Subgroups — C₅×#21071 #11943791

Order 1280.

1050 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#430	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₅×#104	C₂	1	1	yes	maximal, characteristic
3	C₅×#2896	C₂	1	1	yes	maximal, characteristic
4	C₅×#2879	C₂	1	1	yes	maximal, characteristic
5	C₅×#2873	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#1929	C₂	1	8	yes	maximal, complemented
7	C₂×C₅×#339	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1728	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×C₅×#41	C₂²	1	1	yes	characteristic
10	C₂²×C₅×M₁₆	C₂²	1	1	yes	characteristic
11	C₂²×C₅×M₁₆	C₂²	1	1	yes	characteristic
12	C₂²×C₅×M₁₆	C₂²	1	1	yes	characteristic
13	C₂²×C₅×M₁₆	C₂²	1	1	yes	characteristic
14	C₂×C₅×#117	C₂²	1	1	yes	characteristic
15	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
16	C₅×#430	—	2	4	no	—
17	C₂×C₅×#108	C₂²	1	4	yes	complemented
18	C₂×C₅×#104	—	2	4	no	—
19	C₂×C₅×#104	C₂²	1	4	yes	—
20	C₅×#419	C₄	1	2	yes	complemented
21	C₅×#418	C₄	1	2	yes	complemented
22	C₅×#417	C₄	1	4	yes	complemented
23	C₅×#416	C₂²	1	4	yes	—
24	C₅×#408	—	2	2	no	—
25	C₅×#408	C₂²	1	4	yes	—
26	C₅×#407	—	2	2	no	—
27	C₅×#405	—	2	2	no	—
28	C₅×#405	C₂²	1	4	yes	complemented
29	C₄×C₅×M₁₆	—	2	2	no	—
30	C₅×#339	C₂²	1	4	yes	complemented
31	C₅×#336	C₂²	1	4	yes	complemented
32	#21071	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
33	C₂×C₅×#41	—	2	1	no	—
34	C₂×C₅×#41	—	2	1	no	—
35	C₂×C₅×#41	—	2	2	no	—
36	C₂×C₅×#41	—	2	2	no	—
37	C₂×C₅×#41	—	2	2	no	—
38	C₂×C₅×#41	—	2	2	no	—
39	C₂×C₅×#41	C₂×C₄	1	2	yes	—
40	C₂×C₅×#41	C₂³	1	2	yes	—
41	C₂²×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
42	C₂²×C₅×D₄	—	2	1	no	—
43	C₂²×C₅×D₄	C₂×C₄	1	1	yes	characteristic
44	C₂³×C₄×C₅	—	2	1	no	—
45	C₂³×C₄×C₅	—	2	1	no	—
46	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
47	C₂×C₅×M₁₆	—	2	1	no	—
48	C₂×C₅×M₁₆	—	2	2	no	—
49	C₂×C₅×M₁₆	—	2	2	no	—
50	C₂×C₅×M₁₆	—	2	2	no	—
51	C₂×C₅×M₁₆	—	2	2	no	—
52	C₂×C₅×M₁₆	—	2	2	no	—
53	C₂×C₅×M₁₆	—	2	1	no	—
54	C₂×C₅×M₁₆	—	2	2	no	—
55	C₂×C₅×M₁₆	—	2	2	no	—
56	C₂×C₅×M₁₆	C₂×C₄	1	2	yes	—
57	C₂×C₅×M₁₆	C₂×C₄	1	2	yes	—
58	C₂×C₅×M₁₆	D₄	1	4	yes	—
59	C₂×C₅×M₁₆	D₄	1	2	yes	—
60	C₂×C₅×M₁₆	D₄	1	2	yes	—
61	C₂×C₅×M₁₆	C₂³	1	2	yes	—
62	C₂×C₅×M₁₆	C₂³	1	2	yes	—
63	C₂²×C₅×C₈	—	2	1	no	—
64	C₂²×C₅×C₈	—	2	1	no	—
65	C₂²×C₅×C₈	C₂³	1	2	yes	—
66	C₂²×C₅×C₈	C₂³	1	2	yes	—
67	C₅×#117	—	2	1	no	—
68	C₅×#117	—	2	1	no	—
69	C₅×#117	C₂×C₄	1	2	yes	—
70	C₅×#117	C₂³	1	2	yes	—
71	C₂×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
72	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
