Subgroups — C₅×#19318 #11942038

Order 1280.

620 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3141	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×#1704	C₂	1	2	yes	maximal, complemented
6	C₅×#1698	C₂	1	2	yes	maximal, complemented
7	C₅×#1683	C₂	1	2	yes	maximal, complemented
8	C₅×#1677	C₂	1	2	yes	maximal, complemented
9	C₅×#1569	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1558	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1557	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#532	C₂²	1	1	yes	characteristic
13	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
14	C₄×C₅×#41	C₂²	1	1	yes	characteristic
15	C₅×#489	—	2	1	no	—
16	C₅×#489	—	2	1	no	—
17	C₅×#487	C₂²	1	2	yes	—
18	C₅×#486	C₂²	1	2	yes	—
19	C₅×#482	—	2	1	no	—
20	C₅×#477	C₂²	1	2	yes	—
21	C₅×#476	C₂²	1	2	yes	—
22	C₅×#475	—	2	1	no	—
23	C₅×#475	C₂²	1	1	yes	characteristic
24	C₅×#474	—	2	1	no	—
25	C₅×#474	C₂²	1	1	yes	characteristic
26	C₅×#460	C₂²	1	1	yes	characteristic
27	C₅×#459	C₂²	1	1	yes	characteristic
28	C₅×#449	—	2	1	no	—
29	C₅×#446	C₂²	1	2	yes	—
30	C₅×#442	—	2	1	no	—
31	C₅×#440	—	2	1	no	—
32	C₅×#435	—	2	2	no	—
33	C₅×C₈×D₄	C₂²	1	2	yes	—
34	C₅×#432	—	2	1	no	—
35	C₅×#432	C₂²	1	1	yes	characteristic
36	C₅×#432	C₂²	1	1	yes	characteristic
37	C₅×#428	—	2	1	no	—
38	C₅×#423	C₂²	1	1	yes	characteristic
39	C₅×#417	—	2	1	no	—
40	C₅×#417	—	2	2	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×#333	C₂²	1	2	yes	—
46	C₅×#333	C₂²	1	2	yes	—
47	C₅×#332	C₂²	1	2	yes	—
48	C₅×#331	C₂²	1	2	yes	—
49	#19318	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	C₂×C₅×SD₁₆	—	2	1	no	—
54	C₂×C₅×D₈	—	2	1	no	—
55	C₂×C₅×M₁₆	—	2	1	no	—
56	C₂×C₅×M₁₆	D₄	1	2	yes	—
57	C₂²×C₅×C₈	—	2	2	no	—
58	C₅×C₄⋊Q₈	—	2	1	no	—
59	C₅×C₄⋊Q₈	—	2	1	no	—
60	C₅×C₄⋊Q₈	—	2	1	no	—
61	C₅×C₄⋊Q₈	C₂³	1	1	yes	characteristic
62	C₅×C₄⋊Q₈	C₂³	1	2	yes	—
63	C₅×#127	C₂³	1	1	yes	characteristic
64	C₅×#124	—	2	1	no	—
65	C₅×#121	—	2	1	no	—
66	C₅×#121	—	2	1	no	—
67	C₄×C₅×Q₈	D₄	1	1	yes	characteristic
68	C₄×C₅×Q₈	C₂³	1	1	yes	characteristic
69	C₄×C₅×D₄	—	2	1	no	—
70	C₄×C₅×D₄	—	2	1	no	—
71	C₄×C₅×D₄	—	2	1	no	—
72	C₄×C₅×D₄	—	2	1	no	—
73	C₄×C₅×D₄	D₄	1	1	yes	characteristic
74	C₄×C₅×D₄	C₂³	1	1	yes	characteristic
75	C₅×#117	—	2	1	no	—
76	C₅×#117	D₄	1	1	yes	characteristic
77	C₂×C₅×C₄⋊C₄	—	2	1	no	—
78	C₂×C₅×C₄⋊C₄	—	2	1	no	—
79	C₂×C₄²×C₅	—	2	1	no	—
