Subgroups — C₅×#22286 #11945006

Order 1280.

820 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3155	C₂	1	1	yes	maximal, characteristic
2	C₅×#2957	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#2948	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#1978	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#1976	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#1911	C₂	1	2	yes	maximal, complemented
7	C₅×#1910	C₂	1	2	yes	maximal, complemented
8	C₅×#1904	C₂	1	2	yes	maximal, complemented
9	C₅×#1903	C₂	1	2	yes	maximal, complemented
10	C₅×#1833	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1747	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₅×AGL(1,ℤ/8)	C₂²	1	2	yes	—
13	C₂×C₅×#135	C₂²	1	1	yes	characteristic
14	C₂²×C₅×D₈	C₂²	1	1	yes	characteristic
15	C₅×#568	C₂²	1	2	yes	—
16	C₅×#535	C₂²	1	2	yes	—
17	C₅×#518	C₂²	1	2	yes	—
18	C₅×#496	C₄	1	4	yes	complemented
19	C₅×#495	C₄	1	2	yes	complemented
20	C₅×#493	C₄	1	2	yes	complemented
21	C₅×#444	—	2	2	no	—
22	C₅×#443	—	2	2	no	—
23	C₅×#442	—	2	2	no	—
24	C₄×C₅×D₈	—	2	2	no	—
25	C₂×C₅×#108	C₂²	1	1	yes	characteristic
26	C₅×#427	C₂²	1	1	yes	characteristic
27	C₅×#421	C₂²	1	2	yes	—
28	C₅×#421	C₂²	1	2	yes	—
29	C₅×#418	C₂²	1	2	yes	—
30	C₅×#418	C₂²	1	2	yes	—
31	C₂×C₅×#100	C₂²	1	2	yes	—
32	C₅×#410	C₂²	1	2	yes	—
33	C₅×#405	C₂²	1	1	yes	characteristic
34	C₅×#405	C₂²	1	1	yes	characteristic
35	C₅×#405	C₂²	1	1	yes	characteristic
36	C₅×#344	C₂²	1	2	yes	—
37	C₅×#338	C₂²	1	1	yes	characteristic
38	C₅×H(3,ℤ/4)	C₂²	1	2	yes	—
39	C₅×H(3,ℤ/4)	C₂²	1	1	yes	characteristic
40	C₅×H(3,ℤ/4)	C₂²	1	1	yes	characteristic
41	C₅×H(3,ℤ/4)	C₂²	1	1	yes	characteristic
42	#22286	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
43	C₂×C₅×#41	C₂³	1	2	yes	—
44	C₂²×C₅×D₄	C₂³	1	2	yes	—
45	C₅×AGL(1,ℤ/8)	—	4	2	no	—
46	C₅×AGL(1,ℤ/8)	—	4	2	no	—
47	C₅×#135	—	2	1	no	—
48	C₅×#135	—	2	1	no	—
49	C₅×#135	—	2	1	no	—
50	C₅×#135	—	2	1	no	—
51	C₂×C₅×Q₁₆	C₂×C₄	1	1	yes	characteristic, complemented
52	C₂×C₅×SD₁₆	C₂×C₄	1	2	yes	complemented
53	C₂×C₅×SD₁₆	C₂×C₄	1	4	yes	complemented
54	C₂×C₅×D₈	—	2	1	no	—
55	C₂×C₅×D₈	—	2	1	no	—
56	C₂×C₅×D₈	—	2	1	no	—
57	C₂×C₅×D₈	—	2	1	no	—
58	C₂×C₅×D₈	C₂×C₄	1	2	yes	—
59	C₂×C₅×D₈	C₂×C₄	1	2	yes	—
