Subgroups — C₅×#19328 #11942048

Order 1280.

650 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3235	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#3214	C₂	1	1	yes	maximal, characteristic
3	C₅×#3167	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#2931	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#1699	C₂	1	2	yes	maximal, complemented
6	C₅×#1697	C₂	1	2	yes	maximal, complemented
7	C₅×#1671	C₂	1	2	yes	maximal, complemented
8	C₅×#1665	C₂	1	2	yes	maximal, complemented
9	C₅×#1568	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1559	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1557	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₅×#131	—	2	1	no	—
13	C₅×#533	C₂²	1	1	yes	characteristic
14	C₅×#532	C₂²	1	1	yes	characteristic
15	C₅×#532	C₂²	1	1	yes	characteristic
16	C₅×#501	—	2	1	no	—
17	C₅×#498	C₂²	1	1	yes	characteristic
18	C₅×#496	—	2	1	no	—
19	C₅×#492	C₂²	1	1	yes	characteristic
20	C₅×#490	—	2	1	no	—
21	C₅×#489	—	2	1	no	—
22	C₅×#487	C₂²	1	1	yes	characteristic
23	C₅×#486	C₂²	1	1	yes	characteristic
24	C₅×#482	—	2	2	no	—
25	C₅×#476	C₂²	1	2	yes	—
26	C₅×#474	C₂²	1	2	yes	—
27	C₅×#465	—	2	1	no	—
28	C₅×#465	—	2	1	no	—
29	C₅×#461	C₂²	1	2	yes	—
30	C₅×#459	C₂²	1	2	yes	—
31	C₅×#449	—	2	2	no	—
32	C₄×C₅×SD₁₆	—	2	1	no	—
33	C₄×C₅×SD₁₆	—	2	1	no	—
34	C₅×#436	—	2	1	no	—
35	C₅×#436	C₂²	1	2	yes	—
36	C₅×C₈×D₄	—	2	1	no	—
37	C₅×C₈×D₄	C₂²	1	2	yes	—
38	C₅×#432	C₂²	1	1	yes	characteristic
39	C₅×#432	C₂²	1	1	yes	characteristic
40	C₅×#423	C₂²	1	1	yes	characteristic
41	C₅×#408	—	2	1	no	—
42	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
43	C₅×#335	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	#19328	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
50	C₂×C₅×#41	—	2	1	no	—
51	C₂×C₅×#41	—	2	1	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×D₈	—	2	2	no	—
56	C₅×#131	—	4	4	no	—
57	C₂×C₅×M₁₆	—	2	1	no	—
58	C₂×C₅×M₁₆	—	2	2	no	—
59	C₂²×C₅×C₈	—	2	2	no	—
60	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
61	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
62	C₅×C₄⋊Q₈	D₄	1	1	yes	characteristic
63	C₅×C₄⋊Q₈	C₂³	1	1	yes	characteristic
64	C₅×C₄⋊Q₈	C₂³	1	1	yes	characteristic
65	C₅×C₄⋊Q₈	C₂³	1	1	yes	characteristic
66	C₅×#127	D₄	1	1	yes	characteristic
67	C₅×#127	C₂³	1	1	yes	characteristic
68	C₅×#125	—	2	1	no	—
69	C₅×#124	—	2	1	no	—
70	C₅×#124	—	2	1	no	—
71	C₅×C₂²⋊Q₈	—	2	1	no	—
72	C₅×C₂²⋊Q₈	—	2	1	no	—
73	C₅×#121	—	2	1	no	—