80	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
81	C₅×#107	—	2	2	no	—
82	C₅×#107	—	2	1	no	—
83	C₅×#106	—	2	2	no	—
84	C₅×#106	—	2	1	no	—
85	C₅×C₄⋊C₈	—	2	2	no	—
86	C₅×C₄⋊C₈	—	2	1	no	—
87	C₅×C₄⋊C₈	C₂³	1	2	yes	—
88	C₅×C₄⋊C₈	C₂³	1	2	yes	—
89	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
90	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
91	C₅×#103	—	2	2	no	—
92	C₅×#103	—	2	1	no	—
93	C₅×#103	—	2	2	no	—
94	C₅×#103	—	2	2	no	—
95	C₅×#102	—	2	2	no	—
96	C₅×#102	—	2	1	no	—
97	C₅×#102	—	2	2	no	—
98	C₅×#102	—	2	2	no	—
99	C₅×#102	—	2	1	no	—
100	C₅×#102	—	2	1	no	—
101	C₅×C₂²⋊C₈	—	2	1	no	—
102	C₅×C₂²⋊C₈	—	2	1	no	—
103	C₅×C₂²⋊C₈	—	2	2	no	—
104	C₅×#97	—	2	2	no	—
105	C₅×#97	—	2	1	no	—
106	C₅×#97	—	2	1	no	—
107	C₅×#97	D₄	1	1	yes	characteristic
108	C₅×#97	D₄	1	1	yes	characteristic
109	C₄×C₅×C₈	C₂³	1	2	yes	—
110	#3141	C₂×C₅	1	1	yes	characteristic, complemented
111	#3115	C₂×C₅	1	1	yes	characteristic
112	#3079	C₂×C₅	1	1	yes	characteristic, complemented
113	#2970	C₂×C₅	1	1	yes	characteristic, complemented
114	#1704	C₂×C₅	1	2	yes	complemented
115	#1698	C₂×C₅	1	2	yes	complemented
116	#1683	C₂×C₅	1	2	yes	complemented
117	#1677	C₂×C₅	1	2	yes	complemented
118	#1569	C₂×C₅	1	1	yes	characteristic, complemented
119	#1558	C₂×C₅	1	1	yes	characteristic, complemented
120	#1557	C₂×C₅	1	1	yes	characteristic, complemented
121	C₅×#41	—	2	2	no	—
122	C₅×#41	—	4	1	no	—
123	C₅×#41	—	4	4	no	—
124	C₂×C₅×Q₈	—	2	1	no	—
125	C₂×C₅×Q₈	—	2	2	no	—
126	C₂×C₅×Q₈	—	4	1	no	—
127	C₂×C₅×Q₈	—	8	2	no	—
128	C₂×C₅×Q₈	C₂×D₄	1	1	yes	characteristic
129	C₂×C₅×D₄	—	2	1	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	—	4	1	no	—
134	C₂×C₅×D₄	C₂×D₄	1	1	yes	characteristic
135	C₂²×C₄×C₅	—	2	1	no	—
136	C₂²×C₄×C₅	—	2	1	no	—
137	C₂²×C₄×C₅	—	2	1	no	—
138	C₂²×C₄×C₅	—	4	1	no	—
139	C₂²×C₄×C₅	—	4	1	no	—
140	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
141	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
142	C₂²×C₄×C₅	#41	1	1	yes	characteristic
143	C₅×SD₁₆	—	4	2	no	—
144	C₅×D₈	—	4	2	no	—
145	C₅×M₁₆	—	4	2	no	—
146	C₅×M₁₆	—	4	2	no	—
147	C₂×C₅×C₈	—	2	2	no	—
148	C₂×C₅×C₈	—	2	2	no	—
149	C₂×C₅×C₈	—	2	1	no	—
150	C₂×C₅×C₈	—	2	1	no	—
151	C₂×C₅×C₈	—	4	4	no	—
152	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
153	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
