Subgroups — C₅×#21140 #11943860

Order 1280.

764 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₅×#135	C₂	1	1	yes	maximal, characteristic
2	C₅×#2923	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#2875	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#1929	C₂	1	2	yes	maximal, complemented
5	C₅×#1922	C₂	1	2	yes	maximal, complemented
6	C₅×#1876	C₂	1	2	yes	maximal
7	C₅×#1866	C₂	1	2	yes	maximal, complemented
8	C₄×C₅×#108	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1759	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1759	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1746	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₅×#135	C₂²	1	1	yes	characteristic
13	C₂×C₅×#131	C₂²	1	2	yes	—
14	C₄×C₅×#41	C₂²	1	1	yes	characteristic
15	C₄×C₅×#41	C₂²	1	1	yes	characteristic
16	C₄×C₅×Q₁₆	C₄	1	2	yes	complemented
17	C₄×C₅×SD₁₆	C₄	1	2	yes	complemented
18	C₄×C₅×SD₁₆	C₄	1	2	yes	complemented
19	C₄×C₅×D₈	C₄	1	2	yes	complemented
20	C₅×#433	—	2	2	no	—
21	C₅×#432	—	2	1	no	—
22	C₅×#432	—	2	1	no	—
23	C₂×C₅×#108	C₂²	1	2	yes	—
24	C₅×#427	C₂²	1	1	yes	characteristic
25	C₅×#424	C₂²	1	2	yes	—
26	C₂×C₅×#104	C₂²	1	2	yes	—
27	C₂×C₅×#104	C₂²	1	2	yes	—
28	C₅×#416	C₂²	1	1	yes	characteristic
29	C₅×#416	C₂²	1	1	yes	characteristic
30	C₅×#408	C₂²	1	2	yes	—
31	C₅×#405	—	2	2	no	—
32	C₅×#405	C₂²	1	2	yes	—
33	C₄×C₅×M₁₆	—	2	1	no	—
34	C₄×C₅×M₁₆	C₂²	1	1	yes	characteristic
35	C₄×C₅×M₁₆	C₂²	1	1	yes	characteristic
36	C₂×C₅×#97	—	2	1	no	—
37	C₂×C₅×#97	C₂²	1	1	yes	characteristic
38	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
39	C₅×#376	C₂²	1	1	yes	characteristic
40	C₅×#341	C₂²	1	2	yes	—
41	C₅×#339	C₂²	1	2	yes	—
42	C₅×#339	C₂²	1	2	yes	—
43	C₅×#336	C₂²	1	2	yes	—
44	C₅×#336	C₂²	1	2	yes	—
45	#21140	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
46	C₂×C₅×#41	C₂³	1	1	yes	characteristic
47	C₂×C₅×#41	C₂³	1	1	yes	characteristic
48	C₅×#135	—	2	4	no	—
49	C₂×C₅×Q₁₆	C₂×C₄	1	1	yes	characteristic
50	C₂×C₅×SD₁₆	C₂×C₄	1	1	yes	characteristic
51	C₂×C₅×SD₁₆	C₂×C₄	1	1	yes	characteristic
52	C₂×C₅×D₈	C₂×C₄	1	1	yes	characteristic
53	C₅×#131	—	2	4	no	—
54	C₅×#131	—	2	4	no	—
55	C₂×C₅×M₁₆	—	2	2	no	—
56	C₂×C₅×M₁₆	C₂³	1	2	yes	—
57	C₂×C₅×M₁₆	C₂³	1	2	yes	—
58	C₂²×C₅×C₈	—	2	2	no	—
59	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
60	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
61	C₂²×C₅×C₈	C₂³	1	2	yes	—
62	C₄×C₅×Q₈	C₂×C₄	1	2	yes	—
63	C₄×C₅×Q₈	C₂×C₄	1	2	yes	—
