Subgroups — C₅×#24986 #11947706

Order 1280.

642 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3067	C₂	1	1	yes	maximal, characteristic
2	C₅×#2943	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#2080	C₂	1	2	yes	maximal, complemented
4	C₅×#2053	C₂	1	2	yes	maximal, complemented
5	C₅×#1976	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#1946	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#1906	C₂	1	2	yes	maximal, complemented
8	C₅×#1833	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1827	C₂	1	2	yes	maximal, complemented
10	C₅×#1812	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1765	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#575	C₂²	1	2	yes	—
13	C₂×C₅×#135	C₂²	1	1	yes	characteristic
14	C₂×C₅×#131	C₂²	1	1	yes	characteristic
15	C₄×C₅×#41	C₂²	1	2	yes	—
16	C₅×#473	—	2	1	no	—
17	C₅×#472	—	2	1	no	—
18	C₅×#471	—	2	2	no	—
19	C₅×#442	—	2	1	no	—
20	C₅×#441	—	2	1	no	—
21	C₅×#440	—	2	2	no	—
22	C₂×C₅×#108	C₂²	1	1	yes	characteristic
23	C₅×#427	C₂²	1	1	yes	characteristic
24	C₅×#427	C₂²	1	1	yes	characteristic
25	C₅×#424	C₂²	1	2	yes	—
26	C₅×#421	C₂²	1	2	yes	—
27	C₂×C₅×#104	C₂²	1	1	yes	characteristic
28	C₅×#416	C₂²	1	1	yes	characteristic
29	C₅×#416	C₂²	1	2	yes	—
30	C₅×#413	C₂²	1	2	yes	—
31	C₅×#410	C₂²	1	2	yes	—
32	C₅×#410	C₂²	1	2	yes	—
33	C₅×#405	C₂²	1	1	yes	characteristic
34	C₂×C₅×#97	C₂²	1	1	yes	characteristic
35	C₅×#344	C₂²	1	2	yes	—
36	C₅×#341	C₂²	1	1	yes	characteristic
37	C₅×#339	C₂²	1	1	yes	characteristic
38	C₅×#339	C₂²	1	2	yes	—
39	C₅×H(3,ℤ/4)	C₂²	1	2	yes	—
40	C₅×H(3,ℤ/4)	C₂²	1	2	yes	—
41	#24986	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
42	C₂×C₅×#41	C₂³	1	2	yes	—
43	C₂×C₅×#41	C₂³	1	1	yes	characteristic
44	C₅×#137	—	2	2	no	—
45	C₅×#137	—	2	2	no	—
46	C₅×AGL(1,ℤ/8)	—	2	2	no	—
47	C₅×AGL(1,ℤ/8)	—	2	2	no	—
48	C₅×#135	—	2	1	no	—
49	C₅×#135	—	2	1	no	—
50	C₅×#135	—	2	1	no	—
51	C₅×#135	—	2	1	no	—
52	C₅×#135	—	4	2	no	—
53	C₂×C₅×Q₁₆	D₄	1	1	yes	characteristic
54	C₂×C₅×SD₁₆	D₄	1	2	yes	—
55	C₂×C₅×D₈	D₄	1	1	yes	characteristic
56	C₅×#131	—	2	1	no	—
57	C₅×#131	—	2	1	no	—
58	C₅×#131	—	2	1	no	—
59	C₅×#131	—	2	1	no	—
60	C₂×C₅×M₁₆	—	2	1	no	—
61	C₂×C₅×M₁₆	C₂³	1	1	yes	characteristic
62	C₂×C₅×M₁₆	C₂³	1	1	yes	characteristic
63	C₂×C₅×M₁₆	C₂³	1	2	yes	—
64	C₂²×C₅×C₈	—	2	1	no	—
65	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