73	C₂×C₄²×C₅	—	2	1	no	—
74	C₂×C₄²×C₅	—	2	2	no	—
75	C₂×C₄²×C₅	—	2	2	no	—
76	C₂×C₄²×C₅	—	2	1	no	—
77	C₂×C₄²×C₅	C₂³	1	2	yes	—
78	C₅×#108	—	2	8	no	—
79	C₅×#104	—	2	8	no	—
80	C₅×#103	C₂×C₄	1	8	yes	complemented
81	C₅×#102	C₂×C₄	1	8	yes	complemented
82	C₅×C₂²⋊C₈	—	2	8	no	—
83	C₅×#97	—	2	4	no	—
84	C₄×C₅×C₈	—	2	4	no	—
85	C₂×#430	C₂×C₅	1	1	yes	characteristic, complemented
86	C₂²×#104	C₂×C₅	1	1	yes	characteristic
87	#2896	C₂×C₅	1	1	yes	characteristic
88	#2879	C₂×C₅	1	1	yes	characteristic
89	#2873	C₂×C₅	1	1	yes	characteristic, complemented
90	#1929	C₂×C₅	1	8	yes	complemented
91	C₂×#339	C₂×C₅	1	1	yes	characteristic, complemented
92	#1728	C₂×C₅	1	1	yes	characteristic, complemented
93	C₂⁴×C₅	—	2	1	no	—
94	C₂⁴×C₅	#41	1	1	yes	characteristic
95	C₅×#41	—	2	4	no	—
96	C₅×#41	—	2	4	no	—
97	C₅×#41	—	2	2	no	—
98	C₅×#41	—	2	2	no	—
99	C₅×#41	—	2	2	no	—
100	C₅×#41	—	2	2	no	—
101	C₅×#41	—	4	2	no	—
102	C₅×#41	—	4	2	no	—
103	C₅×#41	—	4	2	no	—
104	C₅×#41	—	4	2	no	—
105	C₂×C₅×Q₈	—	2	1	no	—
106	C₂×C₅×Q₈	—	2	2	no	—
107	C₂×C₅×Q₈	—	2	2	no	—
108	C₂×C₅×Q₈	C₂²×C₄	1	2	yes	—
109	C₂×C₅×D₄	—	2	2	no	—
110	C₂×C₅×D₄	—	2	2	no	—
111	C₂×C₅×D₄	—	2	2	no	—
112	C₂×C₅×D₄	—	2	2	no	—
113	C₂×C₅×D₄	—	2	1	no	—
114	C₂×C₅×D₄	—	4	2	no	—
115	C₂×C₅×D₄	—	4	2	no	—
116	C₂×C₅×D₄	C₂²×C₄	1	2	yes	—
117	C₂²×C₄×C₅	—	2	1	no	—
118	C₂²×C₄×C₅	—	2	2	no	—
119	C₂²×C₄×C₅	—	2	2	no	—
120	C₂²×C₄×C₅	—	2	2	no	—
121	C₂²×C₄×C₅	—	2	2	no	—
122	C₂²×C₄×C₅	—	4	4	no	—
123	C₂²×C₄×C₅	—	4	2	no	—
124	C₂²×C₄×C₅	—	4	2	no	—
125	C₂²×C₄×C₅	—	4	2	no	—
126	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
127	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
128	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
129	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
130	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₅	#41	1	2	yes	—
132	C₂²×C₄×C₅	#41	1	2	yes	—
133	C₂²×C₄×C₅	#41	1	2	yes	—
134	C₂²×C₄×C₅	#41	1	1	yes	characteristic
135	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
136	C₅×M₁₆	—	2	4	no	—
137	C₅×M₁₆	—	2	4	no	—
138	C₅×M₁₆	—	2	4	no	—
139	C₅×M₁₆	—	2	4	no	—
140	C₅×M₁₆	—	2	4	no	—
141	C₅×M₁₆	—	2	2	no	—
142	C₅×M₁₆	—	2	2	no	—
143	C₅×M₁₆	—	2	2	no	—
144	C₅×M₁₆	—	4	2	no	—
145	C₅×M₁₆	C₂×D₄	1	4	yes	—
146	C₂×C₅×C₈	—	2	4	no	—
147	C₂×C₅×C₈	—	2	2	no	—
148	C₂×C₅×C₈	—	2	2	no	—
149	C₂×C₅×C₈	—	2	2	no	—
150	C₂×C₅×C₈	—	2	2	no	—
151	C₂×C₅×C₈	—	2	2	no	—
152	C₂×C₅×C₈	—	2	2	no	—
153	C₂×C₅×C₈	—	4	2	no	—
154	C₂×C₅×C₈	C₂²×C₄	1	4	yes	—
155	C₂×C₅×C₈	C₂×D₄	1	4	yes	—
156	C₅×C₄⋊C₄	—	2	2	no	—
157	C₅×C₄⋊C₄	C₂²×C₄	1	4	yes	—
158	C₅×C₂²⋊C₄	—	2	2	no	—
