Subgroups — C₅×#19294 #11942014

Order 1280.

694 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×#3147	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#3115	C₂	1	2	yes	maximal, complemented
3	C₅×#2965	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#1690	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#1689	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#1688	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#1687	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1686	C₂	1	2	yes	maximal, complemented
9	C₅×#1685	C₂	1	2	yes	maximal, complemented
10	C₅×#1568	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1553	C₂	1	2	yes	maximal, complemented
12	C₂×C₅×#135	—	2	1	no	—
13	C₂×C₅×#135	—	2	1	no	—
14	C₅×#532	C₂²	1	2	yes	—
15	C₄×C₅×#41	C₂²	1	1	yes	characteristic
16	C₅×#495	—	2	1	no	—
17	C₅×#495	—	2	1	no	—
18	C₅×#494	C₂²	1	1	yes	characteristic
19	C₅×#493	C₂²	1	1	yes	characteristic
20	C₅×#492	C₂²	1	2	yes	—
21	C₅×#482	—	2	2	no	—
22	C₅×#475	C₂²	1	2	yes	—
23	C₅×#474	C₂²	1	2	yes	—
24	C₅×#460	C₂²	1	2	yes	—
25	C₅×#459	C₂²	1	2	yes	—
26	C₅×#449	—	2	2	no	—
27	C₅×#446	C₂²	1	1	yes	characteristic
28	C₅×#446	C₂²	1	1	yes	characteristic
29	C₅×#442	—	2	2	no	—
30	C₅×#440	—	2	2	no	—
31	C₅×#436	C₂²	1	1	yes	characteristic
32	C₅×#436	C₂²	1	1	yes	characteristic
33	C₅×#435	—	2	1	no	—
34	C₅×#435	—	2	1	no	—
35	C₅×#432	C₂²	1	2	yes	—
36	C₅×#431	—	2	1	no	—
37	C₅×#431	C₂²	1	1	yes	characteristic
38	C₄×C₅×M₁₆	—	2	1	no	—
39	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
40	C₅×#335	C₂²	1	2	yes	—
41	C₅×#334	C₂²	1	1	yes	characteristic
42	C₅×#334	C₂²	1	1	yes	characteristic
43	C₅×#332	C₂²	1	2	yes	—
44	C₅×#332	C₂²	1	2	yes	—
45	C₅×#331	C₂²	1	2	yes	—
46	C₅×#331	C₂²	1	2	yes	—
47	#19294	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
48	C₂×C₅×#41	—	2	2	no	—
49	C₂×C₅×#41	D₄	1	1	yes	characteristic
50	C₅×#135	—	4	4	no	—
51	C₅×#135	—	4	4	no	—
52	C₂×C₅×Q₁₆	—	2	1	no	—
53	C₂×C₅×Q₁₆	—	2	1	no	—
54	C₂×C₅×SD₁₆	—	2	2	no	—
55	C₂×C₅×SD₁₆	—	2	2	no	—
56	C₂×C₅×SD₁₆	—	2	2	no	—
57	C₂×C₅×D₈	—	2	2	no	—
58	C₂×C₅×D₈	—	2	1	no	—
59	C₂×C₅×D₈	—	2	1	no	—
60	C₂×C₅×M₁₆	—	2	1	no	—
61	C₂×C₅×M₁₆	—	2	1	no	—
62	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
63	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
64	C₅×C₄⋊Q₈	C₂³	1	2	yes	—
65	C₅×#127	C₂³	1	2	yes	—
66	C₅×#124	—	2	2	no	—
67	C₅×#121	—	2	2	no	—
68	C₅×#121	—	2	2	no	—
69	C₄×C₅×Q₈	D₄	1	1	yes	characteristic
70	C₄×C₅×Q₈	C₂³	1	1	yes	characteristic