66	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
67	C₄×C₅×Q₈	—	2	2	no	—
68	C₄×C₅×D₄	—	2	2	no	—
69	C₄×C₅×D₄	—	4	2	no	—
70	C₅×#117	—	2	2	no	—
71	C₅×#117	C₂³	1	1	yes	characteristic
72	C₅×#117	C₂³	1	2	yes	—
73	C₅×#117	C₂³	1	2	yes	—
74	C₂×C₄²×C₅	—	2	2	no	—
75	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
76	C₅×#108	—	2	1	no	—
77	C₅×#108	—	2	1	no	—
78	C₅×#107	—	2	1	no	—
79	C₅×#107	—	2	1	no	—
80	C₅×#106	—	2	1	no	—
81	C₅×#106	—	2	1	no	—
82	C₅×C₄⋊C₈	—	4	2	no	—
83	C₅×#104	—	2	2	no	—
84	C₅×#104	—	4	2	no	—
85	C₅×#103	—	2	2	no	—
86	C₅×#103	—	2	1	no	—
87	C₅×#102	—	2	2	no	—
88	C₅×#102	—	2	1	no	—
89	C₅×#101	—	2	2	no	—
90	C₅×#100	—	2	2	no	—
91	C₅×#99	—	4	2	no	—
92	C₅×#99	—	4	2	no	—
93	C₅×#97	—	2	1	no	—
94	C₅×#97	—	2	1	no	—
95	C₅×#97	—	2	1	no	—
96	C₄×C₅×C₈	—	2	1	no	—
97	#3067	C₂×C₅	1	1	yes	characteristic
98	#2943	C₂×C₅	1	1	yes	characteristic, complemented
99	#2080	C₂×C₅	1	2	yes	complemented
100	#2053	C₂×C₅	1	2	yes	complemented
101	#1976	C₂×C₅	1	1	yes	characteristic, complemented
102	#1946	C₂×C₅	1	1	yes	characteristic, complemented
103	#1906	C₂×C₅	1	2	yes	complemented
104	#1833	C₂×C₅	1	1	yes	characteristic, complemented
105	#1827	C₂×C₅	1	2	yes	complemented
106	#1812	C₂×C₅	1	1	yes	characteristic, complemented
107	#1765	C₂×C₅	1	1	yes	characteristic, complemented
108	C₅×#41	—	2	1	no	—
109	C₅×#41	—	2	1	no	—
110	C₅×#41	—	2	2	no	—
111	C₅×#41	—	2	2	no	—
112	C₅×#41	—	2	2	no	—
113	C₅×#41	—	2	1	no	—
114	C₅×#41	—	2	1	no	—
115	C₅×#41	—	2	2	no	—
116	C₂×C₅×Q₈	C₂×D₄	1	2	yes	—
117	C₂×C₅×Q₈	#41	1	1	yes	characteristic
118	C₂×C₅×D₄	—	2	2	no	—
119	C₂×C₅×D₄	—	2	1	no	—
120	C₂×C₅×D₄	C₂×D₄	1	2	yes	—
121	C₂×C₅×D₄	#41	1	1	yes	characteristic
122	C₂²×C₄×C₅	—	2	1	no	—
123	C₂²×C₄×C₅	—	2	2	no	—
124	C₂²×C₄×C₅	—	2	1	no	—
125	C₂²×C₄×C₅	—	4	2	no	—
126	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
127	C₅×Q₁₆	—	2	1	no	—
128	C₅×Q₁₆	—	2	1	no	—
129	C₅×Q₁₆	—	4	2	no	—
130	C₅×SD₁₆	—	2	2	no	—
131	C₅×SD₁₆	—	2	2	no	—
132	C₅×SD₁₆	—	4	2	no	—
133	C₅×SD₁₆	—	4	2	no	—
134	C₅×D₈	—	2	1	no	—
135	C₅×D₈	—	2	1	no	—
136	C₅×D₈	—	4	2	no	—
137	C₅×M₁₆	—	2	1	no	—
138	C₅×M₁₆	—	2	2	no	—
139	C₅×M₁₆	—	2	1	no	—
140	C₅×M₁₆	—	2	2	no	—
141	C₅×M₁₆	—	2	1	no	—
142	C₅×M₁₆	—	2	1	no	—
143	C₅×M₁₆	—	4	1	no	—
144	C₅×M₁₆	—	4	1	no	—
145	C₂×C₅×C₈	—	2	1	no	—
146	C₂×C₅×C₈	—	2	1	no	—
147	C₂×C₅×C₈	—	2	1	no	—
148	C₂×C₅×C₈	—	2	1	no	—
149	C₂×C₅×C₈	—	2	1	no	—