74	C₅×#121	—	2	1	no	—
75	C₅×#121	—	2	1	no	—
76	C₅×#121	D₄	1	2	yes	—
77	C₄×C₅×Q₈	—	2	1	no	—
78	C₄×C₅×Q₈	—	2	1	no	—
79	C₄×C₅×D₄	—	2	1	no	—
80	C₄×C₅×D₄	—	2	1	no	—
81	C₄×C₅×D₄	—	2	1	no	—
82	C₄×C₅×D₄	C₂³	1	2	yes	—
83	C₅×#117	—	2	1	no	—
84	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
85	C₅×#107	—	2	2	no	—
86	C₅×#106	—	2	1	no	—
87	C₅×#106	—	2	1	no	—
88	C₅×#106	—	2	2	no	—
89	C₅×C₄⋊C₈	—	2	1	no	—
90	C₅×C₄⋊C₈	C₂³	1	2	yes	—
91	C₅×C₄⋊C₈	C₂³	1	2	yes	—
92	C₅×C₄⋊C₈	C₂³	1	2	yes	—
93	C₅×#103	—	2	1	no	—
94	C₅×#103	—	2	1	no	—
95	C₅×#103	—	2	2	no	—
96	C₅×#102	—	2	2	no	—
97	C₅×#102	—	2	2	no	—
98	C₅×#102	—	2	1	no	—
99	C₅×#102	—	2	1	no	—
100	C₅×#102	—	2	2	no	—
101	C₅×C₂²⋊C₈	—	2	1	no	—
102	C₅×C₂²⋊C₈	—	2	1	no	—
103	C₅×C₂²⋊C₈	—	2	2	no	—
104	C₅×C₂²⋊C₈	—	2	2	no	—
105	C₅×#97	—	2	1	no	—
106	C₅×#97	—	2	1	no	—
107	C₄×C₅×C₈	D₄	1	1	yes	characteristic
108	C₄×C₅×C₈	D₄	1	1	yes	characteristic
109	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
110	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
111	#3235	C₂×C₅	1	1	yes	characteristic, complemented
112	#3214	C₂×C₅	1	1	yes	characteristic
113	#3167	C₂×C₅	1	1	yes	characteristic, complemented
114	#2931	C₂×C₅	1	1	yes	characteristic, complemented
115	#1699	C₂×C₅	1	2	yes	complemented
116	#1697	C₂×C₅	1	2	yes	complemented
117	#1671	C₂×C₅	1	2	yes	complemented
118	#1665	C₂×C₅	1	2	yes	complemented
119	#1568	C₂×C₅	1	1	yes	characteristic, complemented
120	#1559	C₂×C₅	1	1	yes	characteristic, complemented
121	#1557	C₂×C₅	1	1	yes	characteristic, complemented
122	C₅×#41	—	4	2	no	—
123	C₅×#41	—	4	2	no	—
124	C₅×#41	—	8	2	no	—
125	C₂×C₅×Q₈	—	2	1	no	—
126	C₂×C₅×Q₈	—	2	1	no	—
127	C₂×C₅×Q₈	—	2	1	no	—
128	C₂×C₅×Q₈	—	2	1	no	—
129	C₂×C₅×D₄	—	2	2	no	—
130	C₂×C₅×D₄	—	2	1	no	—
131	C₂×C₅×D₄	—	2	1	no	—
132	C₂×C₅×D₄	—	2	1	no	—
133	C₂×C₅×D₄	—	2	1	no	—
134	C₂×C₅×D₄	—	2	1	no	—
135	C₂×C₅×D₄	—	4	1	no	—
136	C₂×C₅×D₄	C₂×D₄	1	2	yes	—
137	C₂²×C₄×C₅	—	2	2	no	—
138	C₂²×C₄×C₅	—	4	1	no	—
139	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
140	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
141	C₂²×C₄×C₅	#41	1	1	yes	characteristic
142	C₅×SD₁₆	—	4	2	no	—
143	C₅×SD₁₆	—	4	2	no	—
144	C₅×SD₁₆	—	8	2	no	—
145	C₅×D₈	—	8	2	no	—
146	C₅×M₁₆	—	4	4	no	—
147	C₅×M₁₆	—	4	2	no	—
148	C₂×C₅×C₈	—	2	2	no	—
149	C₂×C₅×C₈	—	2	2	no	—
150	C₂×C₅×C₈	—	2	2	no	—
151	C₂×C₅×C₈	—	2	2	no	—
152	C₂×C₅×C₈	—	4	1	no	—
153	C₂×C₅×C₈	—	4	4	no	—
154	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