71	C₄×C₅×D₄	—	2	1	no	—
72	C₄×C₅×D₄	—	2	1	no	—
73	C₄×C₅×D₄	—	2	2	no	—
74	C₄×C₅×D₄	—	2	2	no	—
75	C₄×C₅×D₄	D₄	1	1	yes	characteristic
76	C₄×C₅×D₄	C₂³	1	1	yes	characteristic
77	C₅×#117	—	2	1	no	—
78	C₅×#117	D₄	1	1	yes	characteristic
79	C₂×C₄²×C₅	—	2	1	no	—
80	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
81	C₅×#107	—	2	2	no	—
82	C₅×#106	—	2	2	no	—
83	C₅×C₄⋊C₈	—	2	1	no	—
84	C₅×C₄⋊C₈	—	2	1	no	—
85	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
86	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
87	C₅×C₄⋊C₈	C₂³	1	2	yes	—
88	C₅×C₄⋊C₈	C₂³	1	2	yes	—
89	C₅×#103	—	2	2	no	—
90	C₅×#102	—	2	2	no	—
91	C₅×#102	—	2	2	no	—
92	C₅×#102	—	2	2	no	—
93	C₅×C₂²⋊C₈	—	2	1	no	—
94	C₅×C₂²⋊C₈	—	2	2	no	—
95	C₅×C₂²⋊C₈	—	2	1	no	—
96	C₅×C₂²⋊C₈	—	2	1	no	—
97	C₅×#97	—	2	1	no	—
98	C₅×#97	—	2	1	no	—
99	C₅×#97	—	2	2	no	—
100	C₄×C₅×C₈	—	2	1	no	—
101	C₄×C₅×C₈	D₄	1	1	yes	characteristic
102	C₄×C₅×C₈	D₄	1	1	yes	characteristic
103	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
104	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
105	#3147	C₂×C₅	1	1	yes	characteristic, complemented
106	#3115	C₂×C₅	1	2	yes	complemented
107	#2965	C₂×C₅	1	1	yes	characteristic, complemented
108	#1690	C₂×C₅	1	1	yes	characteristic, complemented
109	#1689	C₂×C₅	1	1	yes	characteristic, complemented
110	#1688	C₂×C₅	1	1	yes	characteristic, complemented
111	#1687	C₂×C₅	1	1	yes	characteristic, complemented
112	#1686	C₂×C₅	1	2	yes	complemented
113	#1685	C₂×C₅	1	2	yes	complemented
114	#1568	C₂×C₅	1	1	yes	characteristic, complemented
115	#1553	C₂×C₅	1	2	yes	complemented
116	C₅×#41	—	4	2	no	—
117	C₅×#41	—	4	4	no	—
118	C₅×#41	—	4	4	no	—
119	C₂×C₅×Q₈	—	2	2	no	—
120	C₂×C₅×Q₈	C₂×D₄	1	1	yes	characteristic
121	C₂×C₅×D₄	—	2	1	no	—
122	C₂×C₅×D₄	—	2	2	no	—
123	C₂×C₅×D₄	—	2	2	no	—
124	C₂×C₅×D₄	—	2	2	no	—
125	C₂×C₅×D₄	—	4	2	no	—
126	C₂×C₅×D₄	C₂×D₄	1	1	yes	characteristic
127	C₂²×C₄×C₅	—	2	1	no	—
128	C₂²×C₄×C₅	—	2	1	no	—
129	C₂²×C₄×C₅	—	2	1	no	—
130	C₂²×C₄×C₅	—	4	2	no	—
131	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₅	#41	1	1	yes	characteristic
134	C₅×Q₁₆	—	4	2	no	—
135	C₅×Q₁₆	—	4	2	no	—
136	C₅×SD₁₆	—	4	4	no	—
137	C₅×SD₁₆	—	4	4	no	—
138	C₅×SD₁₆	—	4	4	no	—
139	C₅×D₈	—	4	2	no	—
140	C₅×D₈	—	4	4	no	—
141	C₅×D₈	—	4	2	no	—
142	C₅×M₁₆	—	4	2	no	—
143	C₅×M₁₆	—	4	2	no	—
144	C₂×C₅×C₈	—	2	2	no	—
145	C₂×C₅×C₈	—	2	2	no	—
146	C₂×C₅×C₈	—	2	1	no	—
147	C₂×C₅×C₈	—	2	1	no	—
148	C₂×C₅×C₈	—	2	2	no	—
149	C₂×C₅×C₈	—	2	2	no	—