159	C₅×C₂²⋊C₄	—	2	2	no	—
160	C₄²×C₅	—	2	2	no	—
161	C₄²×C₅	—	2	2	no	—
162	C₄²×C₅	—	2	2	no	—
163	C₄²×C₅	—	2	2	no	—
164	C₄²×C₅	—	4	2	no	—
165	C₂²×#41	C₂²×C₅	1	1	yes	characteristic
166	C₂²×M₁₆	C₂²×C₅	1	1	yes	characteristic
167	C₂²×M₁₆	C₂²×C₅	1	1	yes	characteristic
168	C₂²×M₁₆	C₂²×C₅	1	1	yes	characteristic
169	C₂²×M₁₆	C₂²×C₅	1	1	yes	characteristic
170	C₂×#117	C₂²×C₅	1	1	yes	characteristic
171	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
172	#430	—	2	4	no	—
173	C₂×#108	C₂²×C₅	1	4	yes	complemented
174	C₂×#104	—	2	4	no	—
175	C₂×#104	C₂²×C₅	1	4	yes	—
176	#419	C₄×C₅	1	2	yes	complemented
177	#418	C₄×C₅	1	2	yes	complemented
178	#417	C₄×C₅	1	4	yes	complemented
179	#416	C₂²×C₅	1	4	yes	—
180	#408	—	2	2	no	—
181	#408	C₂²×C₅	1	4	yes	—
182	#407	—	2	2	no	—
183	#405	—	2	2	no	—
184	#405	C₂²×C₅	1	4	yes	complemented
185	C₄×M₁₆	—	2	2	no	—
186	#339	C₂²×C₅	1	4	yes	complemented
187	#336	C₂²×C₅	1	4	yes	complemented
188	C₂³×C₅	—	2	2	no	—
189	C₂³×C₅	—	4	2	no	—
190	C₂³×C₅	—	4	2	no	—
191	C₂³×C₅	—	8	2	no	—
192	C₂³×C₅	C₄×D₄	1	1	yes	characteristic
193	C₂³×C₅	C₄×D₄	1	1	yes	characteristic
194	C₂³×C₅	#124	1	2	yes	—
195	C₂³×C₅	#126	1	2	yes	—
196	C₂³×C₅	C₂×#41	1	1	yes	characteristic
197	C₅×Q₈	—	2	2	no	—
198	C₅×Q₈	—	2	2	no	—
199	C₅×Q₈	—	4	2	no	—
200	C₅×D₄	—	2	2	no	—
201	C₅×D₄	—	2	2	no	—
202	C₅×D₄	—	4	2	no	—
203	C₅×D₄	—	4	2	no	—
204	C₅×D₄	—	4	4	no	—
205	C₅×D₄	—	4	2	no	—
206	C₂×C₄×C₅	—	2	4	no	—
207	C₂×C₄×C₅	—	2	4	no	—
208	C₂×C₄×C₅	—	2	2	no	—
209	C₂×C₄×C₅	—	4	2	no	—
210	C₂×C₄×C₅	—	4	8	no	—
211	C₂×C₄×C₅	—	4	2	no	—
212	C₂×C₄×C₅	—	4	2	no	—
213	C₂×C₄×C₅	—	4	2	no	—
214	C₂×C₄×C₅	—	4	2	no	—
215	C₂×C₄×C₅	—	4	4	no	—
216	C₂×C₄×C₅	—	8	2	no	—
217	C₂×C₄×C₅	#117	1	2	yes	—
218	C₂×C₄×C₅	#117	1	2	yes	—
219	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
220	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
221	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
222	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
223	C₂×C₄×C₅	#121	1	2	yes	—
224	C₂×C₄×C₅	#121	1	2	yes	—
225	C₂×C₄×C₅	#123	1	2	yes	—
226	C₂×C₄×C₅	#123	1	2	yes	—
227	C₂×C₄×C₅	#124	1	2	yes	—
228	C₂×C₄×C₅	#126	1	2	yes	—
229	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
230	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
231	C₂×C₄×C₅	C₂²×D₄	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	C₂×#41	1	1	yes	characteristic
235	C₅×C₈	—	2	4	no	—
236	C₅×C₈	—	2	4	no	—
237	C₅×C₈	—	2	4	no	—
238	C₅×C₈	—	4	2	no	—
239	C₂×#41	—	2	1	no	—
240	C₂×#41	—	2	1	no	—
241	C₂×#41	—	2	2	no	—
242	C₂×#41	—	2	2	no	—