155	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
156	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
157	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
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	—	2	1	no	—
163	C₅×C₄⋊C₄	—	2	1	no	—
164	C₅×C₄⋊C₄	—	2	1	no	—
165	C₅×C₄⋊C₄	—	4	1	no	—
166	C₅×C₄⋊C₄	—	4	1	no	—
167	C₅×C₄⋊C₄	C₂×D₄	1	2	yes	—
168	C₅×C₂²⋊C₄	—	2	2	no	—
169	C₅×C₂²⋊C₄	—	2	2	no	—
170	C₅×C₂²⋊C₄	—	4	1	no	—
171	C₅×C₂²⋊C₄	—	4	1	no	—
172	C₅×C₂²⋊C₄	—	4	1	no	—
173	C₄²×C₅	—	4	1	no	—
174	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
175	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
176	C₄²×C₅	#41	1	1	yes	characteristic
177	C₄²×C₅	C₂⁴	1	1	yes	characteristic
178	C₂×#131	—	2	1	no	—
179	#533	C₂²×C₅	1	1	yes	characteristic
180	#532	C₂²×C₅	1	1	yes	characteristic
181	#532	C₂²×C₅	1	1	yes	characteristic
182	#501	—	2	1	no	—
183	#498	C₂²×C₅	1	1	yes	characteristic
184	#496	—	2	1	no	—
185	#492	C₂²×C₅	1	1	yes	characteristic
186	#490	—	2	1	no	—
187	#489	—	2	1	no	—
188	#487	C₂²×C₅	1	1	yes	characteristic
189	#486	C₂²×C₅	1	1	yes	characteristic
190	#482	—	2	2	no	—
191	#476	C₂²×C₅	1	2	yes	—
192	#474	C₂²×C₅	1	2	yes	—
193	#465	—	2	1	no	—
194	#465	—	2	1	no	—
195	#461	C₂²×C₅	1	2	yes	—
196	#459	C₂²×C₅	1	2	yes	—
197	#449	—	2	2	no	—
198	C₄×SD₁₆	—	2	1	no	—
199	C₄×SD₁₆	—	2	1	no	—
200	#436	—	2	1	no	—
201	#436	C₂²×C₅	1	2	yes	—
202	C₈×D₄	—	2	1	no	—
203	C₈×D₄	C₂²×C₅	1	2	yes	—
204	#432	C₂²×C₅	1	1	yes	characteristic
205	#432	C₂²×C₅	1	1	yes	characteristic
206	#423	C₂²×C₅	1	1	yes	characteristic
207	#408	—	2	1	no	—
208	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
209	#335	C₂²×C₅	1	2	yes	—
210	#334	C₂²×C₅	1	2	yes	—
211	#333	C₂²×C₅	1	2	yes	—
212	#332	C₂²×C₅	1	2	yes	—
213	#332	C₂²×C₅	1	2	yes	—
214	#331	C₂²×C₅	1	2	yes	—
215	C₂³×C₅	—	2	2	no	—
216	C₂³×C₅	—	4	1	no	—
217	C₂³×C₅	#121	1	1	yes	characteristic
218	C₅×Q₈	—	4	2	no	—
219	C₅×Q₈	—	4	1	no	—
220	C₅×Q₈	—	4	1	no	—
221	C₅×Q₈	—	4	2	no	—
222	C₅×Q₈	—	8	1	no	—
223	C₅×D₄	—	2	2	no	—
224	C₅×D₄	—	2	2	no	—
225	C₅×D₄	—	4	2	no	—
226	C₅×D₄	—	4	2	no	—
227	C₅×D₄	—	4	4	no	—
228	C₅×D₄	—	4	1	no	—
229	C₅×D₄	—	4	1	no	—
230	C₅×D₄	—	4	2	no	—
231	C₅×D₄	—	8	1	no	—
232	C₅×D₄	—	8	2	no	—
233	C₂×C₄×C₅	—	2	1	no	—
234	C₂×C₄×C₅	—	2	1	no	—
235	C₂×C₄×C₅	—	2	2	no	—
236	C₂×C₄×C₅	—	2	2	no	—
237	C₂×C₄×C₅	—	4	1	no	—
238	C₂×C₄×C₅	—	4	2	no	—
239	C₂×C₄×C₅	—	4	2	no	—
240	C₂×C₄×C₅	—	4	1	no	—
241	C₂×C₄×C₅	—	4	1	no	—