64	C₄×C₅×D₄	—	2	2	no	—
65	C₄×C₅×D₄	—	2	2	no	—
66	C₄×C₅×D₄	C₂×C₄	1	2	yes	—
67	C₄×C₅×D₄	C₂×C₄	1	2	yes	—
68	C₅×#117	—	2	1	no	—
69	C₅×#117	—	2	1	no	—
70	C₅×#117	C₂³	1	1	yes	characteristic
71	C₅×#117	C₂³	1	1	yes	characteristic
72	C₂×C₄²×C₅	—	2	1	no	—
73	C₂×C₄²×C₅	—	2	1	no	—
74	C₂×C₄²×C₅	C₂³	1	2	yes	—
75	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
76	C₅×#108	—	2	4	no	—
77	C₅×#107	C₂×C₄	1	2	yes	—
78	C₅×#106	C₂×C₄	1	2	yes	—
79	C₅×C₄⋊C₈	—	2	2	no	—
80	C₅×C₄⋊C₈	—	2	2	no	—
81	C₅×#104	—	2	4	no	—
82	C₅×#104	—	2	4	no	—
83	C₅×#103	C₂×C₄	1	2	yes	—
84	C₅×#103	C₂×C₄	1	2	yes	—
85	C₅×#102	C₂×C₄	1	2	yes	—
86	C₅×#102	C₂×C₄	1	2	yes	—
87	C₅×C₂²⋊C₈	—	2	2	no	—
88	C₅×C₂²⋊C₈	—	2	2	no	—
89	C₅×#97	—	2	2	no	—
90	C₅×#97	—	2	1	no	—
91	C₅×#97	—	2	1	no	—
92	C₅×#97	D₄	1	1	yes	characteristic
93	C₅×#97	D₄	1	1	yes	characteristic
94	C₅×#97	D₄	1	2	yes	—
95	C₄×C₅×C₈	—	2	2	no	—
96	C₄×C₅×C₈	—	2	1	no	—
97	C₄×C₅×C₈	—	2	1	no	—
98	C₄×C₅×C₈	C₂×C₄	1	2	yes	—
99	C₄×C₅×C₈	C₂×C₄	1	2	yes	—
100	C₅×#95	—	2	2	no	—
101	C₄×#135	C₂×C₅	1	1	yes	characteristic
102	#2923	C₂×C₅	1	1	yes	characteristic, complemented
103	#2875	C₂×C₅	1	1	yes	characteristic, complemented
104	#1929	C₂×C₅	1	2	yes	complemented
105	#1922	C₂×C₅	1	2	yes	complemented
106	#1876	C₂×C₅	1	2	yes	—
107	#1866	C₂×C₅	1	2	yes	complemented
108	C₄×#108	C₂×C₅	1	1	yes	characteristic, complemented
109	#1759	C₂×C₅	1	1	yes	characteristic, complemented
110	#1759	C₂×C₅	1	1	yes	characteristic, complemented
111	#1746	C₂×C₅	1	1	yes	characteristic, complemented
112	C₅×#41	—	2	2	no	—
113	C₅×#41	—	2	2	no	—
114	C₅×#41	—	2	2	no	—
115	C₅×#41	#41	1	4	yes	—
116	C₂×C₅×Q₈	C₂²×C₄	1	1	yes	characteristic
117	C₂×C₅×Q₈	C₂²×C₄	1	1	yes	characteristic
118	C₂×C₅×D₄	—	2	1	no	—
119	C₂×C₅×D₄	—	2	1	no	—
120	C₂×C₅×D₄	C₂²×C₄	1	1	yes	characteristic
121	C₂×C₅×D₄	C₂²×C₄	1	1	yes	characteristic
122	C₂²×C₄×C₅	—	2	1	no	—
123	C₂²×C₄×C₅	—	2	1	no	—
124	C₂²×C₄×C₅	—	2	2	no	—
125	C₂²×C₄×C₅	—	2	2	no	—
126	C₂²×C₄×C₅	—	2	2	no	—
127	C₂²×C₄×C₅	#41	1	2	yes	—
128	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
129	C₅×Q₁₆	—	2	2	no	—
130	C₅×SD₁₆	—	2	2	no	—
131	C₅×SD₁₆	—	2	2	no	—
132	C₅×D₈	—	2	2	no	—
133	C₅×M₁₆	—	2	8	no	—
134	C₅×M₁₆	—	2	2	no	—
135	C₅×M₁₆	—	2	2	no	—
136	C₅×M₁₆	—	2	2	no	—
137	C₅×M₁₆	#41	1	4	yes	—
138	C₂×C₅×C₈	—	2	8	no	—
139	C₂×C₅×C₈	—	2	2	no	—
140	C₂×C₅×C₈	—	2	2	no	—
141	C₂×C₅×C₈	—	2	2	no	—
142	C₂×C₅×C₈	—	2	2	no	—
143	C₂×C₅×C₈	—	2	2	no	—
144	C₂×C₅×C₈	—	2	2	no	—