60	C₂×C₅×D₈	C₂×C₄	1	1	yes	characteristic, complemented
61	C₂×C₅×D₈	C₂×C₄	1	4	yes	complemented
62	C₅×#131	—	2	4	no	—
63	C₅×#131	—	4	2	no	—
64	C₂×C₅×M₁₆	—	4	2	no	—
65	C₂×C₅×M₁₆	C₂³	1	1	yes	characteristic
66	C₂×C₅×M₁₆	C₂³	1	2	yes	—
67	C₂×C₅×M₁₆	C₂³	1	1	yes	characteristic
68	C₂×C₅×M₁₆	C₂³	1	1	yes	characteristic
69	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
70	C₅×#127	C₂×C₄	1	4	yes	complemented
71	C₅×#124	C₂×C₄	1	4	yes	complemented
72	C₅×#121	—	4	2	no	—
73	C₅×#120	—	4	2	no	—
74	C₄×C₅×D₄	—	2	4	no	—
75	C₄×C₅×D₄	—	4	2	no	—
76	C₅×#117	C₂³	1	1	yes	characteristic
77	C₅×#117	C₂³	1	2	yes	—
78	C₅×#117	C₂³	1	1	yes	characteristic
79	C₅×#117	C₂³	1	1	yes	characteristic
80	C₂×C₅×C₂²⋊C₄	—	4	2	no	—
81	C₅×#108	—	2	1	no	—
82	C₅×#108	—	2	1	no	—
83	C₅×#107	—	2	1	no	—
84	C₅×#106	—	2	1	no	—
85	C₅×#104	—	2	4	no	—
86	C₅×#104	—	4	2	no	—
87	C₅×#102	—	2	4	no	—
88	C₅×#102	—	4	2	no	—
89	C₅×#100	—	4	2	no	—
90	C₅×#99	—	4	2	no	—
91	C₅×#97	—	2	1	no	—
92	C₅×#97	C₂×C₄	1	2	yes	complemented
93	C₅×#97	D₄	1	2	yes	complemented
94	C₄×C₅×C₈	—	2	1	no	—
95	C₄×C₅×C₈	C₂×C₄	1	2	yes	complemented
96	C₄×C₅×C₈	D₄	1	2	yes	complemented
97	#3155	C₂×C₅	1	1	yes	characteristic
98	#2957	C₂×C₅	1	1	yes	characteristic, complemented
99	#2948	C₂×C₅	1	1	yes	characteristic, complemented
100	#1978	C₂×C₅	1	1	yes	characteristic, complemented
101	#1976	C₂×C₅	1	1	yes	characteristic, complemented
102	#1911	C₂×C₅	1	2	yes	complemented
103	#1910	C₂×C₅	1	2	yes	complemented
104	#1904	C₂×C₅	1	2	yes	complemented
105	#1903	C₂×C₅	1	2	yes	complemented
106	#1833	C₂×C₅	1	1	yes	characteristic, complemented
107	#1747	C₂×C₅	1	1	yes	characteristic, complemented
108	C₂⁴×C₅	—	2	2	no	—
109	C₅×#41	—	2	2	no	—
110	C₅×#41	—	2	2	no	—
111	C₅×#41	—	2	2	no	—
112	C₅×#41	—	2	2	no	—
113	C₂×C₅×Q₈	C₂²×C₄	1	2	yes	—
114	C₂×C₅×D₄	—	2	2	no	—
115	C₂×C₅×D₄	—	2	2	no	—
116	C₂×C₅×D₄	—	2	2	no	—
117	C₂×C₅×D₄	—	2	2	no	—
118	C₂×C₅×D₄	—	2	2	no	—
119	C₂×C₅×D₄	—	2	2	no	—
120	C₂×C₅×D₄	—	4	4	no	—
121	C₂×C₅×D₄	C₂²×C₄	1	4	yes	—
122	C₂×C₅×D₄	C₂²×C₄	1	2	yes	—
123	C₂²×C₄×C₅	—	2	2	no	—
124	C₂²×C₄×C₅	—	4	4	no	—
125	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
126	C₅×Q₁₆	—	2	1	no	—
127	C₅×Q₁₆	—	2	1	no	—
128	C₅×SD₁₆	—	2	2	no	—