242	C₂×C₄×C₅	—	4	1	no	—
243	C₂×C₄×C₅	—	8	2	no	—
244	C₂×C₄×C₅	#121	1	1	yes	characteristic
245	C₂×C₄×C₅	#121	1	1	yes	characteristic
246	C₂×C₄×C₅	#121	1	1	yes	characteristic
247	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
248	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
249	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
250	C₅×C₈	—	2	1	no	—
251	C₅×C₈	—	2	1	no	—
252	C₅×C₈	—	2	1	no	—
253	C₅×C₈	—	4	2	no	—
254	C₅×C₈	—	4	2	no	—
255	C₅×C₈	—	4	2	no	—
256	C₅×C₈	AGL(1,ℤ/8)	1	2	yes	—
257	C₂×#41	—	2	1	no	—
258	C₂×#41	—	2	1	no	—
259	C₂×SD₁₆	—	2	2	no	—
260	C₂×SD₁₆	—	2	1	no	—
261	C₂×SD₁₆	—	2	1	no	—
262	C₂×D₈	—	2	2	no	—
263	#131	—	4	4	no	—
264	C₂×M₁₆	—	2	1	no	—
265	C₂×M₁₆	—	2	2	no	—
266	C₂²×C₈	—	2	2	no	—
267	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
268	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
269	C₄⋊Q₈	C₅×D₄	1	1	yes	characteristic
270	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
271	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
272	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
273	#127	C₅×D₄	1	1	yes	characteristic
274	#127	C₂³×C₅	1	1	yes	characteristic
275	#125	—	2	1	no	—
276	#124	—	2	1	no	—
277	#124	—	2	1	no	—
278	C₂²⋊Q₈	—	2	1	no	—
279	C₂²⋊Q₈	—	2	1	no	—
280	#121	—	2	1	no	—
281	#121	—	2	1	no	—
282	#121	—	2	1	no	—
283	#121	C₅×D₄	1	2	yes	—
284	C₄×Q₈	—	2	1	no	—
285	C₄×Q₈	—	2	1	no	—
286	C₄×D₄	—	2	1	no	—
287	C₄×D₄	—	2	1	no	—
288	C₄×D₄	—	2	1	no	—
289	C₄×D₄	C₂³×C₅	1	2	yes	—
290	#117	—	2	1	no	—
291	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
292	#107	—	2	2	no	—
293	#106	—	2	1	no	—
294	#106	—	2	1	no	—
295	#106	—	2	2	no	—
296	C₄⋊C₈	—	2	1	no	—
297	C₄⋊C₈	C₂³×C₅	1	2	yes	—
298	C₄⋊C₈	C₂³×C₅	1	2	yes	—
299	C₄⋊C₈	C₂³×C₅	1	2	yes	—
300	#103	—	2	1	no	—
301	#103	—	2	1	no	—
302	#103	—	2	2	no	—
303	#102	—	2	2	no	—
304	#102	—	2	2	no	—
305	#102	—	2	1	no	—
306	#102	—	2	1	no	—
307	#102	—	2	2	no	—
308	C₂²⋊C₈	—	2	1	no	—
309	C₂²⋊C₈	—	2	1	no	—
310	C₂²⋊C₈	—	2	2	no	—
311	C₂²⋊C₈	—	2	2	no	—
312	#97	—	2	1	no	—
313	#97	—	2	1	no	—
314	C₄×C₈	C₅×D₄	1	1	yes	characteristic
315	C₄×C₈	C₅×D₄	1	1	yes	characteristic
316	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
317	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
318	C₂²×C₅	—	2	1	no	—
319	C₂²×C₅	—	2	1	no	—
320	C₂²×C₅	—	2	1	no	—
321	C₂²×C₅	—	4	2	no	—
322	C₂²×C₅	—	4	2	no	—
323	C₂²×C₅	—	4	2	no	—
324	C₂²×C₅	—	8	1	no	—
325	C₂²×C₅	—	8	1	no	—