145	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
146	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
147	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
148	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
149	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
150	C₅×C₄⋊C₄	—	2	2	no	—
151	C₅×C₄⋊C₄	—	2	2	no	—
152	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
153	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
154	C₅×C₂²⋊C₄	—	2	1	no	—
155	C₅×C₂²⋊C₄	—	2	1	no	—
156	C₅×C₂²⋊C₄	—	2	2	no	—
157	C₅×C₂²⋊C₄	—	2	2	no	—
158	C₄²×C₅	—	2	2	no	—
159	C₄²×C₅	—	2	2	no	—
160	C₄²×C₅	—	2	1	no	—
161	C₄²×C₅	—	2	1	no	—
162	C₄²×C₅	—	2	2	no	—
163	C₄²×C₅	—	2	2	no	—
164	C₄²×C₅	C₂²×C₄	1	2	yes	—
165	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
166	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
167	C₂×#135	C₂²×C₅	1	1	yes	characteristic
168	C₂×#131	C₂²×C₅	1	2	yes	—
169	C₄×#41	C₂²×C₅	1	1	yes	characteristic
170	C₄×#41	C₂²×C₅	1	1	yes	characteristic
171	C₄×Q₁₆	C₄×C₅	1	2	yes	complemented
172	C₄×SD₁₆	C₄×C₅	1	2	yes	complemented
173	C₄×SD₁₆	C₄×C₅	1	2	yes	complemented
174	C₄×D₈	C₄×C₅	1	2	yes	complemented
175	#433	—	2	2	no	—
176	#432	—	2	1	no	—
177	#432	—	2	1	no	—
178	C₂×#108	C₂²×C₅	1	2	yes	—
179	#427	C₂²×C₅	1	1	yes	characteristic
180	#424	C₂²×C₅	1	2	yes	—
181	C₂×#104	C₂²×C₅	1	2	yes	—
182	C₂×#104	C₂²×C₅	1	2	yes	—
183	#416	C₂²×C₅	1	1	yes	characteristic
184	#416	C₂²×C₅	1	1	yes	characteristic
185	#408	C₂²×C₅	1	2	yes	—
186	#405	—	2	2	no	—
187	#405	C₂²×C₅	1	2	yes	—
188	C₄×M₁₆	—	2	1	no	—
189	C₄×M₁₆	C₂²×C₅	1	1	yes	characteristic
190	C₄×M₁₆	C₂²×C₅	1	1	yes	characteristic
191	C₂×#97	—	2	1	no	—
192	C₂×#97	C₂²×C₅	1	1	yes	characteristic
193	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
194	#376	C₂²×C₅	1	1	yes	characteristic
195	#341	C₂²×C₅	1	2	yes	—
196	#339	C₂²×C₅	1	2	yes	—
197	#339	C₂²×C₅	1	2	yes	—
198	#336	C₂²×C₅	1	2	yes	—
199	#336	C₂²×C₅	1	2	yes	—
200	C₂³×C₅	—	2	1	no	—
201	C₂³×C₅	—	2	1	no	—
202	C₂³×C₅	C₂×#41	1	1	yes	characteristic
203	C₅×Q₈	—	2	1	no	—
204	C₅×Q₈	—	2	1	no	—
205	C₅×Q₈	—	2	1	no	—
206	C₅×Q₈	#117	1	2	yes	—
207	C₅×D₄	—	2	4	no	—
208	C₅×D₄	—	2	1	no	—
209	C₅×D₄	—	2	1	no	—
210	C₅×D₄	—	2	1	no	—
211	C₅×D₄	—	4	2	no	—
212	C₅×D₄	#117	1	2	yes	—
213	C₂×C₄×C₅	—	2	1	no	—
214	C₂×C₄×C₅	—	2	4	no	—
215	C₂×C₄×C₅	—	2	2	no	—
216	C₂×C₄×C₅	—	2	2	no	—
217	C₂×C₄×C₅	—	2	1	no	—
218	C₂×C₄×C₅	—	4	2	no	—
219	C₂×C₄×C₅	—	4	2	no	—
220	C₂×C₄×C₅	—	4	4	no	—