243	C₂×#41	—	2	2	no	—
244	C₂×#41	—	2	2	no	—
245	C₂×#41	C₂×C₄×C₅	1	2	yes	—
246	C₂×#41	C₂³×C₅	1	2	yes	—
247	C₂²×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
248	C₂²×D₄	—	2	1	no	—
249	C₂²×D₄	C₂×C₄×C₅	1	1	yes	characteristic
250	C₂³×C₄	—	2	1	no	—
251	C₂³×C₄	—	2	1	no	—
252	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
253	C₂×M₁₆	—	2	1	no	—
254	C₂×M₁₆	—	2	2	no	—
255	C₂×M₁₆	—	2	2	no	—
256	C₂×M₁₆	—	2	2	no	—
257	C₂×M₁₆	—	2	2	no	—
258	C₂×M₁₆	—	2	2	no	—
259	C₂×M₁₆	—	2	1	no	—
260	C₂×M₁₆	—	2	2	no	—
261	C₂×M₁₆	—	2	2	no	—
262	C₂×M₁₆	C₂×C₄×C₅	1	2	yes	—
263	C₂×M₁₆	C₂×C₄×C₅	1	2	yes	—
264	C₂×M₁₆	C₅×D₄	1	4	yes	—
265	C₂×M₁₆	C₅×D₄	1	2	yes	—
266	C₂×M₁₆	C₅×D₄	1	2	yes	—
267	C₂×M₁₆	C₂³×C₅	1	2	yes	—
268	C₂×M₁₆	C₂³×C₅	1	2	yes	—
269	C₂²×C₈	—	2	1	no	—
270	C₂²×C₈	—	2	1	no	—
271	C₂²×C₈	C₂³×C₅	1	2	yes	—
272	C₂²×C₈	C₂³×C₅	1	2	yes	—
273	#117	—	2	1	no	—
274	#117	—	2	1	no	—
275	#117	C₂×C₄×C₅	1	2	yes	—
276	#117	C₂³×C₅	1	2	yes	—
277	C₂×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
278	C₂×C₂²⋊C₄	—	2	1	no	—
279	C₂×C₄²	—	2	1	no	—
280	C₂×C₄²	—	2	2	no	—
281	C₂×C₄²	—	2	2	no	—
282	C₂×C₄²	—	2	1	no	—
283	C₂×C₄²	C₂³×C₅	1	2	yes	—
284	#108	—	2	8	no	—
285	#104	—	2	8	no	—
286	#103	C₂×C₄×C₅	1	8	yes	complemented
287	#102	C₂×C₄×C₅	1	8	yes	complemented
288	C₂²⋊C₈	—	2	8	no	—
289	#97	—	2	4	no	—
290	C₄×C₈	—	2	4	no	—
291	C₂²×C₅	—	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	4	no	—
297	C₂²×C₅	—	4	2	no	—
298	C₂²×C₅	—	8	4	no	—
299	C₂²×C₅	#388	1	2	yes	—
300	C₂²×C₅	#388	1	2	yes	—
301	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
302	C₂²×C₅	C₂×#124	1	1	yes	characteristic
303	C₂²×C₅	C₂×#126	1	1	yes	characteristic
304	C₄×C₅	—	4	4	no	—
305	C₄×C₅	—	4	4	no	—
306	C₄×C₅	—	4	2	no	—
307	C₄×C₅	#388	1	2	yes	—
308	C₄×C₅	#388	1	2	yes	—
309	C₄×C₅	C₂×#117	1	1	yes	characteristic
310	C₄×C₅	C₂×C₄×D₄	1	1	yes	characteristic
311	C₄×C₅	C₂×#121	1	1	yes	characteristic
312	C₄×C₅	C₂×#123	1	1	yes	characteristic
313	C₂⁴	—	2	1	no	—
314	C₂⁴	C₅×#41	1	1	yes	characteristic
315	#41	—	2	4	no	—
316	#41	—	2	4	no	—
317	#41	—	2	2	no	—
318	#41	—	2	2	no	—
319	#41	—	2	2	no	—
320	#41	—	2	2	no	—
321	#41	—	4	2	no	—
322	#41	—	4	2	no	—
323	#41	—	4	2	no	—
324	#41	—	4	2	no	—
325	C₂×Q₈	—	2	1	no	—
326	C₂×Q₈	—	2	2	no	—
327	C₂×Q₈	—	2	2	no	—
328	C₂×Q₈	C₂²×C₄×C₅	1	2	yes	—
329	C₂×D₄	—	2	2	no	—
330	C₂×D₄	—	2	2	no	—
331	C₂×D₄	—	2	2	no	—
332	C₂×D₄	—	2	2	no	—
333	C₂×D₄	—	2	1	no	—
334	C₂×D₄	—	4	2	no	—
335	C₂×D₄	—	4	2	no	—
336	C₂×D₄	C₂²×C₄×C₅	1	2	yes	—
337	C₂²×C₄	—	2	1	no	—
338	C₂²×C₄	—	2	2	no	—
339	C₂²×C₄	—	2	2	no	—
340	C₂²×C₄	—	2	2	no	—
