Subgroups — C₅×#19313 #11942033

Order 1280.

684 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3152	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#3115	C₂	1	1	yes	maximal, characteristic
3	C₅×#3079	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#2970	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#1690	C₂	1	2	yes	maximal, complemented
6	C₅×#1686	C₂	1	2	yes	maximal, complemented
7	C₅×#1669	C₂	1	2	yes	maximal, complemented
8	C₅×#1665	C₂	1	2	yes	maximal, complemented
9	C₅×#1569	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1557	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1556	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₅×#137	—	2	2	no	—
13	C₅×#532	C₂²	1	1	yes	characteristic
14	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
15	C₄×C₅×#41	C₂²	1	1	yes	characteristic
16	C₅×#497	—	2	1	no	—
17	C₅×#497	—	2	1	no	—
18	C₅×#494	C₂²	1	2	yes	—
19	C₅×#492	C₂²	1	2	yes	—
20	C₅×#482	—	2	1	no	—
21	C₅×#477	—	2	1	no	—
22	C₅×#476	—	2	1	no	—
23	C₅×#475	C₂²	1	2	yes	—
24	C₅×#475	C₂²	1	1	yes	characteristic
25	C₅×#474	C₂²	1	2	yes	—
26	C₅×#474	C₂²	1	1	yes	characteristic
27	C₅×#460	C₂²	1	1	yes	characteristic
28	C₅×#459	C₂²	1	1	yes	characteristic
29	C₅×#449	—	2	1	no	—
30	C₅×#446	C₂²	1	2	yes	—
31	C₅×#442	—	2	1	no	—
32	C₅×#440	—	2	1	no	—
33	C₅×#435	—	2	2	no	—
34	C₅×C₈×D₄	C₂²	1	2	yes	—
35	C₅×#432	—	2	1	no	—
36	C₅×#432	C₂²	1	1	yes	characteristic
37	C₅×#432	C₂²	1	1	yes	characteristic
38	C₅×#428	—	2	1	no	—
39	C₅×#423	C₂²	1	1	yes	characteristic
40	C₅×#417	—	2	1	no	—
41	C₄×C₅×M₁₆	C₂²	1	1	yes	characteristic
42	C₂×C₅×#97	—	2	1	no	—
43	C₅×#335	C₂²	1	2	yes	—
44	C₅×#334	C₂²	1	2	yes	—
45	C₅×#332	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	#19313	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
50	C₂×C₅×#41	—	2	1	no	—
51	C₂×C₅×#41	D₄	1	1	yes	characteristic
52	C₂²×C₅×Q₈	—	2	1	no	—
53	C₅×#137	—	4	8	no	—
54	C₂×C₅×Q₁₆	—	2	2	no	—
55	C₂×C₅×Q₁₆	—	2	2	no	—
56	C₂×C₅×SD₁₆	—	2	1	no	—
57	C₂×C₅×SD₁₆	—	2	2	no	—
58	C₂×C₅×SD₁₆	—	2	2	no	—
59	C₂×C₅×D₈	—	2	1	no	—
60	C₂×C₅×M₁₆	—	2	1	no	—
61	C₂×C₅×M₁₆	D₄	1	2	yes	—
62	C₂²×C₅×C₈	—	2	2	no	—
63	C₅×C₄⋊Q₈	—	2	1	no	—
64	C₅×C₄⋊Q₈	—	2	1	no	—
65	C₅×C₄⋊Q₈	—	2	1	no	—
66	C₅×C₄⋊Q₈	C₂³	1	2	yes	—
67	C₅×C₄⋊Q₈	C₂³	1	1	yes	characteristic
68	C₅×#127	C₂³	1	1	yes	characteristic
69	C₅×#124	—	2	1	no	—
70	C₅×#121	—	2	1	no	—
71	C₅×#121	—	2	1	no	—
72	C₄×C₅×Q₈	D₄	1	1	yes	characteristic
73	C₄×C₅×Q₈	C₂³	1	1	yes	characteristic
74	C₄×C₅×D₄	—	2	1	no	—