221	C₂×C₄×C₅	—	4	2	no	—
222	C₂×C₄×C₅	—	8	2	no	—
223	C₂×C₄×C₅	—	8	2	no	—
224	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
225	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
226	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
227	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
228	C₂×C₄×C₅	C₂×#41	1	2	yes	—
229	C₂×C₄×C₅	C₂×#41	1	2	yes	—
230	C₅×C₈	—	2	1	no	—
231	C₅×C₈	—	2	1	no	—
232	C₅×C₈	—	2	2	no	—
233	C₅×C₈	—	2	2	no	—
234	C₅×C₈	—	2	4	no	—
235	C₅×C₈	—	2	2	no	—
236	C₅×C₈	—	4	2	no	—
237	C₂×#41	C₂³×C₅	1	1	yes	characteristic
238	C₂×#41	C₂³×C₅	1	1	yes	characteristic
239	#135	—	2	4	no	—
240	C₂×Q₁₆	C₂×C₄×C₅	1	1	yes	characteristic
241	C₂×SD₁₆	C₂×C₄×C₅	1	1	yes	characteristic
242	C₂×SD₁₆	C₂×C₄×C₅	1	1	yes	characteristic
243	C₂×D₈	C₂×C₄×C₅	1	1	yes	characteristic
244	#131	—	2	4	no	—
245	#131	—	2	4	no	—
246	C₂×M₁₆	—	2	2	no	—
247	C₂×M₁₆	C₂³×C₅	1	2	yes	—
248	C₂×M₁₆	C₂³×C₅	1	2	yes	—
249	C₂²×C₈	—	2	2	no	—
250	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
251	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
252	C₂²×C₈	C₂³×C₅	1	2	yes	—
253	C₄×Q₈	C₂×C₄×C₅	1	2	yes	—
254	C₄×Q₈	C₂×C₄×C₅	1	2	yes	—
255	C₄×D₄	—	2	2	no	—
256	C₄×D₄	—	2	2	no	—
257	C₄×D₄	C₂×C₄×C₅	1	2	yes	—
258	C₄×D₄	C₂×C₄×C₅	1	2	yes	—
259	#117	—	2	1	no	—
260	#117	—	2	1	no	—
261	#117	C₂³×C₅	1	1	yes	characteristic
262	#117	C₂³×C₅	1	1	yes	characteristic
263	C₂×C₄²	—	2	1	no	—
264	C₂×C₄²	—	2	1	no	—
265	C₂×C₄²	C₂³×C₅	1	2	yes	—
266	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
267	#108	—	2	4	no	—
268	#107	C₂×C₄×C₅	1	2	yes	—
269	#106	C₂×C₄×C₅	1	2	yes	—
270	C₄⋊C₈	—	2	2	no	—
271	C₄⋊C₈	—	2	2	no	—
272	#104	—	2	4	no	—
273	#104	—	2	4	no	—
274	#103	C₂×C₄×C₅	1	2	yes	—
275	#103	C₂×C₄×C₅	1	2	yes	—
276	#102	C₂×C₄×C₅	1	2	yes	—
277	#102	C₂×C₄×C₅	1	2	yes	—
278	C₂²⋊C₈	—	2	2	no	—
279	C₂²⋊C₈	—	2	2	no	—
280	#97	—	2	2	no	—
281	#97	—	2	1	no	—
282	#97	—	2	1	no	—
283	#97	C₅×D₄	1	1	yes	characteristic
284	#97	C₅×D₄	1	1	yes	characteristic
285	#97	C₅×D₄	1	2	yes	—
286	C₄×C₈	—	2	2	no	—
287	C₄×C₈	—	2	1	no	—
288	C₄×C₈	—	2	1	no	—
289	C₄×C₈	C₂×C₄×C₅	1	2	yes	—
290	C₄×C₈	C₂×C₄×C₅	1	2	yes	—
291	#95	—	2	2	no	—
292	C₂²×C₅	—	2	2	no	—
293	C₂²×C₅	—	2	2	no	—
294	C₂²×C₅	—	4	2	no	—
295	C₂²×C₅	—	4	2	no	—
296	C₂²×C₅	—	4	1	no	—
297	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
298	C₂²×C₅	#529	1	2	yes	—
299	C₄×C₅	—	2	2	no	—
300	C₄×C₅	—	2	2	no	—
301	C₄×C₅	—	2	2	no	—
302	C₄×C₅	—	4	2	no	—