150	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
151	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
152	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
153	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
154	C₅×C₄⋊C₄	—	2	1	no	—
155	C₅×C₄⋊C₄	—	2	1	no	—
156	C₅×C₄⋊C₄	—	2	2	no	—
157	C₅×C₄⋊C₄	—	2	2	no	—
158	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
159	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
160	C₅×C₂²⋊C₄	—	2	1	no	—
161	C₅×C₂²⋊C₄	—	2	1	no	—
162	C₅×C₂²⋊C₄	—	2	1	no	—
163	C₅×C₂²⋊C₄	—	4	2	no	—
164	C₅×C₂²⋊C₄	—	4	2	no	—
165	C₄²×C₅	—	2	1	no	—
166	C₄²×C₅	—	2	1	no	—
167	C₄²×C₅	—	2	1	no	—
168	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
169	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
170	C₄²×C₅	#41	1	1	yes	characteristic
171	C₄²×C₅	C₂⁴	1	1	yes	characteristic
172	C₂×#135	—	2	1	no	—
173	C₂×#135	—	2	1	no	—
174	#532	C₂²×C₅	1	2	yes	—
175	C₄×#41	C₂²×C₅	1	1	yes	characteristic
176	#495	—	2	1	no	—
177	#495	—	2	1	no	—
178	#494	C₂²×C₅	1	1	yes	characteristic
179	#493	C₂²×C₅	1	1	yes	characteristic
180	#492	C₂²×C₅	1	2	yes	—
181	#482	—	2	2	no	—
182	#475	C₂²×C₅	1	2	yes	—
183	#474	C₂²×C₅	1	2	yes	—
184	#460	C₂²×C₅	1	2	yes	—
185	#459	C₂²×C₅	1	2	yes	—
186	#449	—	2	2	no	—
187	#446	C₂²×C₅	1	1	yes	characteristic
188	#446	C₂²×C₅	1	1	yes	characteristic
189	#442	—	2	2	no	—
190	#440	—	2	2	no	—
191	#436	C₂²×C₅	1	1	yes	characteristic
192	#436	C₂²×C₅	1	1	yes	characteristic
193	#435	—	2	1	no	—
194	#435	—	2	1	no	—
195	#432	C₂²×C₅	1	2	yes	—
196	#431	—	2	1	no	—
197	#431	C₂²×C₅	1	1	yes	characteristic
198	C₄×M₁₆	—	2	1	no	—
199	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
200	#335	C₂²×C₅	1	2	yes	—
201	#334	C₂²×C₅	1	1	yes	characteristic
202	#334	C₂²×C₅	1	1	yes	characteristic
203	#332	C₂²×C₅	1	2	yes	—
204	#332	C₂²×C₅	1	2	yes	—
205	#331	C₂²×C₅	1	2	yes	—
206	#331	C₂²×C₅	1	2	yes	—
207	C₂³×C₅	—	2	1	no	—
208	C₂³×C₅	—	4	2	no	—
209	C₂³×C₅	#121	1	1	yes	characteristic
210	C₅×Q₈	—	2	2	no	—
211	C₅×Q₈	—	4	2	no	—
212	C₅×Q₈	—	4	2	no	—
213	C₅×D₄	—	2	2	no	—
214	C₅×D₄	—	4	2	no	—
215	C₅×D₄	—	4	2	no	—
216	C₅×D₄	—	4	2	no	—
217	C₅×D₄	—	4	2	no	—
218	C₅×D₄	—	4	2	no	—
219	C₅×D₄	—	8	2	no	—
220	C₅×D₄	—	8	4	no	—
221	C₂×C₄×C₅	—	2	1	no	—
222	C₂×C₄×C₅	—	2	1	no	—
223	C₂×C₄×C₅	—	2	2	no	—
224	C₂×C₄×C₅	—	2	1	no	—
225	C₂×C₄×C₅	—	2	1	no	—
226	C₂×C₄×C₅	—	2	1	no	—
227	C₂×C₄×C₅	—	4	1	no	—
228	C₂×C₄×C₅	—	4	2	no	—
229	C₂×C₄×C₅	—	4	2	no	—
230	C₂×C₄×C₅	—	4	1	no	—
231	C₂×C₄×C₅	—	4	1	no	—
232	C₂×C₄×C₅	—	4	2	no	—