75	C₄×C₅×D₄	—	2	1	no	—
76	C₄×C₅×D₄	—	2	1	no	—
77	C₄×C₅×D₄	—	2	1	no	—
78	C₄×C₅×D₄	D₄	1	1	yes	characteristic
79	C₄×C₅×D₄	C₂³	1	1	yes	characteristic
80	C₅×#117	—	2	1	no	—
81	C₅×#117	D₄	1	1	yes	characteristic
82	C₂×C₅×C₄⋊C₄	—	2	1	no	—
83	C₂×C₅×C₄⋊C₄	—	2	1	no	—
84	C₂×C₄²×C₅	—	2	1	no	—
85	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
86	C₅×#107	—	2	2	no	—
87	C₅×#107	—	2	1	no	—
88	C₅×#106	—	2	2	no	—
89	C₅×#106	—	2	1	no	—
90	C₅×C₄⋊C₈	—	2	2	no	—
91	C₅×C₄⋊C₈	—	2	1	no	—
92	C₅×C₄⋊C₈	C₂³	1	2	yes	—
93	C₅×C₄⋊C₈	C₂³	1	2	yes	—
94	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
95	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
96	C₅×#103	—	2	2	no	—
97	C₅×#103	—	2	1	no	—
98	C₅×#102	—	2	2	no	—
99	C₅×#102	—	2	1	no	—
100	C₅×#102	—	2	1	no	—
101	C₅×#102	—	2	1	no	—
102	C₅×C₂²⋊C₈	—	2	1	no	—
103	C₅×C₂²⋊C₈	—	2	1	no	—
104	C₅×C₂²⋊C₈	—	2	2	no	—
105	C₅×#97	—	2	2	no	—
106	C₅×#97	—	2	1	no	—
107	C₅×#97	—	2	1	no	—
108	C₅×#97	D₄	1	1	yes	characteristic
109	C₅×#97	D₄	1	1	yes	characteristic
110	C₄×C₅×C₈	C₂³	1	2	yes	—
111	#3152	C₂×C₅	1	1	yes	characteristic, complemented
112	#3115	C₂×C₅	1	1	yes	characteristic
113	#3079	C₂×C₅	1	1	yes	characteristic, complemented
114	#2970	C₂×C₅	1	1	yes	characteristic, complemented
115	#1690	C₂×C₅	1	2	yes	complemented
116	#1686	C₂×C₅	1	2	yes	complemented
117	#1669	C₂×C₅	1	2	yes	complemented
118	#1665	C₂×C₅	1	2	yes	complemented
119	#1569	C₂×C₅	1	1	yes	characteristic, complemented
120	#1557	C₂×C₅	1	1	yes	characteristic, complemented
121	#1556	C₂×C₅	1	1	yes	characteristic, complemented
122	C₅×#41	—	2	2	no	—
123	C₅×#41	—	4	1	no	—
124	C₅×#41	—	4	4	no	—
125	C₂×C₅×Q₈	—	2	1	no	—
126	C₂×C₅×Q₈	—	2	2	no	—
127	C₂×C₅×Q₈	—	4	4	no	—
128	C₂×C₅×Q₈	—	4	1	no	—
129	C₂×C₅×Q₈	C₂×D₄	1	1	yes	characteristic
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	—	4	1	no	—
135	C₂×C₅×D₄	C₂×D₄	1	1	yes	characteristic
136	C₂²×C₄×C₅	—	2	1	no	—
137	C₂²×C₄×C₅	—	2	1	no	—
138	C₂²×C₄×C₅	—	2	1	no	—
139	C₂²×C₄×C₅	—	4	1	no	—
140	C₂²×C₄×C₅	—	4	1	no	—
141	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
142	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
143	C₂²×C₄×C₅	#41	1	1	yes	characteristic
144	C₅×Q₁₆	—	4	4	no	—
145	C₅×Q₁₆	—	4	4	no	—
146	C₅×SD₁₆	—	4	4	no	—
147	C₅×SD₁₆	—	4	2	no	—
148	C₅×SD₁₆	—	4	4	no	—
149	C₅×D₈	—	4	2	no	—
150	C₅×M₁₆	—	2	4	no	—
151	C₅×M₁₆	—	4	2	no	—
152	C₂×C₅×C₈	—	2	2	no	—
153	C₂×C₅×C₈	—	2	2	no	—
154	C₂×C₅×C₈	—	2	1	no	—
155	C₂×C₅×C₈	—	2	1	no	—
156	C₂×C₅×C₈	—	4	4	no	—