129	C₅×SD₁₆	—	2	2	no	—
130	C₅×SD₁₆	—	4	4	no	—
131	C₅×D₈	—	2	2	no	—
132	C₅×D₈	—	2	2	no	—
133	C₅×D₈	—	2	2	no	—
134	C₅×D₈	—	2	2	no	—
135	C₅×D₈	—	2	1	no	—
136	C₅×D₈	—	2	1	no	—
137	C₅×D₈	—	4	4	no	—
138	C₅×M₁₆	—	2	1	no	—
139	C₅×M₁₆	—	2	1	no	—
140	C₅×M₁₆	—	2	1	no	—
141	C₅×M₁₆	—	2	1	no	—
142	C₅×M₁₆	—	2	2	no	—
143	C₅×M₁₆	—	2	2	no	—
144	C₅×M₁₆	—	2	1	no	—
145	C₅×M₁₆	—	2	1	no	—
146	C₅×M₁₆	—	4	4	no	—
147	C₂×C₅×C₈	—	2	1	no	—
148	C₂×C₅×C₈	—	2	2	no	—
149	C₂×C₅×C₈	—	4	4	no	—
150	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
151	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
152	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
153	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
154	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
155	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
156	C₂×C₅×C₈	#41	1	1	yes	characteristic
157	C₂×C₅×C₈	#41	1	1	yes	characteristic
158	C₅×C₄⋊C₄	—	2	1	no	—
159	C₅×C₄⋊C₄	—	2	1	no	—
160	C₅×C₄⋊C₄	—	2	2	no	—
161	C₅×C₄⋊C₄	—	2	1	no	—
162	C₅×C₂²⋊C₄	—	2	1	no	—
163	C₅×C₂²⋊C₄	—	2	1	no	—
164	C₅×C₂²⋊C₄	—	2	2	no	—
165	C₅×C₂²⋊C₄	—	2	1	no	—
166	C₅×C₂²⋊C₄	—	4	4	no	—
167	C₅×C₂²⋊C₄	—	4	4	no	—
168	C₄²×C₅	—	2	1	no	—
169	C₄²×C₅	—	2	2	no	—
170	C₄²×C₅	C₂²×C₄	1	2	yes	—
171	C₄²×C₅	C₂×D₄	1	2	yes	—
172	C₂×AGL(1,ℤ/8)	C₂²×C₅	1	2	yes	—
173	C₂×#135	C₂²×C₅	1	1	yes	characteristic
174	C₂²×D₈	C₂²×C₅	1	1	yes	characteristic
175	#568	C₂²×C₅	1	2	yes	—
176	#535	C₂²×C₅	1	2	yes	—
177	#518	C₂²×C₅	1	2	yes	—
178	#496	C₄×C₅	1	4	yes	complemented
179	#495	C₄×C₅	1	2	yes	complemented
180	#493	C₄×C₅	1	2	yes	complemented
181	#444	—	2	2	no	—
182	#443	—	2	2	no	—
183	#442	—	2	2	no	—
184	C₄×D₈	—	2	2	no	—
185	C₂×#108	C₂²×C₅	1	1	yes	characteristic
186	#427	C₂²×C₅	1	1	yes	characteristic
187	#421	C₂²×C₅	1	2	yes	—
188	#421	C₂²×C₅	1	2	yes	—
189	#418	C₂²×C₅	1	2	yes	—
190	#418	C₂²×C₅	1	2	yes	—
191	C₂×#100	C₂²×C₅	1	2	yes	—
192	#410	C₂²×C₅	1	2	yes	—
193	#405	C₂²×C₅	1	1	yes	characteristic
194	#405	C₂²×C₅	1	1	yes	characteristic
195	#405	C₂²×C₅	1	1	yes	characteristic
196	#344	C₂²×C₅	1	2	yes	—
197	#338	C₂²×C₅	1	1	yes	characteristic
198	H(3,ℤ/4)	C₂²×C₅	1	2	yes	—
199	H(3,ℤ/4)	C₂²×C₅	1	1	yes	characteristic
200	H(3,ℤ/4)	C₂²×C₅	1	1	yes	characteristic