150	C₂×C₅×C₈	—	2	2	no	—
151	C₂×C₅×C₈	—	4	1	no	—
152	C₂×C₅×C₈	—	4	1	no	—
153	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
154	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
155	C₂×C₅×C₈	#41	1	1	yes	characteristic
156	C₂×C₅×C₈	#41	1	1	yes	characteristic
157	C₂×C₅×C₈	#41	1	1	yes	characteristic
158	C₂×C₅×C₈	#41	1	1	yes	characteristic
159	C₅×C₄⋊C₄	—	2	2	no	—
160	C₅×C₄⋊C₄	—	2	1	no	—
161	C₅×C₄⋊C₄	—	2	2	no	—
162	C₅×C₄⋊C₄	—	4	2	no	—
163	C₅×C₂²⋊C₄	—	2	2	no	—
164	C₅×C₂²⋊C₄	—	2	2	no	—
165	C₅×C₂²⋊C₄	—	2	1	no	—
166	C₅×C₂²⋊C₄	—	4	2	no	—
167	C₄²×C₅	—	2	1	no	—
168	C₄²×C₅	—	2	2	no	—
169	C₄²×C₅	—	2	1	no	—
170	C₄²×C₅	—	2	2	no	—
171	C₄²×C₅	—	4	2	no	—
172	C₄²×C₅	#41	1	2	yes	—
173	#575	C₂²×C₅	1	2	yes	—
174	C₂×#135	C₂²×C₅	1	1	yes	characteristic
175	C₂×#131	C₂²×C₅	1	1	yes	characteristic
176	C₄×#41	C₂²×C₅	1	2	yes	—
177	#473	—	2	1	no	—
178	#472	—	2	1	no	—
179	#471	—	2	2	no	—
180	#442	—	2	1	no	—
181	#441	—	2	1	no	—
182	#440	—	2	2	no	—
183	C₂×#108	C₂²×C₅	1	1	yes	characteristic
184	#427	C₂²×C₅	1	1	yes	characteristic
185	#427	C₂²×C₅	1	1	yes	characteristic
186	#424	C₂²×C₅	1	2	yes	—
187	#421	C₂²×C₅	1	2	yes	—
188	C₂×#104	C₂²×C₅	1	1	yes	characteristic
189	#416	C₂²×C₅	1	1	yes	characteristic
190	#416	C₂²×C₅	1	2	yes	—
191	#413	C₂²×C₅	1	2	yes	—
192	#410	C₂²×C₅	1	2	yes	—
193	#410	C₂²×C₅	1	2	yes	—
194	#405	C₂²×C₅	1	1	yes	characteristic
195	C₂×#97	C₂²×C₅	1	1	yes	characteristic
196	#344	C₂²×C₅	1	2	yes	—
197	#341	C₂²×C₅	1	1	yes	characteristic
198	#339	C₂²×C₅	1	1	yes	characteristic
199	#339	C₂²×C₅	1	2	yes	—
200	H(3,ℤ/4)	C₂²×C₅	1	2	yes	—
201	H(3,ℤ/4)	C₂²×C₅	1	2	yes	—
202	C₂³×C₅	—	2	2	no	—
203	C₂³×C₅	—	2	1	no	—
204	C₂³×C₅	H(5,𝔽₂)	1	1	yes	characteristic
205	C₅×Q₈	—	2	2	no	—
206	C₅×Q₈	—	2	1	no	—
207	C₅×Q₈	—	2	1	no	—
208	C₅×Q₈	—	2	2	no	—
209	C₅×D₄	—	2	2	no	—
210	C₅×D₄	—	2	1	no	—
211	C₅×D₄	—	2	1	no	—
212	C₅×D₄	—	2	2	no	—
213	C₅×D₄	—	4	2	no	—
214	C₅×D₄	—	4	1	no	—
215	C₅×D₄	—	4	1	no	—
216	C₅×D₄	—	4	2	no	—
217	C₂×C₄×C₅	—	2	2	no	—
218	C₂×C₄×C₅	—	2	2	no	—
219	C₂×C₄×C₅	—	2	1	no	—
220	C₂×C₄×C₅	—	4	1	no	—
221	C₂×C₄×C₅	—	4	2	no	—
222	C₂×C₄×C₅	—	4	2	no	—
223	C₂×C₄×C₅	—	4	1	no	—
224	C₂×C₄×C₅	—	4	2	no	—
225	C₂×C₄×C₅	—	4	2	no	—
226	C₂×C₄×C₅	—	4	1	no	—
227	C₂×C₄×C₅	—	8	1	no	—
228	C₂×C₄×C₅	—	8	4	no	—
229	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
230	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