157	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
158	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
159	C₅×C₄⋊C₄	—	2	1	no	—
160	C₅×C₄⋊C₄	—	2	1	no	—
161	C₅×C₄⋊C₄	—	2	2	no	—
162	C₅×C₄⋊C₄	—	2	1	no	—
163	C₅×C₄⋊C₄	—	2	2	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	1	yes	characteristic
168	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
169	C₅×C₂²⋊C₄	—	2	1	no	—
170	C₅×C₂²⋊C₄	—	2	1	no	—
171	C₅×C₂²⋊C₄	—	2	1	no	—
172	C₅×C₂²⋊C₄	—	4	1	no	—
173	C₅×C₂²⋊C₄	—	4	1	no	—
174	C₄²×C₅	—	2	1	no	—
175	C₄²×C₅	—	2	1	no	—
176	C₄²×C₅	—	2	1	no	—
177	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
178	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
179	C₄²×C₅	#41	1	1	yes	characteristic
180	C₄²×C₅	C₂⁴	1	1	yes	characteristic
181	C₂×#137	—	2	2	no	—
182	#532	C₂²×C₅	1	1	yes	characteristic
183	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
184	C₄×#41	C₂²×C₅	1	1	yes	characteristic
185	#497	—	2	1	no	—
186	#497	—	2	1	no	—
187	#494	C₂²×C₅	1	2	yes	—
188	#492	C₂²×C₅	1	2	yes	—
189	#482	—	2	1	no	—
190	#477	—	2	1	no	—
191	#476	—	2	1	no	—
192	#475	C₂²×C₅	1	2	yes	—
193	#475	C₂²×C₅	1	1	yes	characteristic
194	#474	C₂²×C₅	1	2	yes	—
195	#474	C₂²×C₅	1	1	yes	characteristic
196	#460	C₂²×C₅	1	1	yes	characteristic
197	#459	C₂²×C₅	1	1	yes	characteristic
198	#449	—	2	1	no	—
199	#446	C₂²×C₅	1	2	yes	—
200	#442	—	2	1	no	—
201	#440	—	2	1	no	—
202	#435	—	2	2	no	—
203	C₈×D₄	C₂²×C₅	1	2	yes	—
204	#432	—	2	1	no	—
205	#432	C₂²×C₅	1	1	yes	characteristic
206	#432	C₂²×C₅	1	1	yes	characteristic
207	#428	—	2	1	no	—
208	#423	C₂²×C₅	1	1	yes	characteristic
209	#417	—	2	1	no	—
210	C₄×M₁₆	C₂²×C₅	1	1	yes	characteristic
211	C₂×#97	—	2	1	no	—
212	#335	C₂²×C₅	1	2	yes	—
213	#334	C₂²×C₅	1	2	yes	—
214	#332	C₂²×C₅	1	2	yes	—
215	#332	C₂²×C₅	1	2	yes	—
216	#332	C₂²×C₅	1	2	yes	—
217	#331	C₂²×C₅	1	2	yes	—
218	C₂³×C₅	—	2	1	no	—
219	C₂³×C₅	—	4	1	no	—
220	C₂³×C₅	#121	1	1	yes	characteristic
221	C₅×Q₈	—	2	1	no	—
222	C₅×Q₈	—	2	1	no	—
223	C₅×Q₈	—	4	2	no	—
224	C₅×Q₈	—	4	2	no	—
225	C₅×Q₈	—	4	2	no	—
226	C₅×Q₈	—	8	2	no	—
227	C₅×D₄	—	2	1	no	—
228	C₅×D₄	—	4	2	no	—
229	C₅×D₄	—	4	2	no	—
230	C₅×D₄	—	4	1	no	—
231	C₅×D₄	—	4	1	no	—
232	C₅×D₄	—	8	1	no	—
233	C₅×D₄	—	8	2	no	—
234	C₅×D₄	#137	1	2	yes	complemented
235	C₂×C₄×C₅	—	2	2	no	—
236	C₂×C₄×C₅	—	2	1	no	—
237	C₂×C₄×C₅	—	2	1	no	—
238	C₂×C₄×C₅	—	2	1	no	—
239	C₂×C₄×C₅	—	2	1	no	—
240	C₂×C₄×C₅	—	2	1	no	—
241	C₂×C₄×C₅	—	4	1	no	—
242	C₂×C₄×C₅	—	4	2	no	—
243	C₂×C₄×C₅	—	4	2	no	—
244	C₂×C₄×C₅	—	4	1	no	—