201	H(3,ℤ/4)	C₂²×C₅	1	1	yes	characteristic
202	C₂³×C₅	—	2	4	no	—
203	C₂³×C₅	—	2	2	no	—
204	C₂³×C₅	—	4	2	no	—
205	C₂³×C₅	—	4	2	no	—
206	C₂³×C₅	—	16	2	no	—
207	C₂³×C₅	H(5,𝔽₂)	1	1	yes	characteristic
208	C₅×Q₈	—	2	2	no	—
209	C₅×Q₈	—	2	2	no	—
210	C₅×D₄	—	2	4	no	—
211	C₅×D₄	—	2	2	no	—
212	C₅×D₄	—	2	2	no	—
213	C₅×D₄	—	2	4	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	—	16	4	no	—
219	C₂×C₄×C₅	—	2	2	no	—
220	C₂×C₄×C₅	—	2	2	no	—
221	C₂×C₄×C₅	—	2	2	no	—
222	C₂×C₄×C₅	—	4	2	no	—
223	C₂×C₄×C₅	—	4	2	no	—
224	C₂×C₄×C₅	—	4	2	no	—
225	C₂×C₄×C₅	—	4	1	no	—
226	C₂×C₄×C₅	—	16	4	no	—
227	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
228	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
229	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
230	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
231	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
232	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
233	C₅×C₈	—	2	2	no	—
234	C₅×C₈	—	2	2	no	—
235	C₅×C₈	—	4	2	no	—
236	C₅×C₈	—	4	1	no	—
237	C₅×C₈	C₄×D₄	1	1	yes	characteristic
238	C₅×C₈	C₄×D₄	1	1	yes	characteristic
239	C₅×C₈	C₄×D₄	1	1	yes	characteristic
240	C₅×C₈	C₄×D₄	1	1	yes	characteristic
241	C₂×#41	C₂³×C₅	1	2	yes	—
242	C₂²×D₄	C₂³×C₅	1	2	yes	—
243	AGL(1,ℤ/8)	—	4	2	no	—
244	AGL(1,ℤ/8)	—	4	2	no	—
245	#135	—	2	1	no	—
246	#135	—	2	1	no	—
247	#135	—	2	1	no	—
248	#135	—	2	1	no	—
249	C₂×Q₁₆	C₂×C₄×C₅	1	1	yes	characteristic, complemented
250	C₂×SD₁₆	C₂×C₄×C₅	1	2	yes	complemented
251	C₂×SD₁₆	C₂×C₄×C₅	1	4	yes	complemented
252	C₂×D₈	—	2	1	no	—
253	C₂×D₈	—	2	1	no	—
254	C₂×D₈	—	2	1	no	—
255	C₂×D₈	—	2	1	no	—
256	C₂×D₈	C₂×C₄×C₅	1	2	yes	—
257	C₂×D₈	C₂×C₄×C₅	1	2	yes	—
258	C₂×D₈	C₂×C₄×C₅	1	1	yes	characteristic, complemented
259	C₂×D₈	C₂×C₄×C₅	1	4	yes	complemented
260	#131	—	2	4	no	—
261	#131	—	4	2	no	—
262	C₂×M₁₆	—	4	2	no	—
263	C₂×M₁₆	C₂³×C₅	1	2	yes	—
264	C₂×M₁₆	C₂³×C₅	1	1	yes	characteristic
265	C₂×M₁₆	C₂³×C₅	1	1	yes	characteristic
266	C₂×M₁₆	C₂³×C₅	1	1	yes	characteristic
267	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
268	#127	C₂×C₄×C₅	1	4	yes	complemented
269	#124	C₂×C₄×C₅	1	4	yes	complemented
270	#121	—	4	2	no	—
271	#120	—	4	2	no	—
272	C₄×D₄	—	2	4	no	—
273	C₄×D₄	—	4	2	no	—