326	C₂²×C₅	—	8	1	no	—
327	C₂²×C₅	C₂×#121	1	1	yes	characteristic
328	C₄×C₅	—	2	1	no	—
329	C₄×C₅	—	2	1	no	—
330	C₄×C₅	—	2	1	no	—
331	C₄×C₅	—	2	1	no	—
332	C₄×C₅	—	4	2	no	—
333	C₄×C₅	—	8	1	no	—
334	C₄×C₅	—	8	1	no	—
335	C₄×C₅	—	8	1	no	—
336	C₄×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
337	C₄×C₅	#575	1	1	yes	characteristic
338	C₄×C₅	#577	1	2	yes	—
339	#41	—	4	2	no	—
340	#41	—	4	2	no	—
341	#41	—	8	2	no	—
342	C₂×Q₈	—	2	1	no	—
343	C₂×Q₈	—	2	1	no	—
344	C₂×Q₈	—	2	1	no	—
345	C₂×Q₈	—	2	1	no	—
346	C₂×D₄	—	2	2	no	—
347	C₂×D₄	—	2	1	no	—
348	C₂×D₄	—	2	1	no	—
349	C₂×D₄	—	2	1	no	—
350	C₂×D₄	—	2	1	no	—
351	C₂×D₄	—	2	1	no	—
352	C₂×D₄	—	4	1	no	—
353	C₂×D₄	C₂×C₅×D₄	1	2	yes	—
354	C₂²×C₄	—	2	2	no	—
355	C₂²×C₄	—	4	1	no	—
356	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
357	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
358	C₂²×C₄	C₅×#41	1	1	yes	characteristic
359	SD₁₆	—	4	2	no	—
360	SD₁₆	—	4	2	no	—
361	SD₁₆	—	8	2	no	—
362	D₈	—	8	2	no	—
363	M₁₆	—	4	4	no	—
364	M₁₆	—	4	2	no	—
365	C₂×C₈	—	2	2	no	—
366	C₂×C₈	—	2	2	no	—
367	C₂×C₈	—	2	2	no	—
368	C₂×C₈	—	2	2	no	—
369	C₂×C₈	—	4	1	no	—
370	C₂×C₈	—	4	4	no	—
371	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
372	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
373	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
374	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
375	C₄⋊C₄	—	2	1	no	—
376	C₄⋊C₄	—	2	1	no	—
377	C₄⋊C₄	—	2	1	no	—
378	C₄⋊C₄	—	2	1	no	—
379	C₄⋊C₄	—	2	1	no	—
380	C₄⋊C₄	—	2	1	no	—
381	C₄⋊C₄	—	2	1	no	—
382	C₄⋊C₄	—	4	1	no	—
383	C₄⋊C₄	—	4	1	no	—
384	C₄⋊C₄	C₂×C₅×D₄	1	2	yes	—
385	C₂²⋊C₄	—	2	2	no	—
386	C₂²⋊C₄	—	2	2	no	—
387	C₂²⋊C₄	—	4	1	no	—
388	C₂²⋊C₄	—	4	1	no	—
389	C₂²⋊C₄	—	4	1	no	—
390	C₄²	—	4	1	no	—
391	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
392	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
393	C₄²	C₅×#41	1	1	yes	characteristic
394	C₄²	C₂⁴×C₅	1	1	yes	characteristic
395	C₂×C₅	—	4	1	no	—
396	C₂×C₅	—	8	2	no	—
397	C₂×C₅	—	16	1	no	—
398	C₂×C₅	#3036	1	1	yes	characteristic
399	C₂×C₅	#3057	1	1	yes	characteristic
400	C₂×C₅	#3067	1	1	yes	characteristic
401	C₂³	—	2	2	no	—
402	C₂³	—	4	1	no	—
403	C₂³	C₅×#121	1	1	yes	characteristic
404	Q₈	—	4	2	no	—
405	Q₈	—	4	1	no	—
406	Q₈	—	4	1	no	—
407	Q₈	—	4	2	no	—
408	Q₈	—	8	1	no	—
409	D₄	—	2	2	no	—
410	D₄	—	2	2	no	—
411	D₄	—	4	2	no	—
412	D₄	—	4	2	no	—
413	D₄	—	4	4	no	—
414	D₄	—	4	1	no	—
415	D₄	—	4	1	no	—
416	D₄	—	4	2	no	—
417	D₄	—	8	1	no	—