231	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
232	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
233	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
234	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
235	C₅×C₈	—	4	1	no	—
236	C₅×C₈	—	4	1	no	—
237	C₅×C₈	—	4	2	no	—
238	C₅×C₈	—	4	1	no	—
239	C₅×C₈	#123	1	1	yes	characteristic
240	C₅×C₈	#123	1	1	yes	characteristic
241	C₅×C₈	#123	1	1	yes	characteristic
242	C₅×C₈	#123	1	1	yes	characteristic
243	C₂×#41	C₂³×C₅	1	2	yes	—
244	C₂×#41	C₂³×C₅	1	1	yes	characteristic
245	#137	—	2	2	no	—
246	#137	—	2	2	no	—
247	AGL(1,ℤ/8)	—	2	2	no	—
248	AGL(1,ℤ/8)	—	2	2	no	—
249	#135	—	2	1	no	—
250	#135	—	2	1	no	—
251	#135	—	2	1	no	—
252	#135	—	2	1	no	—
253	#135	—	4	2	no	—
254	C₂×Q₁₆	C₅×D₄	1	1	yes	characteristic
255	C₂×SD₁₆	C₅×D₄	1	2	yes	—
256	C₂×D₈	C₅×D₄	1	1	yes	characteristic
257	#131	—	2	1	no	—
258	#131	—	2	1	no	—
259	#131	—	2	1	no	—
260	#131	—	2	1	no	—
261	C₂×M₁₆	—	2	1	no	—
262	C₂×M₁₆	C₂³×C₅	1	1	yes	characteristic
263	C₂×M₁₆	C₂³×C₅	1	2	yes	—
264	C₂×M₁₆	C₂³×C₅	1	1	yes	characteristic
265	C₂²×C₈	—	2	1	no	—
266	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
267	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
268	C₄×Q₈	—	2	2	no	—
269	C₄×D₄	—	2	2	no	—
270	C₄×D₄	—	4	2	no	—
271	#117	—	2	2	no	—
272	#117	C₂³×C₅	1	2	yes	—
273	#117	C₂³×C₅	1	1	yes	characteristic
274	#117	C₂³×C₅	1	2	yes	—
275	C₂×C₄²	—	2	2	no	—
276	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
277	#108	—	2	1	no	—
278	#108	—	2	1	no	—
279	#107	—	2	1	no	—
280	#107	—	2	1	no	—
281	#106	—	2	1	no	—
282	#106	—	2	1	no	—
283	C₄⋊C₈	—	4	2	no	—
284	#104	—	2	2	no	—
285	#104	—	4	2	no	—
286	#103	—	2	2	no	—
287	#103	—	2	1	no	—
288	#102	—	2	2	no	—
289	#102	—	2	1	no	—
290	#101	—	2	2	no	—
291	#100	—	2	2	no	—
292	#99	—	4	2	no	—
293	#99	—	4	2	no	—
294	#97	—	2	1	no	—
295	#97	—	2	1	no	—
296	#97	—	2	1	no	—
297	C₄×C₈	—	2	1	no	—
298	C₂²×C₅	—	4	1	no	—
299	C₂²×C₅	—	4	1	no	—
300	C₂²×C₅	—	4	2	no	—
301	C₂²×C₅	—	8	2	no	—
302	C₂²×C₅	—	8	1	no	—
303	C₂²×C₅	#540	1	1	yes	characteristic
304	C₂²×C₅	#546	1	1	yes	characteristic
305	C₂²×C₅	#553	1	1	yes	characteristic
306	C₄×C₅	—	4	2	no	—
307	C₄×C₅	—	4	2	no	—
308	C₄×C₅	—	4	1	no	—
309	C₄×C₅	—	8	2	no	—
310	C₄×C₅	—	8	1	no	—
311	C₄×C₅	—	8	2	no	—
312	C₄×C₅	C₂×#123	1	1	yes	characteristic
313	C₄×C₅	#529	1	1	yes	characteristic
314	C₄×C₅	#546	1	1	yes	characteristic