274	#117	C₂³×C₅	1	2	yes	—
275	#117	C₂³×C₅	1	1	yes	characteristic
276	#117	C₂³×C₅	1	1	yes	characteristic
277	#117	C₂³×C₅	1	1	yes	characteristic
278	C₂×C₂²⋊C₄	—	4	2	no	—
279	#108	—	2	1	no	—
280	#108	—	2	1	no	—
281	#107	—	2	1	no	—
282	#106	—	2	1	no	—
283	#104	—	2	4	no	—
284	#104	—	4	2	no	—
285	#102	—	2	4	no	—
286	#102	—	4	2	no	—
287	#100	—	4	2	no	—
288	#99	—	4	2	no	—
289	#97	—	2	1	no	—
290	#97	C₂×C₄×C₅	1	2	yes	complemented
291	#97	C₅×D₄	1	2	yes	complemented
292	C₄×C₈	—	2	1	no	—
293	C₄×C₈	C₂×C₄×C₅	1	2	yes	complemented
294	C₄×C₈	C₅×D₄	1	2	yes	complemented
295	C₂²×C₅	—	4	1	no	—
296	C₂²×C₅	—	4	2	no	—
297	C₂²×C₅	—	4	4	no	—
298	C₂²×C₅	—	8	2	no	—
299	C₂²×C₅	—	8	4	no	—
300	C₂²×C₅	—	8	4	no	—
301	C₂²×C₅	—	16	2	no	—
302	C₂²×C₅	#518	1	1	yes	characteristic
303	C₂²×C₅	#535	1	1	yes	characteristic
304	C₂²×C₅	#540	1	1	yes	characteristic
305	C₄×C₅	—	4	2	no	—
306	C₄×C₅	—	4	2	no	—
307	C₄×C₅	—	4	2	no	—
308	C₄×C₅	—	8	1	no	—
309	C₄×C₅	—	8	2	no	—
310	C₄×C₅	C₂×C₄×D₄	1	1	yes	characteristic
311	C₄×C₅	#518	1	1	yes	characteristic
312	C₄×C₅	#535	1	1	yes	characteristic
313	C₄×C₅	#540	1	1	yes	characteristic
314	C₂⁴	—	2	2	no	—
315	#41	—	2	2	no	—
316	#41	—	2	2	no	—
317	#41	—	2	2	no	—
318	#41	—	2	2	no	—
319	C₂×Q₈	C₂²×C₄×C₅	1	2	yes	—
320	C₂×D₄	—	2	2	no	—
321	C₂×D₄	—	2	2	no	—
322	C₂×D₄	—	2	2	no	—
323	C₂×D₄	—	2	2	no	—
324	C₂×D₄	—	2	2	no	—
325	C₂×D₄	—	2	2	no	—
326	C₂×D₄	—	4	4	no	—
327	C₂×D₄	C₂²×C₄×C₅	1	4	yes	—
328	C₂×D₄	C₂²×C₄×C₅	1	2	yes	—
329	C₂²×C₄	—	2	2	no	—
330	C₂²×C₄	—	4	4	no	—
331	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
332	Q₁₆	—	2	1	no	—
333	Q₁₆	—	2	1	no	—
334	SD₁₆	—	2	2	no	—
335	SD₁₆	—	2	2	no	—
336	SD₁₆	—	4	4	no	—
337	D₈	—	2	2	no	—
338	D₈	—	2	2	no	—
339	D₈	—	2	2	no	—
340	D₈	—	2	2	no	—
341	D₈	—	2	1	no	—
342	D₈	—	2	1	no	—
343	D₈	—	4	4	no	—
344	M₁₆	—	2	1	no	—
345	M₁₆	—	2	1	no	—
346	M₁₆	—	2	1	no	—
347	M₁₆	—	2	1	no	—
348	M₁₆	—	2	2	no	—
349	M₁₆	—	2	1	no	—
350	M₁₆	—	2	2	no	—
351	M₁₆	—	2	1	no	—
352	M₁₆	—	4	4	no	—
353	C₂×C₈	—	2	1	no	—
354	C₂×C₈	—	2	2	no	—
355	C₂×C₈	—	4	4	no	—
356	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
357	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
358	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