341	C₂²×C₄	—	2	2	no	—
342	C₂²×C₄	—	4	4	no	—
343	C₂²×C₄	—	4	2	no	—
344	C₂²×C₄	—	4	2	no	—
345	C₂²×C₄	—	4	2	no	—
346	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
347	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
348	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
349	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
350	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
351	C₂²×C₄	C₅×#41	1	2	yes	—
352	C₂²×C₄	C₅×#41	1	2	yes	—
353	C₂²×C₄	C₅×#41	1	2	yes	—
354	C₂²×C₄	C₅×#41	1	1	yes	characteristic
355	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
356	M₁₆	—	2	4	no	—
357	M₁₆	—	2	4	no	—
358	M₁₆	—	2	4	no	—
359	M₁₆	—	2	4	no	—
360	M₁₆	—	2	4	no	—
361	M₁₆	—	2	2	no	—
362	M₁₆	—	2	2	no	—
363	M₁₆	—	2	2	no	—
364	M₁₆	—	4	2	no	—
365	M₁₆	C₂×C₅×D₄	1	4	yes	—
366	C₂×C₈	—	2	4	no	—
367	C₂×C₈	—	2	2	no	—
368	C₂×C₈	—	2	2	no	—
369	C₂×C₈	—	2	2	no	—
370	C₂×C₈	—	2	2	no	—
371	C₂×C₈	—	2	2	no	—
372	C₂×C₈	—	2	2	no	—
373	C₂×C₈	—	4	2	no	—
374	C₂×C₈	C₂²×C₄×C₅	1	4	yes	—
375	C₂×C₈	C₂×C₅×D₄	1	4	yes	—
376	C₄⋊C₄	—	2	2	no	—
377	C₄⋊C₄	C₂²×C₄×C₅	1	4	yes	—
378	C₂²⋊C₄	—	2	2	no	—
379	C₂²⋊C₄	—	2	2	no	—
380	C₄²	—	2	2	no	—
381	C₄²	—	2	2	no	—
382	C₄²	—	2	2	no	—
383	C₄²	—	2	2	no	—
384	C₄²	—	4	2	no	—
385	C₂×C₅	—	2	1	no	—
386	C₂×C₅	—	2	2	no	—
387	C₂×C₅	—	2	1	no	—
388	C₂×C₅	—	2	2	no	—
389	C₂×C₅	—	8	2	no	—
390	C₂×C₅	C₂×#388	1	1	yes	characteristic
391	C₂×C₅	#2956	1	2	yes	—
392	C₂³	—	2	2	no	—
393	C₂³	—	4	2	no	—
394	C₂³	—	4	2	no	—
395	C₂³	—	8	2	no	—
396	C₂³	C₄×C₅×D₄	1	1	yes	characteristic
397	C₂³	C₄×C₅×D₄	1	1	yes	characteristic
398	C₂³	C₅×#124	1	2	yes	—
399	C₂³	C₅×#126	1	2	yes	—
400	C₂³	C₂×C₅×#41	1	1	yes	characteristic
401	Q₈	—	2	2	no	—
402	Q₈	—	2	2	no	—
403	Q₈	—	4	2	no	—
404	D₄	—	2	2	no	—
405	D₄	—	2	2	no	—
406	D₄	—	4	4	no	—
407	D₄	—	4	2	no	—
408	D₄	—	4	2	no	—
409	D₄	—	4	2	no	—
410	C₂×C₄	—	2	4	no	—
411	C₂×C₄	—	2	4	no	—
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	4	2	no	—
414	C₂×C₄	—	4	8	no	—
415	C₂×C₄	—	4	2	no	—
416	C₂×C₄	—	4	2	no	—
417	C₂×C₄	—	4	4	no	—
418	C₂×C₄	—	4	2	no	—
419	C₂×C₄	—	4	2	no	—
420	C₂×C₄	—	8	2	no	—
421	C₂×C₄	C₅×#117	1	2	yes	—
422	C₂×C₄	C₅×#117	1	2	yes	—
423	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
424	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
425	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
426	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
427	C₂×C₄	C₅×#121	1	2	yes	—
428	C₂×C₄	C₅×#121	1	2	yes	—
429	C₂×C₄	C₅×#123	1	2	yes	—
430	C₂×C₄	C₅×#123	1	2	yes	—
431	C₂×C₄	C₅×#124	1	2	yes	—
432	C₂×C₄	C₅×#126	1	2	yes	—