245	C₂×C₄×C₅	—	4	2	no	—
246	C₂×C₄×C₅	—	8	1	no	—
247	C₂×C₄×C₅	—	8	2	no	—
248	C₂×C₄×C₅	—	8	2	no	—
249	C₂×C₄×C₅	#121	1	1	yes	characteristic
250	C₂×C₄×C₅	#121	1	1	yes	characteristic
251	C₂×C₄×C₅	#121	1	1	yes	characteristic
252	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
253	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
254	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
255	C₅×C₈	—	2	2	no	—
256	C₅×C₈	—	4	2	no	—
257	C₅×C₈	—	4	1	no	—
258	C₅×C₈	—	4	2	no	—
259	C₅×C₈	—	4	1	no	—
260	C₅×C₈	AGL(1,ℤ/8)	1	4	yes	—
261	C₂×#41	—	2	1	no	—
262	C₂×#41	C₅×D₄	1	1	yes	characteristic
263	C₂²×Q₈	—	2	1	no	—
264	#137	—	4	8	no	—
265	C₂×Q₁₆	—	2	2	no	—
266	C₂×Q₁₆	—	2	2	no	—
267	C₂×SD₁₆	—	2	1	no	—
268	C₂×SD₁₆	—	2	2	no	—
269	C₂×SD₁₆	—	2	2	no	—
270	C₂×D₈	—	2	1	no	—
271	C₂×M₁₆	—	2	1	no	—
272	C₂×M₁₆	C₅×D₄	1	2	yes	—
273	C₂²×C₈	—	2	2	no	—
274	C₄⋊Q₈	—	2	1	no	—
275	C₄⋊Q₈	—	2	1	no	—
276	C₄⋊Q₈	—	2	1	no	—
277	C₄⋊Q₈	C₂³×C₅	1	2	yes	—
278	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
279	#127	C₂³×C₅	1	1	yes	characteristic
280	#124	—	2	1	no	—
281	#121	—	2	1	no	—
282	#121	—	2	1	no	—
283	C₄×Q₈	C₅×D₄	1	1	yes	characteristic
284	C₄×Q₈	C₂³×C₅	1	1	yes	characteristic
285	C₄×D₄	—	2	1	no	—
286	C₄×D₄	—	2	1	no	—
287	C₄×D₄	—	2	1	no	—
288	C₄×D₄	—	2	1	no	—
289	C₄×D₄	C₅×D₄	1	1	yes	characteristic
290	C₄×D₄	C₂³×C₅	1	1	yes	characteristic
291	#117	—	2	1	no	—
292	#117	C₅×D₄	1	1	yes	characteristic
293	C₂×C₄⋊C₄	—	2	1	no	—
294	C₂×C₄⋊C₄	—	2	1	no	—
295	C₂×C₄²	—	2	1	no	—
296	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
297	#107	—	2	2	no	—
298	#107	—	2	1	no	—
299	#106	—	2	2	no	—
300	#106	—	2	1	no	—
301	C₄⋊C₈	—	2	2	no	—
302	C₄⋊C₈	—	2	1	no	—
303	C₄⋊C₈	C₂³×C₅	1	2	yes	—
304	C₄⋊C₈	C₂³×C₅	1	2	yes	—
305	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
306	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
307	#103	—	2	2	no	—
308	#103	—	2	1	no	—
309	#102	—	2	2	no	—
310	#102	—	2	1	no	—
311	#102	—	2	1	no	—
312	#102	—	2	1	no	—
313	C₂²⋊C₈	—	2	1	no	—
314	C₂²⋊C₈	—	2	1	no	—
315	C₂²⋊C₈	—	2	2	no	—
316	#97	—	2	2	no	—
317	#97	—	2	1	no	—
318	#97	—	2	1	no	—
319	#97	C₅×D₄	1	1	yes	characteristic
320	#97	C₅×D₄	1	1	yes	characteristic
321	C₄×C₈	C₂³×C₅	1	2	yes	—
322	C₂²×C₅	—	2	1	no	—
323	C₂²×C₅	—	2	1	no	—
324	C₂²×C₅	—	2	2	no	—
325	C₂²×C₅	—	2	1	no	—
326	C₂²×C₅	—	4	1	no	—
327	C₂²×C₅	—	4	1	no	—
328	C₂²×C₅	—	8	1	no	—
329	C₂²×C₅	—	8	1	no	—
330	C₂²×C₅	—	8	1	no	—
331	C₂²×C₅	C₂×#121	1	1	yes	characteristic
332	C₄×C₅	—	2	1	no	—
333	C₄×C₅	—	2	1	no	—