315	C₄×C₅	#555	1	1	yes	characteristic
316	#41	—	2	1	no	—
317	#41	—	2	1	no	—
318	#41	—	2	1	no	—
319	#41	—	2	2	no	—
320	#41	—	2	2	no	—
321	#41	—	2	2	no	—
322	#41	—	2	2	no	—
323	#41	—	2	1	no	—
324	C₂×Q₈	C₂×C₅×D₄	1	2	yes	—
325	C₂×Q₈	C₅×#41	1	1	yes	characteristic
326	C₂×D₄	—	2	1	no	—
327	C₂×D₄	—	2	2	no	—
328	C₂×D₄	C₂×C₅×D₄	1	2	yes	—
329	C₂×D₄	C₅×#41	1	1	yes	characteristic
330	C₂²×C₄	—	2	1	no	—
331	C₂²×C₄	—	2	2	no	—
332	C₂²×C₄	—	2	1	no	—
333	C₂²×C₄	—	4	2	no	—
334	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
335	Q₁₆	—	2	1	no	—
336	Q₁₆	—	2	1	no	—
337	Q₁₆	—	4	2	no	—
338	SD₁₆	—	2	2	no	—
339	SD₁₆	—	2	2	no	—
340	SD₁₆	—	4	2	no	—
341	SD₁₆	—	4	2	no	—
342	D₈	—	2	1	no	—
343	D₈	—	2	1	no	—
344	D₈	—	4	2	no	—
345	M₁₆	—	2	1	no	—
346	M₁₆	—	2	2	no	—
347	M₁₆	—	2	1	no	—
348	M₁₆	—	2	1	no	—
349	M₁₆	—	2	2	no	—
350	M₁₆	—	2	1	no	—
351	M₁₆	—	4	1	no	—
352	M₁₆	—	4	1	no	—
353	C₂×C₈	—	2	1	no	—
354	C₂×C₈	—	2	1	no	—
355	C₂×C₈	—	2	1	no	—
356	C₂×C₈	—	2	1	no	—
357	C₂×C₈	—	2	1	no	—
358	C₂×C₈	—	2	2	no	—
359	C₂×C₈	—	4	1	no	—
360	C₂×C₈	—	4	1	no	—
361	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
362	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
363	C₂×C₈	C₅×#41	1	1	yes	characteristic
364	C₂×C₈	C₅×#41	1	1	yes	characteristic
365	C₂×C₈	C₅×#41	1	1	yes	characteristic
366	C₂×C₈	C₅×#41	1	1	yes	characteristic
367	C₄⋊C₄	—	2	2	no	—
368	C₄⋊C₄	—	2	1	no	—
369	C₄⋊C₄	—	2	2	no	—
370	C₄⋊C₄	—	4	2	no	—
371	C₂²⋊C₄	—	2	2	no	—
372	C₂²⋊C₄	—	2	1	no	—
373	C₂²⋊C₄	—	2	2	no	—
374	C₂²⋊C₄	—	4	2	no	—
375	C₄²	—	2	1	no	—
376	C₄²	—	2	1	no	—
377	C₄²	—	2	2	no	—
378	C₄²	—	2	2	no	—
379	C₄²	—	4	2	no	—
380	C₄²	C₅×#41	1	2	yes	—
381	C₂×C₅	—	2	1	no	—
382	C₂×C₅	—	2	1	no	—
383	C₂×C₅	—	2	1	no	—
384	C₂×C₅	—	8	2	no	—
385	C₂×C₅	—	8	1	no	—
386	C₂×C₅	#2420	1	1	yes	characteristic
387	C₂³	—	2	2	no	—
388	C₂³	—	2	1	no	—
389	C₂³	C₅×H(5,𝔽₂)	1	1	yes	characteristic
390	Q₈	—	2	2	no	—
391	Q₈	—	2	1	no	—
392	Q₈	—	2	1	no	—
393	Q₈	—	2	2	no	—
394	D₄	—	2	2	no	—
395	D₄	—	2	1	no	—
396	D₄	—	2	1	no	—
397	D₄	—	2	2	no	—
398	D₄	—	4	1	no	—
399	D₄	—	4	2	no	—
400	D₄	—	4	1	no	—
401	D₄	—	4	2	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	1	no	—
405	C₂×C₄	—	4	1	no	—
406	C₂×C₄	—	4	2	no	—
407	C₂×C₄	—	4	2	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	—	8	1	no	—
413	C₂×C₄	—	8	4	no	—
414	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