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	—	2	1	no	—
159	C₅×C₄⋊C₄	—	2	1	no	—
160	C₅×C₄⋊C₄	—	4	1	no	—
161	C₅×C₄⋊C₄	—	4	1	no	—
162	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
163	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
164	C₅×C₂²⋊C₄	—	2	1	no	—
165	C₅×C₂²⋊C₄	—	2	1	no	—
166	C₅×C₂²⋊C₄	—	2	1	no	—
167	C₅×C₂²⋊C₄	—	4	1	no	—
168	C₅×C₂²⋊C₄	—	4	1	no	—
169	C₄²×C₅	—	2	1	no	—
170	C₄²×C₅	—	2	1	no	—
171	C₄²×C₅	—	2	1	no	—
172	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
173	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
174	C₄²×C₅	#41	1	1	yes	characteristic
175	C₄²×C₅	C₂⁴	1	1	yes	characteristic
176	#532	C₂²×C₅	1	1	yes	characteristic
177	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
178	C₄×#41	C₂²×C₅	1	1	yes	characteristic
179	#489	—	2	1	no	—
180	#489	—	2	1	no	—
181	#487	C₂²×C₅	1	2	yes	—
182	#486	C₂²×C₅	1	2	yes	—
183	#482	—	2	1	no	—
184	#477	C₂²×C₅	1	2	yes	—
185	#476	C₂²×C₅	1	2	yes	—
186	#475	—	2	1	no	—
187	#475	C₂²×C₅	1	1	yes	characteristic
188	#474	—	2	1	no	—
189	#474	C₂²×C₅	1	1	yes	characteristic
190	#460	C₂²×C₅	1	1	yes	characteristic
191	#459	C₂²×C₅	1	1	yes	characteristic
192	#449	—	2	1	no	—
193	#446	C₂²×C₅	1	2	yes	—
194	#442	—	2	1	no	—
195	#440	—	2	1	no	—
196	#435	—	2	2	no	—
197	C₈×D₄	C₂²×C₅	1	2	yes	—
198	#432	—	2	1	no	—
199	#432	C₂²×C₅	1	1	yes	characteristic
200	#432	C₂²×C₅	1	1	yes	characteristic
201	#428	—	2	1	no	—
202	#423	C₂²×C₅	1	1	yes	characteristic
203	#417	—	2	1	no	—
204	#417	—	2	2	no	—
205	C₄×M₁₆	C₂²×C₅	1	1	yes	characteristic
206	C₂×#97	—	2	1	no	—
207	#335	C₂²×C₅	1	2	yes	—
208	#334	C₂²×C₅	1	2	yes	—
209	#333	C₂²×C₅	1	2	yes	—
210	#333	C₂²×C₅	1	2	yes	—
211	#332	C₂²×C₅	1	2	yes	—
212	#331	C₂²×C₅	1	2	yes	—
213	C₂³×C₅	—	2	1	no	—
214	C₂³×C₅	—	4	1	no	—
215	C₂³×C₅	#121	1	1	yes	characteristic
216	C₅×Q₈	—	2	1	no	—
217	C₅×Q₈	—	2	1	no	—
218	C₅×Q₈	—	4	2	no	—
219	C₅×Q₈	—	8	2	no	—
220	C₅×Q₈	—	8	2	no	—
221	C₅×D₄	—	2	1	no	—
222	C₅×D₄	—	4	2	no	—
223	C₅×D₄	—	4	1	no	—
224	C₅×D₄	—	4	1	no	—
225	C₅×D₄	—	4	2	no	—
226	C₅×D₄	—	8	1	no	—
227	C₅×D₄	—	8	2	no	—
228	C₅×D₄	#137	1	2	yes	—
229	C₂×C₄×C₅	—	2	1	no	—
230	C₂×C₄×C₅	—	2	1	no	—
231	C₂×C₄×C₅	—	2	2	no	—
232	C₂×C₄×C₅	—	2	1	no	—
233	C₂×C₄×C₅	—	2	1	no	—
234	C₂×C₄×C₅	—	2	1	no	—
235	C₂×C₄×C₅	—	4	1	no	—
236	C₂×C₄×C₅	—	4	2	no	—
237	C₂×C₄×C₅	—	4	2	no	—
238	C₂×C₄×C₅	—	4	1	no	—