418	D₄	—	8	2	no	—
419	C₂×C₄	—	2	1	no	—
420	C₂×C₄	—	2	1	no	—
421	C₂×C₄	—	2	2	no	—
422	C₂×C₄	—	2	2	no	—
423	C₂×C₄	—	4	1	no	—
424	C₂×C₄	—	4	2	no	—
425	C₂×C₄	—	4	2	no	—
426	C₂×C₄	—	4	1	no	—
427	C₂×C₄	—	4	1	no	—
428	C₂×C₄	—	4	1	no	—
429	C₂×C₄	—	8	2	no	—
430	C₂×C₄	C₅×#121	1	1	yes	characteristic
431	C₂×C₄	C₅×#121	1	1	yes	characteristic
432	C₂×C₄	C₅×#121	1	1	yes	characteristic
433	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
434	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
435	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
436	C₈	—	2	1	no	—
437	C₈	—	2	1	no	—
438	C₈	—	2	1	no	—
439	C₈	—	4	2	no	—
440	C₈	—	4	2	no	—
441	C₈	—	4	2	no	—
442	C₈	C₅×AGL(1,ℤ/8)	1	2	yes	—
443	C₅	#19328	1	1	yes	characteristic, direct product factor, Sylow
444	C₂²	—	2	1	no	—
445	C₂²	—	2	1	no	—
446	C₂²	—	2	1	no	—
447	C₂²	—	4	2	no	—
448	C₂²	—	4	2	no	—
449	C₂²	—	4	2	no	—
450	C₂²	—	8	1	no	—
451	C₂²	—	8	1	no	—
452	C₂²	—	8	1	no	—
453	C₂²	C₂×C₅×#121	1	1	yes	characteristic
454	C₄	—	2	1	no	—
455	C₄	—	2	1	no	—
456	C₄	—	2	1	no	—
457	C₄	—	2	1	no	—
458	C₄	—	4	2	no	—
459	C₄	—	8	1	no	—
460	C₄	—	8	1	no	—
461	C₄	—	8	1	no	—
462	C₄	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
463	C₄	C₅×#575	1	1	yes	characteristic
464	C₄	C₅×#577	1	2	yes	—
465	C₂	—	4	1	no	—
466	C₂	—	8	2	no	—
467	C₂	—	16	1	no	—
468	C₂	C₅×#3036	1	1	yes	characteristic
469	C₂	C₅×#3057	1	1	yes	characteristic
470	C₂	C₅×#3067	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₅
prime radical	C₅×#3214	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×#3235	C₂	semidirect
3. C₅×#3167	C₂	semidirect
4. C₅×#2931	C₂	semidirect
5. C₅×#1699	C₂	semidirect
6. C₅×#1697	C₂	semidirect
7. C₅×#1671	C₂	semidirect
8. C₅×#1665	C₂	semidirect
9. C₅×#1568	C₂	semidirect
10. C₅×#1559	C₂	semidirect
11. C₅×#1557	C₂	semidirect
49. #19328	C₅	direct (N × H)
111. #3235	C₂×C₅	semidirect
113. #3167	C₂×C₅	semidirect
114. #2931	C₂×C₅	semidirect
115. #1699	C₂×C₅	semidirect
116. #1697	C₂×C₅	semidirect
117. #1671	C₂×C₅	semidirect
118. #1665	C₂×C₅	semidirect
119. #1568	C₂×C₅	semidirect
120. #1559	C₂×C₅	semidirect
121. #1557	C₂×C₅	semidirect
443. C₅	#19328	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×#3235	2
C₅×#3214	2
C₅×#3167	2
C₅×#2931	2
C₅×#1699	2
C₅×#1697	2
C₅×#1671	2
C₅×#1665	2
C₅×#1568	2
C₅×#1559	2
C₅×#1557	2
#19328	5

Subgroups — C5×#19328 #11942048

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#19328 #11942048