	4	1	no	—
213	C₂³×C₅	#121	1	1	yes	characteristic
214	C₅×Q₈	—	2	2	no	—
215	C₅×Q₈	—	2	2	no	—
216	C₅×Q₈	—	4	2	no	—
217	C₅×Q₈	—	4	1	no	—
218	C₅×Q₈	—	4	1	no	—
219	C₅×Q₈	—	4	1	no	—
220	C₅×Q₈	—	4	1	no	—
221	C₅×Q₈	—	8	1	no	—
222	C₅×D₄	—	4	1	no	—
223	C₅×D₄	—	4	1	no	—
224	C₅×D₄	—	4	1	no	—
225	C₅×D₄	—	4	1	no	—
226	C₅×D₄	—	8	1	no	—
227	C₅×D₄	—	8	2	no	—
228	C₂×C₄×C₅	—	2	1	no	—
229	C₂×C₄×C₅	—	2	1	no	—
230	C₂×C₄×C₅	—	2	1	no	—
231	C₂×C₄×C₅	—	2	1	no	—
232	C₂×C₄×C₅	—	2	2	no	—
233	C₂×C₄×C₅	—	2	2	no	—
234	C₂×C₄×C₅	—	2	2	no	—
235	C₂×C₄×C₅	—	4	1	no	—
236	C₂×C₄×C₅	—	4	1	no	—
237	C₂×C₄×C₅	—	4	1	no	—
238	C₂×C₄×C₅	—	8	2	no	—
239	C₂×C₄×C₅	#121	1	1	yes	characteristic
240	C₂×C₄×C₅	#121	1	1	yes	characteristic
241	C₂×C₄×C₅	#121	1	1	yes	characteristic
242	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
243	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
244	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
245	C₅×C₈	—	2	1	no	—
246	C₅×C₈	—	2	1	no	—
247	C₅×C₈	—	2	1	no	—
248	C₅×C₈	—	4	2	no	—
249	C₅×C₈	—	4	2	no	—
250	C₅×C₈	—	4	2	no	—
251	C₅×C₈	#137	1	2	yes	—
252	C₂×#41	—	2	1	no	—
253	C₂×Q₁₆	—	2	2	no	—
254	C₂×SD₁₆	—	2	2	no	—
255	C₂×SD₁₆	—	2	1	no	—
256	C₂×SD₁₆	—	2	1	no	—
257	C₂×M₁₆	—	2	1	no	—
258	C₂×M₁₆	—	2	1	no	—
259	C₂×M₁₆	—	2	1	no	—
260	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
261	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
262	C₄⋊Q₈	C₅×D₄	1	1	yes	characteristic
263	C₄⋊Q₈	C₅×D₄	1	1	yes	characteristic
264	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
265	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
266	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
267	#127	C₂³×C₅	1	1	yes	characteristic
268	#125	—	2	1	no	—
269	#125	—	2	1	no	—
270	#124	—	2	1	no	—
271	C₂²⋊Q₈	—	2	1	no	—
272	C₂²⋊Q₈	—	2	1	no	—
273	C₂²⋊Q₈	—	2	1	no	—
274	C₂²⋊Q₈	C₅×D₄	1	2	yes	—
275	#121	—	2	1	no	—
276	#121	—	2	1	no	—
277	C₄×Q₈	—	2	1	no	—
278	C₄×Q₈	—	2	1	no	—
279	C₄×Q₈	—	2	1	no	—
280	C₄×Q₈	C₂³×C₅	1	2	yes	—
281	C₄×D₄	—	2	1	no	—
282	C₄×D₄	—	2	1	no	—
283	#117	—	2	1	no	—
284	#117	—	2	1	no	—
285	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
286	#107	—	2	2	no	—
287	#106	—	2	1	no	—
288	#106	—	2	1	no	—
289	#106	—	2	2	no	—
290	C₄⋊C₈	—	2	2	no	—
291	C₄⋊C₈	—	2	2	no	—
292	C₄⋊C₈	—	2	1	no	—
293	C₄⋊C₈	—	2	1	no	—
294	C₄⋊C₈	—	2	1	no	—
295	C₄⋊C₈	C₂³×C₅	1	2	yes	—
296	C₄⋊C₈	C₂³×C₅	1	2	yes	—
297	C₄⋊C₈	C₂³×C₅	1	2	yes	—
298	#103	—	2	2	no	—
299	#103	—	2	2	no	—
300	#103	—	2	1	no	—
301	#103	—	2	1	no	—
302	#103	—	2	2	no	—
303	#102	—	2	1	no	—
304	#102	—	2	1	no	—