334	C₄×C₅	—	2	1	no	—
335	C₄×C₅	—	2	1	no	—
336	C₄×C₅	—	4	1	no	—
337	C₄×C₅	—	4	1	no	—
338	C₄×C₅	—	4	1	no	—
339	C₄×C₅	—	8	1	no	—
340	C₄×C₅	—	8	2	no	—
341	C₄×C₅	C₂×AGL(1,ℤ/8)	1	2	yes	—
342	C₄×C₅	C₂×#137	1	1	yes	characteristic
343	C₄×C₅	#575	1	1	yes	characteristic
344	#41	—	2	2	no	—
345	#41	—	4	1	no	—
346	#41	—	4	4	no	—
347	C₂×Q₈	—	2	1	no	—
348	C₂×Q₈	—	2	2	no	—
349	C₂×Q₈	—	4	4	no	—
350	C₂×Q₈	—	4	1	no	—
351	C₂×Q₈	C₂×C₅×D₄	1	1	yes	characteristic
352	C₂×D₄	—	2	1	no	—
353	C₂×D₄	—	2	1	no	—
354	C₂×D₄	—	2	1	no	—
355	C₂×D₄	—	2	1	no	—
356	C₂×D₄	—	4	1	no	—
357	C₂×D₄	C₂×C₅×D₄	1	1	yes	characteristic
358	C₂²×C₄	—	2	1	no	—
359	C₂²×C₄	—	2	1	no	—
360	C₂²×C₄	—	2	1	no	—
361	C₂²×C₄	—	4	1	no	—
362	C₂²×C₄	—	4	1	no	—
363	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
364	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
365	C₂²×C₄	C₅×#41	1	1	yes	characteristic
366	Q₁₆	—	4	4	no	—
367	Q₁₆	—	4	4	no	—
368	SD₁₆	—	4	4	no	—
369	SD₁₆	—	4	2	no	—
370	SD₁₆	—	4	4	no	—
371	D₈	—	4	2	no	—
372	M₁₆	—	2	4	no	—
373	M₁₆	—	4	2	no	—
374	C₂×C₈	—	2	2	no	—
375	C₂×C₈	—	2	1	no	—
376	C₂×C₈	—	2	1	no	—
377	C₂×C₈	—	2	2	no	—
378	C₂×C₈	—	4	4	no	—
379	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
380	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
381	C₄⋊C₄	—	2	1	no	—
382	C₄⋊C₄	—	2	1	no	—
383	C₄⋊C₄	—	2	2	no	—
384	C₄⋊C₄	—	2	1	no	—
385	C₄⋊C₄	—	2	2	no	—
386	C₄⋊C₄	—	2	1	no	—
387	C₄⋊C₄	—	4	1	no	—
388	C₄⋊C₄	—	4	1	no	—
389	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
390	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
391	C₂²⋊C₄	—	2	1	no	—
392	C₂²⋊C₄	—	2	1	no	—
393	C₂²⋊C₄	—	2	1	no	—
394	C₂²⋊C₄	—	4	1	no	—
395	C₂²⋊C₄	—	4	1	no	—
396	C₄²	—	2	1	no	—
397	C₄²	—	2	1	no	—
398	C₄²	—	2	1	no	—
399	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
400	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
401	C₄²	C₅×#41	1	1	yes	characteristic
402	C₄²	C₂⁴×C₅	1	1	yes	characteristic
403	C₂×C₅	—	4	1	no	—
404	C₂×C₅	—	4	2	no	—
405	C₂×C₅	—	16	1	no	—
406	C₂×C₅	#3038	1	1	yes	characteristic
407	C₂×C₅	#3056	1	1	yes	characteristic
408	C₂×C₅	#3069	1	1	yes	characteristic
409	C₂³	—	2	1	no	—
410	C₂³	—	4	1	no	—
411	C₂³	C₅×#121	1	1	yes	characteristic
412	Q₈	—	2	1	no	—
413	Q₈	—	2	1	no	—
414	Q₈	—	4	2	no	—
415	Q₈	—	4	2	no	—
416	Q₈	—	4	2	no	—
417	Q₈	—	8	2	no	—
418	D₄	—	2	1	no	—
419	D₄	—	4	2	no	—
420	D₄	—	4	2	no	—
421	D₄	—	4	1	no	—
422	D₄	—	4	1	no	—
423	D₄	—	8	1	no	—
424	D₄	—	8	2	no	—
425	D₄	C₅×#137	1	2	yes	complemented
426	C₂×C₄	—	2	2	no	—