233	C₂×C₄×C₅	—	8	4	no	—
234	C₂×C₄×C₅	#121	1	1	yes	characteristic
235	C₂×C₄×C₅	#121	1	1	yes	characteristic
236	C₂×C₄×C₅	#121	1	1	yes	characteristic
237	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
238	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
239	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
240	C₅×C₈	—	2	1	no	—
241	C₅×C₈	—	2	1	no	—
242	C₅×C₈	—	4	1	no	—
243	C₅×C₈	—	4	1	no	—
244	C₅×C₈	—	4	2	no	—
245	C₅×C₈	—	4	2	no	—
246	C₅×C₈	AGL(1,ℤ/8)	1	2	yes	—
247	C₅×C₈	AGL(1,ℤ/8)	1	2	yes	—
248	C₂×#41	—	2	2	no	—
249	C₂×#41	C₅×D₄	1	1	yes	characteristic
250	#135	—	4	4	no	—
251	#135	—	4	4	no	—
252	C₂×Q₁₆	—	2	1	no	—
253	C₂×Q₁₆	—	2	1	no	—
254	C₂×SD₁₆	—	2	2	no	—
255	C₂×SD₁₆	—	2	2	no	—
256	C₂×SD₁₆	—	2	2	no	—
257	C₂×D₈	—	2	2	no	—
258	C₂×D₈	—	2	1	no	—
259	C₂×D₈	—	2	1	no	—
260	C₂×M₁₆	—	2	1	no	—
261	C₂×M₁₆	—	2	1	no	—
262	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
263	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
264	C₄⋊Q₈	C₂³×C₅	1	2	yes	—
265	#127	C₂³×C₅	1	2	yes	—
266	#124	—	2	2	no	—
267	#121	—	2	2	no	—
268	#121	—	2	2	no	—
269	C₄×Q₈	C₅×D₄	1	1	yes	characteristic
270	C₄×Q₈	C₂³×C₅	1	1	yes	characteristic
271	C₄×D₄	—	2	1	no	—
272	C₄×D₄	—	2	1	no	—
273	C₄×D₄	—	2	2	no	—
274	C₄×D₄	—	2	2	no	—
275	C₄×D₄	C₅×D₄	1	1	yes	characteristic
276	C₄×D₄	C₂³×C₅	1	1	yes	characteristic
277	#117	—	2	1	no	—
278	#117	C₅×D₄	1	1	yes	characteristic
279	C₂×C₄²	—	2	1	no	—
280	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
281	#107	—	2	2	no	—
282	#106	—	2	2	no	—
283	C₄⋊C₈	—	2	1	no	—
284	C₄⋊C₈	—	2	1	no	—
285	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
286	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
287	C₄⋊C₈	C₂³×C₅	1	2	yes	—
288	C₄⋊C₈	C₂³×C₅	1	2	yes	—
289	#103	—	2	2	no	—
290	#102	—	2	2	no	—
291	#102	—	2	2	no	—
292	#102	—	2	2	no	—
293	C₂²⋊C₈	—	2	1	no	—
294	C₂²⋊C₈	—	2	2	no	—
295	C₂²⋊C₈	—	2	1	no	—
296	C₂²⋊C₈	—	2	1	no	—
297	#97	—	2	1	no	—
298	#97	—	2	1	no	—
299	#97	—	2	2	no	—
300	C₄×C₈	—	2	1	no	—
301	C₄×C₈	C₅×D₄	1	1	yes	characteristic
302	C₄×C₈	C₅×D₄	1	1	yes	characteristic
303	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
304	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
305	C₂²×C₅	—	2	1	no	—
306	C₂²×C₅	—	2	1	no	—
307	C₂²×C₅	—	2	1	no	—
308	C₂²×C₅	—	4	1	no	—
309	C₂²×C₅	—	4	1	no	—
310	C₂²×C₅	—	4	1	no	—
311	C₂²×C₅	—	8	2	no	—
312	C₂²×C₅	—	8	2	no	—
313	C₂²×C₅	—	8	2	no	—
314	C₂²×C₅	C₂×#121	1	1	yes	characteristic
315	C₄×C₅	—	2	1	no	—
316	C₄×C₅	—	2	1	no	—
317	C₄×C₅	—	2	1	no	—