303	C₄×C₅	—	4	2	no	—
304	C₄×C₅	—	4	1	no	—
305	C₄×C₅	—	8	2	no	—
306	C₄×C₅	C₂×#117	1	1	yes	characteristic
307	C₄×C₅	C₄×#41	1	1	yes	characteristic
308	C₄×C₅	#525	1	2	yes	—
309	#41	—	2	2	no	—
310	#41	—	2	2	no	—
311	#41	—	2	2	no	—
312	#41	C₅×#41	1	4	yes	—
313	C₂×Q₈	C₂²×C₄×C₅	1	1	yes	characteristic
314	C₂×Q₈	C₂²×C₄×C₅	1	1	yes	characteristic
315	C₂×D₄	—	2	1	no	—
316	C₂×D₄	—	2	1	no	—
317	C₂×D₄	C₂²×C₄×C₅	1	1	yes	characteristic
318	C₂×D₄	C₂²×C₄×C₅	1	1	yes	characteristic
319	C₂²×C₄	—	2	1	no	—
320	C₂²×C₄	—	2	1	no	—
321	C₂²×C₄	—	2	2	no	—
322	C₂²×C₄	—	2	2	no	—
323	C₂²×C₄	—	2	2	no	—
324	C₂²×C₄	C₅×#41	1	2	yes	—
325	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
326	Q₁₆	—	2	2	no	—
327	SD₁₆	—	2	2	no	—
328	SD₁₆	—	2	2	no	—
329	D₈	—	2	2	no	—
330	M₁₆	—	2	8	no	—
331	M₁₆	—	2	2	no	—
332	M₁₆	—	2	2	no	—
333	M₁₆	—	2	2	no	—
334	M₁₆	C₅×#41	1	4	yes	—
335	C₂×C₈	—	2	8	no	—
336	C₂×C₈	—	2	2	no	—
337	C₂×C₈	—	2	2	no	—
338	C₂×C₈	—	2	2	no	—
339	C₂×C₈	—	2	2	no	—
340	C₂×C₈	—	2	2	no	—
341	C₂×C₈	—	2	2	no	—
342	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
343	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
344	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
345	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
346	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
347	C₄⋊C₄	—	2	2	no	—
348	C₄⋊C₄	—	2	2	no	—
349	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
350	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
351	C₂²⋊C₄	—	2	1	no	—
352	C₂²⋊C₄	—	2	1	no	—
353	C₂²⋊C₄	—	2	2	no	—
354	C₂²⋊C₄	—	2	2	no	—
355	C₄²	—	2	2	no	—
356	C₄²	—	2	2	no	—
357	C₄²	—	2	1	no	—
358	C₄²	—	2	1	no	—
359	C₄²	—	2	2	no	—
360	C₄²	—	2	2	no	—
361	C₄²	C₂²×C₄×C₅	1	2	yes	—
362	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
363	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
364	C₂×C₅	—	2	2	no	—
365	C₂×C₅	—	4	2	no	—
366	C₂×C₅	—	8	1	no	—
367	C₂×C₅	#2290	1	1	yes	characteristic
368	C₂×C₅	#2957	1	2	yes	—
369	C₂³	—	2	1	no	—
370	C₂³	—	2	1	no	—
371	C₂³	C₂×C₅×#41	1	1	yes	characteristic
372	Q₈	—	2	1	no	—
373	Q₈	—	2	1	no	—
374	Q₈	—	2	1	no	—
375	Q₈	C₅×#117	1	2	yes	—
376	D₄	—	2	4	no	—
377	D₄	—	2	1	no	—
378	D₄	—	2	1	no	—
379	D₄	—	2	1	no	—
380	D₄	—	4	2	no	—
381	D₄	C₅×#117	1	2	yes	—
382	C₂×C₄	—	2	1	no	—
383	C₂×C₄	—	2	4	no	—
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	2	1	no	—
387	C₂×C₄	—	4	2	no	—
388	C₂×C₄	—	4	2	no	—
389	C₂×C₄	—	4	4	no	—
390	C₂×C₄	—	4	2	no	—
391	C₂×C₄	—	8	2	no	—