239	C₂×C₄×C₅	—	4	2	no	—
240	C₂×C₄×C₅	—	8	1	no	—
241	C₂×C₄×C₅	—	8	2	no	—
242	C₂×C₄×C₅	—	8	2	no	—
243	C₂×C₄×C₅	#121	1	1	yes	characteristic
244	C₂×C₄×C₅	#121	1	1	yes	characteristic
245	C₂×C₄×C₅	#121	1	1	yes	characteristic
246	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
247	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
248	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
249	C₅×C₈	—	2	2	no	—
250	C₅×C₈	—	2	2	no	—
251	C₅×C₈	—	4	1	no	—
252	C₅×C₈	—	4	2	no	—
253	C₅×C₈	—	4	2	no	—
254	C₅×C₈	—	4	1	no	—
255	C₂×#41	—	2	1	no	—
256	C₂×#41	C₅×D₄	1	1	yes	characteristic
257	C₂²×Q₈	—	2	1	no	—
258	C₂×SD₁₆	—	2	1	no	—
259	C₂×D₈	—	2	1	no	—
260	C₂×M₁₆	—	2	1	no	—
261	C₂×M₁₆	C₅×D₄	1	2	yes	—
262	C₂²×C₈	—	2	2	no	—
263	C₄⋊Q₈	—	2	1	no	—
264	C₄⋊Q₈	—	2	1	no	—
265	C₄⋊Q₈	—	2	1	no	—
266	C₄⋊Q₈	C₂³×C₅	1	2	yes	—
267	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
268	#127	C₂³×C₅	1	1	yes	characteristic
269	#124	—	2	1	no	—
270	#121	—	2	1	no	—
271	#121	—	2	1	no	—
272	C₄×Q₈	C₅×D₄	1	1	yes	characteristic
273	C₄×Q₈	C₂³×C₅	1	1	yes	characteristic
274	C₄×D₄	—	2	1	no	—
275	C₄×D₄	—	2	1	no	—
276	C₄×D₄	—	2	1	no	—
277	C₄×D₄	—	2	1	no	—
278	C₄×D₄	C₅×D₄	1	1	yes	characteristic
279	C₄×D₄	C₂³×C₅	1	1	yes	characteristic
280	#117	—	2	1	no	—
281	#117	C₅×D₄	1	1	yes	characteristic
282	C₂×C₄⋊C₄	—	2	1	no	—
283	C₂×C₄⋊C₄	—	2	1	no	—
284	C₂×C₄²	—	2	1	no	—
285	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
286	#107	—	2	2	no	—
287	#107	—	2	1	no	—
288	#106	—	2	2	no	—
289	#106	—	2	1	no	—
290	C₄⋊C₈	—	2	2	no	—
291	C₄⋊C₈	—	2	1	no	—
292	C₄⋊C₈	C₂³×C₅	1	2	yes	—
293	C₄⋊C₈	C₂³×C₅	1	2	yes	—
294	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
295	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
296	#103	—	2	2	no	—
297	#103	—	2	1	no	—
298	#103	—	2	2	no	—
299	#103	—	2	2	no	—
300	#102	—	2	2	no	—
301	#102	—	2	1	no	—
302	#102	—	2	2	no	—
303	#102	—	2	2	no	—
304	#102	—	2	1	no	—
305	#102	—	2	1	no	—
306	C₂²⋊C₈	—	2	1	no	—
307	C₂²⋊C₈	—	2	1	no	—
308	C₂²⋊C₈	—	2	2	no	—
309	#97	—	2	2	no	—
310	#97	—	2	1	no	—
311	#97	—	2	1	no	—
312	#97	C₅×D₄	1	1	yes	characteristic
313	#97	C₅×D₄	1	1	yes	characteristic
314	C₄×C₈	C₂³×C₅	1	2	yes	—
315	C₂²×C₅	—	2	1	no	—
316	C₂²×C₅	—	2	1	no	—
317	C₂²×C₅	—	2	2	no	—
318	C₂²×C₅	—	2	1	no	—
319	C₂²×C₅	—	4	1	no	—
320	C₂²×C₅	—	4	1	no	—
321	C₂²×C₅	—	8	1	no	—
322	C₂²×C₅	—	8	1	no	—