433	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
434	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
435	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
436	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
437	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
438	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
439	C₈	—	2	4	no	—
440	C₈	—	2	4	no	—
441	C₈	—	2	4	no	—
442	C₈	—	4	2	no	—
443	C₅	#21071	1	1	yes	characteristic, direct product factor, Sylow
444	C₂²	—	2	2	no	—
445	C₂²	—	2	2	no	—
446	C₂²	—	2	2	no	—
447	C₂²	—	4	2	no	—
448	C₂²	—	4	2	no	—
449	C₂²	—	4	2	no	—
450	C₂²	—	4	4	no	—
451	C₂²	—	8	4	no	—
452	C₂²	C₅×#388	1	2	yes	—
453	C₂²	C₅×#388	1	2	yes	—
454	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
455	C₂²	C₂×C₅×#124	1	1	yes	characteristic
456	C₂²	C₂×C₅×#126	1	1	yes	characteristic
457	C₄	—	4	4	no	—
458	C₄	—	4	2	no	—
459	C₄	—	4	4	no	—
460	C₄	C₅×#388	1	2	yes	—
461	C₄	C₅×#388	1	2	yes	—
462	C₄	C₂×C₅×#117	1	1	yes	characteristic
463	C₄	C₂×C₄×C₅×D₄	1	1	yes	characteristic
464	C₄	C₂×C₅×#121	1	1	yes	characteristic
465	C₄	C₂×C₅×#123	1	1	yes	characteristic
466	C₂	—	2	1	no	—
467	C₂	—	2	2	no	—
468	C₂	—	2	2	no	—
469	C₂	—	2	1	no	—
470	C₂	—	8	2	no	—
471	C₂	C₂×C₅×#388	1	1	yes	characteristic
472	C₂	C₅×#2956	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	C₂²×C₅×#41	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₂²×C₅×M₁₆ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×#430	C₂	semidirect
5. C₅×#2873	C₂	semidirect
6. C₅×#1929	C₂	semidirect
7. C₂×C₅×#339	C₂	semidirect
8. C₅×#1728	C₂	semidirect
17. C₂×C₅×#108	C₂²	semidirect
20. C₅×#419	C₄	semidirect
21. C₅×#418	C₄	semidirect
22. C₅×#417	C₄	semidirect
28. C₅×#405	C₂²	semidirect
30. C₅×#339	C₂²	semidirect
31. C₅×#336	C₂²	semidirect
32. #21071	C₅	direct (N × H)
80. C₅×#103	C₂×C₄	semidirect
81. C₅×#102	C₂×C₄	semidirect
85. C₂×#430	C₂×C₅	semidirect
89. #2873	C₂×C₅	semidirect
90. #1929	C₂×C₅	semidirect
91. C₂×#339	C₂×C₅	semidirect
92. #1728	C₂×C₅	semidirect
173. C₂×#108	C₂²×C₅	semidirect
176. #419	C₄×C₅	semidirect
177. #418	C₄×C₅	semidirect
178. #417	C₄×C₅	semidirect
184. #405	C₂²×C₅	semidirect
186. #339	C₂²×C₅	semidirect
187. #336	C₂²×C₅	semidirect
286. #103	C₂×C₄×C₅	semidirect
287. #102	C₂×C₄×C₅	semidirect
443. C₅	#21071	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₅×#430	2
C₂²×C₅×#104	2
C₅×#2896	2
C₅×#2879	2
C₅×#2873	2
C₅×#1929	2
C₂×C₅×#339	2
C₅×#1728	2
#21071	5

Subgroups — C5×#21071 #11943791

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#21071 #11943791