427	C₂×C₄	—	2	1	no	—
428	C₂×C₄	—	2	1	no	—
429	C₂×C₄	—	2	1	no	—
430	C₂×C₄	—	2	1	no	—
431	C₂×C₄	—	2	1	no	—
432	C₂×C₄	—	4	1	no	—
433	C₂×C₄	—	4	2	no	—
434	C₂×C₄	—	4	2	no	—
435	C₂×C₄	—	4	1	no	—
436	C₂×C₄	—	4	2	no	—
437	C₂×C₄	—	8	1	no	—
438	C₂×C₄	—	8	2	no	—
439	C₂×C₄	—	8	2	no	—
440	C₂×C₄	C₅×#121	1	1	yes	characteristic
441	C₂×C₄	C₅×#121	1	1	yes	characteristic
442	C₂×C₄	C₅×#121	1	1	yes	characteristic
443	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
444	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
445	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
446	C₈	—	2	2	no	—
447	C₈	—	4	2	no	—
448	C₈	—	4	1	no	—
449	C₈	—	4	2	no	—
450	C₈	—	4	1	no	—
451	C₈	C₅×AGL(1,ℤ/8)	1	4	yes	—
452	C₅	#19313	1	1	yes	characteristic, direct product factor, Sylow
453	C₂²	—	2	1	no	—
454	C₂²	—	2	1	no	—
455	C₂²	—	2	2	no	—
456	C₂²	—	2	1	no	—
457	C₂²	—	4	1	no	—
458	C₂²	—	4	1	no	—
459	C₂²	—	8	1	no	—
460	C₂²	—	8	1	no	—
461	C₂²	—	8	1	no	—
462	C₂²	C₂×C₅×#121	1	1	yes	characteristic
463	C₄	—	2	1	no	—
464	C₄	—	2	1	no	—
465	C₄	—	2	1	no	—
466	C₄	—	2	1	no	—
467	C₄	—	4	1	no	—
468	C₄	—	4	1	no	—
469	C₄	—	4	1	no	—
470	C₄	—	8	1	no	—
471	C₄	—	8	2	no	—
472	C₄	C₂×C₅×AGL(1,ℤ/8)	1	2	yes	—
473	C₄	C₂×C₅×#137	1	1	yes	characteristic
474	C₄	C₅×#575	1	1	yes	characteristic
475	C₂	—	4	1	no	—
476	C₂	—	4	2	no	—
477	C₂	—	16	1	no	—
478	C₂	C₅×#3038	1	1	yes	characteristic
479	C₂	C₅×#3056	1	1	yes	characteristic
480	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×#3115	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×#3152	C₂	semidirect
3. C₅×#3079	C₂	semidirect
4. C₅×#2970	C₂	semidirect
5. C₅×#1690	C₂	semidirect
6. C₅×#1686	C₂	semidirect
7. C₅×#1669	C₂	semidirect
8. C₅×#1665	C₂	semidirect
9. C₅×#1569	C₂	semidirect
10. C₅×#1557	C₂	semidirect
11. C₅×#1556	C₂	semidirect
49. #19313	C₅	direct (N × H)
111. #3152	C₂×C₅	semidirect
113. #3079	C₂×C₅	semidirect
114. #2970	C₂×C₅	semidirect
115. #1690	C₂×C₅	semidirect
116. #1686	C₂×C₅	semidirect
117. #1669	C₂×C₅	semidirect
118. #1665	C₂×C₅	semidirect
119. #1569	C₂×C₅	semidirect
120. #1557	C₂×C₅	semidirect
121. #1556	C₂×C₅	semidirect
234. C₅×D₄	#137	semidirect
425. D₄	C₅×#137	semidirect
452. C₅	#19313	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×#3152	2
C₅×#3115	2
C₅×#3079	2
C₅×#2970	2
C₅×#1690	2
C₅×#1686	2
C₅×#1669	2
C₅×#1665	2
C₅×#1569	2
C₅×#1557	2
C₅×#1556	2
#19313	5

Subgroups — C5×#19313 #11942033

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#19313 #11942033