323	C₂²×C₅	—	8	1	no	—
324	C₂²×C₅	C₂×#121	1	1	yes	characteristic
325	C₄×C₅	—	2	1	no	—
326	C₄×C₅	—	2	1	no	—
327	C₄×C₅	—	2	1	no	—
328	C₄×C₅	—	2	1	no	—
329	C₄×C₅	—	4	1	no	—
330	C₄×C₅	—	4	1	no	—
331	C₄×C₅	—	4	1	no	—
332	C₄×C₅	—	8	1	no	—
333	C₄×C₅	—	8	2	no	—
334	C₄×C₅	C₂×#137	1	1	yes	characteristic
335	C₄×C₅	#575	1	2	yes	—
336	C₄×C₅	#575	1	1	yes	characteristic
337	#41	—	2	2	no	—
338	#41	—	4	1	no	—
339	#41	—	4	4	no	—
340	C₂×Q₈	—	2	1	no	—
341	C₂×Q₈	—	2	2	no	—
342	C₂×Q₈	—	4	1	no	—
343	C₂×Q₈	—	8	2	no	—
344	C₂×Q₈	C₂×C₅×D₄	1	1	yes	characteristic
345	C₂×D₄	—	2	1	no	—
346	C₂×D₄	—	2	1	no	—
347	C₂×D₄	—	2	1	no	—
348	C₂×D₄	—	2	1	no	—
349	C₂×D₄	—	4	1	no	—
350	C₂×D₄	C₂×C₅×D₄	1	1	yes	characteristic
351	C₂²×C₄	—	2	1	no	—
352	C₂²×C₄	—	2	1	no	—
353	C₂²×C₄	—	2	1	no	—
354	C₂²×C₄	—	4	1	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	D₈	—	4	2	no	—
361	M₁₆	—	4	2	no	—
362	M₁₆	—	4	2	no	—
363	C₂×C₈	—	2	2	no	—
364	C₂×C₈	—	2	1	no	—
365	C₂×C₈	—	2	1	no	—
366	C₂×C₈	—	2	2	no	—
367	C₂×C₈	—	4	4	no	—
368	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
369	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
370	C₄⋊C₄	—	2	1	no	—
371	C₄⋊C₄	—	2	1	no	—
372	C₄⋊C₄	—	2	2	no	—
373	C₄⋊C₄	—	2	2	no	—
374	C₄⋊C₄	—	2	1	no	—
375	C₄⋊C₄	—	2	1	no	—
376	C₄⋊C₄	—	4	1	no	—
377	C₄⋊C₄	—	4	1	no	—
378	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
379	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
380	C₂²⋊C₄	—	2	1	no	—
381	C₂²⋊C₄	—	2	1	no	—
382	C₂²⋊C₄	—	2	1	no	—
383	C₂²⋊C₄	—	4	1	no	—
384	C₂²⋊C₄	—	4	1	no	—
385	C₄²	—	2	1	no	—
386	C₄²	—	2	1	no	—
387	C₄²	—	2	1	no	—
388	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
389	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
390	C₄²	C₅×#41	1	1	yes	characteristic
391	C₄²	C₂⁴×C₅	1	1	yes	characteristic
392	C₂×C₅	—	4	1	no	—
393	C₂×C₅	—	4	2	no	—
394	C₂×C₅	—	16	1	no	—
395	C₂×C₅	#3040	1	1	yes	characteristic
396	C₂×C₅	#3056	1	1	yes	characteristic
397	C₂×C₅	#3068	1	1	yes	characteristic
398	C₂³	—	2	1	no	—
399	C₂³	—	4	1	no	—
400	C₂³	C₅×#121	1	1	yes	characteristic
401	Q₈	—	2	1	no	—
402	Q₈	—	2	1	no	—
403	Q₈	—	4	2	no	—
404	Q₈	—	8	2	no	—
405	Q₈	—	8	2	no	—
406	D₄	—	2	1	no	—
407	D₄	—	4	2	no	—
408	D₄	—	4	1	no	—
409	D₄	—	4	1	no	—
410	D₄	—	4	2	no	—
411	D₄	—	8	1	no	—
412	D₄	—	8	2	no	—
413	D₄	C₅×#137	1	2	yes	—
414	C₂×C₄	—	2	1	no	—
415	C₂×C₄	—	2	1	no	—