359	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
360	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
361	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
362	C₂×C₈	C₅×#41	1	1	yes	characteristic
363	C₂×C₈	C₅×#41	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	1	no	—
368	C₂²⋊C₄	—	2	1	no	—
369	C₂²⋊C₄	—	2	1	no	—
370	C₂²⋊C₄	—	2	1	no	—
371	C₂²⋊C₄	—	2	2	no	—
372	C₂²⋊C₄	—	4	4	no	—
373	C₂²⋊C₄	—	4	4	no	—
374	C₄²	—	2	1	no	—
375	C₄²	—	2	2	no	—
376	C₄²	C₂²×C₄×C₅	1	2	yes	—
377	C₄²	C₂×C₅×D₄	1	2	yes	—
378	C₂×C₅	—	2	1	no	—
379	C₂×C₅	—	2	1	no	—
380	C₂×C₅	—	2	1	no	—
381	C₂×C₅	—	8	2	no	—
382	C₂×C₅	—	8	4	no	—
383	C₂×C₅	#2328	1	1	yes	characteristic
384	C₂³	—	2	4	no	—
385	C₂³	—	2	2	no	—
386	C₂³	—	4	2	no	—
387	C₂³	—	4	2	no	—
388	C₂³	—	16	2	no	—
389	C₂³	C₅×H(5,𝔽₂)	1	1	yes	characteristic
390	Q₈	—	2	2	no	—
391	Q₈	—	2	2	no	—
392	D₄	—	2	4	no	—
393	D₄	—	2	2	no	—
394	D₄	—	2	2	no	—
395	D₄	—	2	4	no	—
396	D₄	—	4	2	no	—
397	D₄	—	4	2	no	—
398	D₄	—	4	2	no	—
399	D₄	—	4	2	no	—
400	D₄	—	16	4	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	4	2	no	—
405	C₂×C₄	—	4	2	no	—
406	C₂×C₄	—	4	2	no	—
407	C₂×C₄	—	4	1	no	—
408	C₂×C₄	—	16	4	no	—
409	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
410	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
411	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
412	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
413	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
414	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
415	C₈	—	2	2	no	—
416	C₈	—	2	2	no	—
417	C₈	—	4	2	no	—
418	C₈	—	4	1	no	—
419	C₈	C₄×C₅×D₄	1	1	yes	characteristic
420	C₈	C₄×C₅×D₄	1	1	yes	characteristic
421	C₈	C₄×C₅×D₄	1	1	yes	characteristic
422	C₈	C₄×C₅×D₄	1	1	yes	characteristic
423	C₅	#22286	1	1	yes	characteristic, direct product factor, Sylow
424	C₂²	—	4	1	no	—
425	C₂²	—	4	2	no	—
426	C₂²	—	4	4	no	—
427	C₂²	—	8	2	no	—
428	C₂²	—	8	4	no	—
429	C₂²	—	8	4	no	—
430	C₂²	—	16	2	no	—
431	C₂²	C₅×#518	1	1	yes	characteristic
432	C₂²	C₅×#535	1	1	yes	characteristic
433	C₂²	C₅×#540	1	1	yes	characteristic
434	C₄	—	4	2	no	—
435	C₄	—	4	2	no	—
436	C₄	—	4	2	no	—
437	C₄	—	8	2	no	—
438	C₄	—	8	1	no	—
439	C₄	C₂×C₄×C₅×D₄	1	1	yes	characteristic