318	C₄×C₅	—	2	1	no	—
319	C₄×C₅	—	4	1	no	—
320	C₄×C₅	—	4	1	no	—
321	C₄×C₅	—	4	1	no	—
322	C₄×C₅	—	8	2	no	—
323	C₄×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
324	C₄×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
325	C₄×C₅	#575	1	2	yes	—
326	#41	—	4	2	no	—
327	#41	—	4	4	no	—
328	#41	—	4	4	no	—
329	C₂×Q₈	—	2	2	no	—
330	C₂×Q₈	C₂×C₅×D₄	1	1	yes	characteristic
331	C₂×D₄	—	2	1	no	—
332	C₂×D₄	—	2	2	no	—
333	C₂×D₄	—	2	2	no	—
334	C₂×D₄	—	2	2	no	—
335	C₂×D₄	—	4	2	no	—
336	C₂×D₄	C₂×C₅×D₄	1	1	yes	characteristic
337	C₂²×C₄	—	2	1	no	—
338	C₂²×C₄	—	2	1	no	—
339	C₂²×C₄	—	2	1	no	—
340	C₂²×C₄	—	4	2	no	—
341	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
342	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
343	C₂²×C₄	C₅×#41	1	1	yes	characteristic
344	Q₁₆	—	4	2	no	—
345	Q₁₆	—	4	2	no	—
346	SD₁₆	—	4	4	no	—
347	SD₁₆	—	4	4	no	—
348	SD₁₆	—	4	4	no	—
349	D₈	—	4	2	no	—
350	D₈	—	4	4	no	—
351	D₈	—	4	2	no	—
352	M₁₆	—	4	2	no	—
353	M₁₆	—	4	2	no	—
354	C₂×C₈	—	2	2	no	—
355	C₂×C₈	—	2	2	no	—
356	C₂×C₈	—	2	1	no	—
357	C₂×C₈	—	2	1	no	—
358	C₂×C₈	—	2	2	no	—
359	C₂×C₈	—	2	2	no	—
360	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
361	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
362	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
363	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
364	C₄⋊C₄	—	2	1	no	—
365	C₄⋊C₄	—	2	1	no	—
366	C₄⋊C₄	—	2	2	no	—
367	C₄⋊C₄	—	2	2	no	—
368	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
369	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
370	C₂²⋊C₄	—	2	1	no	—
371	C₂²⋊C₄	—	2	1	no	—
372	C₂²⋊C₄	—	2	1	no	—
373	C₂²⋊C₄	—	4	2	no	—
374	C₂²⋊C₄	—	4	2	no	—
375	C₄²	—	2	1	no	—
376	C₄²	—	2	1	no	—
377	C₄²	—	2	1	no	—
378	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
379	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
380	C₄²	C₅×#41	1	1	yes	characteristic
381	C₄²	C₂⁴×C₅	1	1	yes	characteristic
382	C₂×C₅	—	4	1	no	—
383	C₂×C₅	—	8	1	no	—
384	C₂×C₅	—	16	2	no	—
385	C₂×C₅	#3038	1	1	yes	characteristic
386	C₂×C₅	#3054	1	1	yes	characteristic
387	C₂×C₅	#3067	1	1	yes	characteristic
388	C₂³	—	2	1	no	—
389	C₂³	—	4	2	no	—
390	C₂³	C₅×#121	1	1	yes	characteristic
391	Q₈	—	2	2	no	—
392	Q₈	—	4	2	no	—
393	Q₈	—	4	2	no	—
394	D₄	—	2	2	no	—
395	D₄	—	4	2	no	—
396	D₄	—	4	2	no	—
397	D₄	—	4	2	no	—
398	D₄	—	4	2	no	—
399	D₄	—	4	2	no	—
400	D₄	—	8	2	no	—
401	D₄	—	8	4	no	—
402	C₂×C₄	—	2	1	no	—
403	C₂×C₄	—	2	1	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	1	no	—