416	C₂×C₄	—	2	2	no	—
417	C₂×C₄	—	2	1	no	—
418	C₂×C₄	—	2	1	no	—
419	C₂×C₄	—	2	1	no	—
420	C₂×C₄	—	4	1	no	—
421	C₂×C₄	—	4	2	no	—
422	C₂×C₄	—	4	2	no	—
423	C₂×C₄	—	4	1	no	—
424	C₂×C₄	—	4	2	no	—
425	C₂×C₄	—	8	1	no	—
426	C₂×C₄	—	8	2	no	—
427	C₂×C₄	—	8	2	no	—
428	C₂×C₄	C₅×#121	1	1	yes	characteristic
429	C₂×C₄	C₅×#121	1	1	yes	characteristic
430	C₂×C₄	C₅×#121	1	1	yes	characteristic
431	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
432	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
433	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
434	C₈	—	2	2	no	—
435	C₈	—	2	2	no	—
436	C₈	—	4	1	no	—
437	C₈	—	4	2	no	—
438	C₈	—	4	2	no	—
439	C₈	—	4	1	no	—
440	C₅	#19318	1	1	yes	characteristic, direct product factor, Sylow
441	C₂²	—	2	1	no	—
442	C₂²	—	2	1	no	—
443	C₂²	—	2	2	no	—
444	C₂²	—	2	1	no	—
445	C₂²	—	4	1	no	—
446	C₂²	—	4	1	no	—
447	C₂²	—	8	1	no	—
448	C₂²	—	8	1	no	—
449	C₂²	—	8	1	no	—
450	C₂²	C₂×C₅×#121	1	1	yes	characteristic
451	C₄	—	2	1	no	—
452	C₄	—	2	1	no	—
453	C₄	—	2	1	no	—
454	C₄	—	2	1	no	—
455	C₄	—	4	1	no	—
456	C₄	—	4	1	no	—
457	C₄	—	4	1	no	—
458	C₄	—	8	1	no	—
459	C₄	—	8	2	no	—
460	C₄	C₂×C₅×#137	1	1	yes	characteristic
461	C₄	C₅×#575	1	2	yes	—
462	C₄	C₅×#575	1	1	yes	characteristic
463	C₂	—	4	1	no	—
464	C₂	—	4	2	no	—
465	C₂	—	16	1	no	—
466	C₂	C₅×#3040	1	1	yes	characteristic
467	C₂	C₅×#3056	1	1	yes	characteristic
468	C₂	C₅×#3068	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×#3141	C₂	semidirect
3. C₅×#3079	C₂	semidirect
4. C₅×#2970	C₂	semidirect
5. C₅×#1704	C₂	semidirect
6. C₅×#1698	C₂	semidirect
7. C₅×#1683	C₂	semidirect
8. C₅×#1677	C₂	semidirect
9. C₅×#1569	C₂	semidirect
10. C₅×#1558	C₂	semidirect
11. C₅×#1557	C₂	semidirect
49. #19318	C₅	direct (N × H)
110. #3141	C₂×C₅	semidirect
112. #3079	C₂×C₅	semidirect
113. #2970	C₂×C₅	semidirect
114. #1704	C₂×C₅	semidirect
115. #1698	C₂×C₅	semidirect
116. #1683	C₂×C₅	semidirect
117. #1677	C₂×C₅	semidirect
118. #1569	C₂×C₅	semidirect
119. #1558	C₂×C₅	semidirect
120. #1557	C₂×C₅	semidirect
440. C₅	#19318	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×#3141	2
C₅×#3115	2
C₅×#3079	2
C₅×#2970	2
C₅×#1704	2
C₅×#1698	2
C₅×#1683	2
C₅×#1677	2
C₅×#1569	2
C₅×#1558	2
C₅×#1557	2
#19318	5

Subgroups — C5×#19318 #11942038

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#19318 #11942038