440	C₄	C₅×#518	1	1	yes	characteristic
441	C₄	C₅×#535	1	1	yes	characteristic
442	C₄	C₅×#540	1	1	yes	characteristic
443	C₂	—	2	1	no	—
444	C₂	—	2	1	no	—
445	C₂	—	2	1	no	—
446	C₂	—	8	4	no	—
447	C₂	—	8	2	no	—
448	C₂	C₅×#2328	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₅	#2328
commutator	C₂×C₄	C₂³×C₄×C₅
Frattini, cosocle	C₂²×C₄	C₂⁴×C₅
prime radical	C₅×#3155	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₅ ◁ C₂²×C₄×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₅×#2957	C₂	semidirect
3. C₅×#2948	C₂	semidirect
4. C₅×#1978	C₂	semidirect
5. C₅×#1976	C₂	semidirect
6. C₅×#1911	C₂	semidirect
7. C₅×#1910	C₂	semidirect
8. C₅×#1904	C₂	semidirect
9. C₅×#1903	C₂	semidirect
10. C₅×#1833	C₂	semidirect
11. C₅×#1747	C₂	semidirect
18. C₅×#496	C₄	semidirect
19. C₅×#495	C₄	semidirect
20. C₅×#493	C₄	semidirect
42. #22286	C₅	direct (N × H)
51. C₂×C₅×Q₁₆	C₂×C₄	semidirect
52. C₂×C₅×SD₁₆	C₂×C₄	semidirect
53. C₂×C₅×SD₁₆	C₂×C₄	semidirect
60. C₂×C₅×D₈	C₂×C₄	semidirect
61. C₂×C₅×D₈	C₂×C₄	semidirect
70. C₅×#127	C₂×C₄	semidirect
71. C₅×#124	C₂×C₄	semidirect
92. C₅×#97	C₂×C₄	semidirect
93. C₅×#97	D₄	semidirect
95. C₄×C₅×C₈	C₂×C₄	semidirect
96. C₄×C₅×C₈	D₄	semidirect
98. #2957	C₂×C₅	semidirect
99. #2948	C₂×C₅	semidirect
100. #1978	C₂×C₅	semidirect
101. #1976	C₂×C₅	semidirect
102. #1911	C₂×C₅	semidirect
103. #1910	C₂×C₅	semidirect
104. #1904	C₂×C₅	semidirect
105. #1903	C₂×C₅	semidirect
106. #1833	C₂×C₅	semidirect
107. #1747	C₂×C₅	semidirect
178. #496	C₄×C₅	semidirect
179. #495	C₄×C₅	semidirect
180. #493	C₄×C₅	semidirect
249. C₂×Q₁₆	C₂×C₄×C₅	semidirect
250. C₂×SD₁₆	C₂×C₄×C₅	semidirect
251. C₂×SD₁₆	C₂×C₄×C₅	semidirect
258. C₂×D₈	C₂×C₄×C₅	semidirect
259. C₂×D₈	C₂×C₄×C₅	semidirect
268. #127	C₂×C₄×C₅	semidirect
269. #124	C₂×C₄×C₅	semidirect
290. #97	C₂×C₄×C₅	semidirect
291. #97	C₅×D₄	semidirect
293. C₄×C₈	C₂×C₄×C₅	semidirect
294. C₄×C₈	C₅×D₄	semidirect
423. C₅	#22286	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×#3155	2
C₅×#2957	2
C₅×#2948	2
C₅×#1978	2
C₅×#1976	2
C₅×#1911	2
C₅×#1910	2
C₅×#1904	2
C₅×#1903	2
C₅×#1833	2
C₅×#1747	2
#22286	5

Subgroups — C5×#22286 #11945006

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#22286 #11945006