406	C₂×C₄	—	2	1	no	—
407	C₂×C₄	—	2	1	no	—
408	C₂×C₄	—	4	1	no	—
409	C₂×C₄	—	4	2	no	—
410	C₂×C₄	—	4	2	no	—
411	C₂×C₄	—	4	1	no	—
412	C₂×C₄	—	4	1	no	—
413	C₂×C₄	—	4	2	no	—
414	C₂×C₄	—	8	4	no	—
415	C₂×C₄	C₅×#121	1	1	yes	characteristic
416	C₂×C₄	C₅×#121	1	1	yes	characteristic
417	C₂×C₄	C₅×#121	1	1	yes	characteristic
418	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
419	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
420	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
421	C₈	—	2	1	no	—
422	C₈	—	2	1	no	—
423	C₈	—	4	1	no	—
424	C₈	—	4	1	no	—
425	C₈	—	4	2	no	—
426	C₈	—	4	2	no	—
427	C₈	C₅×AGL(1,ℤ/8)	1	2	yes	—
428	C₈	C₅×AGL(1,ℤ/8)	1	2	yes	—
429	C₅	#19294	1	1	yes	characteristic, direct product factor, Sylow
430	C₂²	—	2	1	no	—
431	C₂²	—	2	1	no	—
432	C₂²	—	2	1	no	—
433	C₂²	—	4	1	no	—
434	C₂²	—	4	1	no	—
435	C₂²	—	4	1	no	—
436	C₂²	—	8	2	no	—
437	C₂²	—	8	2	no	—
438	C₂²	—	8	2	no	—
439	C₂²	C₂×C₅×#121	1	1	yes	characteristic
440	C₄	—	2	1	no	—
441	C₄	—	2	1	no	—
442	C₄	—	2	1	no	—
443	C₄	—	2	1	no	—
444	C₄	—	4	1	no	—
445	C₄	—	4	1	no	—
446	C₄	—	4	1	no	—
447	C₄	—	8	2	no	—
448	C₄	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
449	C₄	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
450	C₄	C₅×#575	1	2	yes	—
451	C₂	—	4	1	no	—
452	C₂	—	8	1	no	—
453	C₂	—	16	2	no	—
454	C₂	C₅×#3038	1	1	yes	characteristic
455	C₂	C₅×#3054	1	1	yes	characteristic
456	C₂	C₅×#3067	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₅
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×#3147	C₂	semidirect
2. C₅×#3115	C₂	semidirect
3. C₅×#2965	C₂	semidirect
4. C₅×#1690	C₂	semidirect
5. C₅×#1689	C₂	semidirect
6. C₅×#1688	C₂	semidirect
7. C₅×#1687	C₂	semidirect
8. C₅×#1686	C₂	semidirect
9. C₅×#1685	C₂	semidirect
10. C₅×#1568	C₂	semidirect
11. C₅×#1553	C₂	semidirect
47. #19294	C₅	direct (N × H)
105. #3147	C₂×C₅	semidirect
106. #3115	C₂×C₅	semidirect
107. #2965	C₂×C₅	semidirect
108. #1690	C₂×C₅	semidirect
109. #1689	C₂×C₅	semidirect
110. #1688	C₂×C₅	semidirect
111. #1687	C₂×C₅	semidirect
112. #1686	C₂×C₅	semidirect
113. #1685	C₂×C₅	semidirect
114. #1568	C₂×C₅	semidirect
115. #1553	C₂×C₅	semidirect
429. C₅	#19294	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×#3147	2
C₅×#3115	2
C₅×#2965	2
C₅×#1690	2
C₅×#1689	2
C₅×#1688	2
C₅×#1687	2
C₅×#1686	2
C₅×#1685	2
C₅×#1568	2
C₅×#1553	2
#19294	5

Subgroups — C5×#19294 #11942014

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#19294 #11942014