305	#102	—	2	2	no	—
306	#97	—	2	2	no	—
307	C₄×C₈	—	2	2	no	—
308	C₄×C₈	C₅×D₄	1	1	yes	characteristic
309	C₄×C₈	C₅×D₄	1	1	yes	characteristic
310	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
311	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
312	C₂²×C₅	—	2	1	no	—
313	C₂²×C₅	—	2	1	no	—
314	C₂²×C₅	—	2	1	no	—
315	C₂²×C₅	—	8	1	no	—
316	C₂²×C₅	—	8	1	no	—
317	C₂²×C₅	—	8	1	no	—
318	C₂²×C₅	C₂×#121	1	1	yes	characteristic
319	C₄×C₅	—	2	1	no	—
320	C₄×C₅	—	2	1	no	—
321	C₄×C₅	—	2	1	no	—
322	C₄×C₅	—	4	2	no	—
323	C₄×C₅	—	4	2	no	—
324	C₄×C₅	—	8	1	no	—
325	C₄×C₅	—	8	1	no	—
326	C₄×C₅	—	8	1	no	—
327	C₄×C₅	#471	1	2	yes	—
328	C₄×C₅	C₂×#137	1	1	yes	characteristic
329	C₄×C₅	#575	1	1	yes	characteristic
330	C₄×C₅	#577	1	1	yes	characteristic
331	C₄×C₅	#577	1	1	yes	characteristic
332	#41	—	8	2	no	—
333	C₂×Q₈	—	2	1	no	—
334	C₂×Q₈	—	2	1	no	—
335	C₂×Q₈	—	2	1	no	—
336	C₂×Q₈	—	2	1	no	—
337	C₂×Q₈	C₂×C₅×D₄	1	2	yes	—
338	C₂×D₄	—	2	1	no	—
339	C₂×D₄	—	2	1	no	—
340	C₂×D₄	—	2	1	no	—
341	C₂×D₄	—	4	1	no	—
342	C₂²×C₄	—	4	1	no	—
343	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
344	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
345	C₂²×C₄	C₅×#41	1	1	yes	characteristic
346	Q₁₆	—	8	2	no	—
347	SD₁₆	—	4	2	no	—
348	SD₁₆	—	4	2	no	—
349	SD₁₆	—	8	2	no	—
350	M₁₆	—	4	2	no	—
351	M₁₆	—	8	1	no	—
352	M₁₆	—	8	1	no	—
353	C₂×C₈	—	2	2	no	—
354	C₂×C₈	—	2	2	no	—
355	C₂×C₈	—	2	2	no	—
356	C₂×C₈	—	2	2	no	—
357	C₂×C₈	—	4	1	no	—
358	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
359	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
360	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
361	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
362	C₄⋊C₄	—	2	1	no	—
363	C₄⋊C₄	—	2	1	no	—
364	C₄⋊C₄	—	2	1	no	—
365	C₄⋊C₄	—	2	2	no	—
366	C₄⋊C₄	—	2	2	no	—
367	C₄⋊C₄	—	2	1	no	—
368	C₄⋊C₄	—	2	1	no	—
369	C₄⋊C₄	—	2	1	no	—
370	C₄⋊C₄	—	2	1	no	—
371	C₄⋊C₄	—	2	1	no	—
372	C₄⋊C₄	—	2	1	no	—
373	C₄⋊C₄	—	4	1	no	—
374	C₄⋊C₄	—	4	1	no	—
375	C₄⋊C₄	C₂×C₅×D₄	1	2	yes	—
376	C₂²⋊C₄	—	2	2	no	—
377	C₂²⋊C₄	—	4	1	no	—
378	C₂²⋊C₄	—	4	1	no	—
379	C₂²⋊C₄	—	4	1	no	—
380	C₄²	—	2	2	no	—
381	C₄²	—	4	1	no	—
382	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
383	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
384	C₄²	C₅×#41	1	1	yes	characteristic
385	C₄²	C₂⁴×C₅	1	1	yes	characteristic
386	C₂×C₅	—	4	1	no	—
387	C₂×C₅	—	16	1	no	—
388	C₂×C₅	#3037	1	1	yes	characteristic
389	C₂×C₅	#3060	1	1	yes	characteristic
390	C₂×C₅	C₂×#471	1	1	yes	characteristic
391	C₂³	—	4	1	no	—
392	C₂³	C₅×#121	1	1	yes	characteristic