392	C₂×C₄	—	8	2	no	—
393	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
394	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
395	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
396	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
397	C₂×C₄	C₂×C₅×#41	1	2	yes	—
398	C₂×C₄	C₂×C₅×#41	1	2	yes	—
399	C₈	—	2	1	no	—
400	C₈	—	2	1	no	—
401	C₈	—	2	2	no	—
402	C₈	—	2	2	no	—
403	C₈	—	2	4	no	—
404	C₈	—	2	2	no	—
405	C₈	—	4	2	no	—
406	C₅	#21140	1	1	yes	characteristic, direct product factor, Sylow
407	C₂²	—	2	2	no	—
408	C₂²	—	2	2	no	—
409	C₂²	—	4	2	no	—
410	C₂²	—	4	1	no	—
411	C₂²	—	4	2	no	—
412	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
413	C₂²	C₅×#529	1	2	yes	—
414	C₄	—	2	2	no	—
415	C₄	—	2	2	no	—
416	C₄	—	2	2	no	—
417	C₄	—	4	1	no	—
418	C₄	—	4	2	no	—
419	C₄	—	4	2	no	—
420	C₄	—	8	2	no	—
421	C₄	C₂×C₅×#117	1	1	yes	characteristic
422	C₄	C₄×C₅×#41	1	1	yes	characteristic
423	C₄	C₅×#525	1	2	yes	—
424	C₂	—	2	2	no	—
425	C₂	—	4	2	no	—
426	C₂	—	8	1	no	—
427	C₂	C₅×#2290	1	1	yes	characteristic
428	C₂	C₅×#2957	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₅	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₅
Frattini, cosocle	C₂²×C₄	C₂⁴×C₅
socle	C₂²×C₅	C₂×C₄×D₄
prime radical	C₂×C₅×#135	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₂×C₅×#97 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₅×#2923	C₂	semidirect
3. C₅×#2875	C₂	semidirect
4. C₅×#1929	C₂	semidirect
5. C₅×#1922	C₂	semidirect
7. C₅×#1866	C₂	semidirect
8. C₄×C₅×#108	C₂	semidirect
9. C₅×#1759	C₂	semidirect
10. C₅×#1759	C₂	semidirect
11. C₅×#1746	C₂	semidirect
16. C₄×C₅×Q₁₆	C₄	semidirect
17. C₄×C₅×SD₁₆	C₄	semidirect
18. C₄×C₅×SD₁₆	C₄	semidirect
19. C₄×C₅×D₈	C₄	semidirect
45. #21140	C₅	direct (N × H)
102. #2923	C₂×C₅	semidirect
103. #2875	C₂×C₅	semidirect
104. #1929	C₂×C₅	semidirect
105. #1922	C₂×C₅	semidirect
107. #1866	C₂×C₅	semidirect
108. C₄×#108	C₂×C₅	semidirect
109. #1759	C₂×C₅	semidirect
110. #1759	C₂×C₅	semidirect
111. #1746	C₂×C₅	semidirect
171. C₄×Q₁₆	C₄×C₅	semidirect
172. C₄×SD₁₆	C₄×C₅	semidirect
173. C₄×SD₁₆	C₄×C₅	semidirect
174. C₄×D₈	C₄×C₅	semidirect
406. C₅	#21140	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₄×C₅×#135	2
C₅×#2923	2
C₅×#2875	2
C₅×#1929	2
C₅×#1922	2
C₅×#1876	2
C₅×#1866	2
C₄×C₅×#108	2
C₅×#1759	2
C₅×#1746	2
#21140	5

Subgroups — C5×#21140 #11943860

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#21140 #11943860