415	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
416	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
417	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
418	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
419	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
420	C₈	—	4	1	no	—
421	C₈	—	4	1	no	—
422	C₈	—	4	2	no	—
423	C₈	—	4	1	no	—
424	C₈	C₅×#123	1	1	yes	characteristic
425	C₈	C₅×#123	1	1	yes	characteristic
426	C₈	C₅×#123	1	1	yes	characteristic
427	C₈	C₅×#123	1	1	yes	characteristic
428	C₅	#24986	1	1	yes	characteristic, direct product factor, Sylow
429	C₂²	—	4	1	no	—
430	C₂²	—	4	1	no	—
431	C₂²	—	4	2	no	—
432	C₂²	—	8	2	no	—
433	C₂²	—	8	1	no	—
434	C₂²	C₅×#540	1	1	yes	characteristic
435	C₂²	C₅×#546	1	1	yes	characteristic
436	C₂²	C₅×#553	1	1	yes	characteristic
437	C₄	—	4	2	no	—
438	C₄	—	4	2	no	—
439	C₄	—	4	1	no	—
440	C₄	—	8	2	no	—
441	C₄	—	8	2	no	—
442	C₄	—	8	1	no	—
443	C₄	C₂×C₅×#123	1	1	yes	characteristic
444	C₄	C₅×#529	1	1	yes	characteristic
445	C₄	C₅×#546	1	1	yes	characteristic
446	C₄	C₅×#555	1	1	yes	characteristic
447	C₂	—	2	1	no	—
448	C₂	—	2	1	no	—
449	C₂	—	2	1	no	—
450	C₂	—	8	2	no	—
451	C₂	—	8	1	no	—
452	C₂	C₅×#2420	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₅	#555
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₅
socle	C₂×C₅	#2420
prime radical	C₅×#3067	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₅ ◁ C₂²×C₄×C₅ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₅×#2943	C₂	semidirect
3. C₅×#2080	C₂	semidirect
4. C₅×#2053	C₂	semidirect
5. C₅×#1976	C₂	semidirect
6. C₅×#1946	C₂	semidirect
7. C₅×#1906	C₂	semidirect
8. C₅×#1833	C₂	semidirect
9. C₅×#1827	C₂	semidirect
10. C₅×#1812	C₂	semidirect
11. C₅×#1765	C₂	semidirect
41. #24986	C₅	direct (N × H)
98. #2943	C₂×C₅	semidirect
99. #2080	C₂×C₅	semidirect
100. #2053	C₂×C₅	semidirect
101. #1976	C₂×C₅	semidirect
102. #1946	C₂×C₅	semidirect
103. #1906	C₂×C₅	semidirect
104. #1833	C₂×C₅	semidirect
105. #1827	C₂×C₅	semidirect
106. #1812	C₂×C₅	semidirect
107. #1765	C₂×C₅	semidirect
428. C₅	#24986	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×#3067	2
C₅×#2943	2
C₅×#2080	2
C₅×#2053	2
C₅×#1976	2
C₅×#1946	2
C₅×#1906	2
C₅×#1833	2
C₅×#1827	2
C₅×#1812	2
C₅×#1765	2
#24986	5

Subgroups — C5×#24986 #11947706

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#24986 #11947706