393	Q₈	—	2	2	no	—
394	Q₈	—	2	2	no	—
395	Q₈	—	4	2	no	—
396	Q₈	—	4	1	no	—
397	Q₈	—	4	1	no	—
398	Q₈	—	4	1	no	—
399	Q₈	—	4	1	no	—
400	Q₈	—	8	1	no	—
401	D₄	—	4	1	no	—
402	D₄	—	4	1	no	—
403	D₄	—	4	1	no	—
404	D₄	—	4	1	no	—
405	D₄	—	8	1	no	—
406	D₄	—	8	2	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	2	1	no	—
409	C₂×C₄	—	2	1	no	—
410	C₂×C₄	—	2	1	no	—
411	C₂×C₄	—	2	1	no	—
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	4	1	no	—
415	C₂×C₄	—	4	1	no	—
416	C₂×C₄	—	4	1	no	—
417	C₂×C₄	—	8	2	no	—
418	C₂×C₄	C₅×#121	1	1	yes	characteristic
419	C₂×C₄	C₅×#121	1	1	yes	characteristic
420	C₂×C₄	C₅×#121	1	1	yes	characteristic
421	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
422	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
423	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
424	C₈	—	2	1	no	—
425	C₈	—	2	1	no	—
426	C₈	—	2	1	no	—
427	C₈	—	4	2	no	—
428	C₈	—	4	2	no	—
429	C₈	—	4	2	no	—
430	C₈	C₅×#137	1	2	yes	—
431	C₅	#19343	1	1	yes	characteristic, direct product factor, Sylow
432	C₂²	—	2	1	no	—
433	C₂²	—	2	1	no	—
434	C₂²	—	2	1	no	—
435	C₂²	—	8	1	no	—
436	C₂²	—	8	1	no	—
437	C₂²	—	8	1	no	—
438	C₂²	C₂×C₅×#121	1	1	yes	characteristic
439	C₄	—	2	1	no	—
440	C₄	—	2	1	no	—
441	C₄	—	2	1	no	—
442	C₄	—	4	2	no	—
443	C₄	—	4	2	no	—
444	C₄	—	8	1	no	—
445	C₄	—	8	1	no	—
446	C₄	—	8	1	no	—
447	C₄	C₅×#471	1	2	yes	—
448	C₄	C₂×C₅×#137	1	1	yes	characteristic
449	C₄	C₅×#575	1	1	yes	characteristic
450	C₄	C₅×#577	1	1	yes	characteristic
451	C₄	C₅×#577	1	1	yes	characteristic
452	C₂	—	4	1	no	—
453	C₂	—	16	1	no	—
454	C₂	C₅×#3037	1	1	yes	characteristic
455	C₂	C₅×#3060	1	1	yes	characteristic
456	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×#532	C₂²
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×#3255	C₂	semidirect
4. C₅×#2960	C₂	semidirect
5. C₅×#1704	C₂	semidirect
6. C₅×#1702	C₂	semidirect
7. C₅×#1672	C₂	semidirect
8. C₅×#1666	C₂	semidirect
9. C₅×#1566	C₂	semidirect
10. C₅×#1561	C₂	semidirect
49. #19343	C₅	direct (N × H)
110. #3255	C₂×C₅	semidirect
113. #2960	C₂×C₅	semidirect
114. #1704	C₂×C₅	semidirect
115. #1702	C₂×C₅	semidirect
116. #1672	C₂×C₅	semidirect
117. #1666	C₂×C₅	semidirect
118. #1566	C₂×C₅	semidirect
119. #1561	C₂×C₅	semidirect
431. C₅	#19343	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×#3255	2
C₅×#3254	2
C₅×#3167	2
C₅×#2960	2
C₅×#1704	2
C₅×#1702	2
C₅×#1672	2
C₅×#1666	2
C₅×#1566	2
C₅×#1561	2
C₅×#1560	2
#19343	5

Subgroups — C5×#19343 #11942063

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#19343 #11942063