Subgroups — C₅×#21556 #11944276

Order 1280.

874 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	C₂×C₅×#473	C₂	1	1	yes	maximal, characteristic
2	C₄×C₅×#137	C₂	1	2	yes	maximal
3	C₂×C₅×#441	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#2875	C₂	1	1	yes	maximal, characteristic
5	C₅×#1979	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#1951	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#1930	C₂	1	2	yes	maximal, complemented
8	C₅×#1908	C₂	1	2	yes	maximal
9	C₅×#1815	C₂	1	1	yes	maximal, characteristic
10	C₅×#1778	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₅×#101	C₂	1	2	yes	maximal, complemented
12	C₂×C₅×#137	C₂²	1	2	yes	—
13	C₂²×C₅×Q₁₆	C₂²	1	1	yes	characteristic
14	C₂×C₅×#131	C₂²	1	1	yes	characteristic
15	C₂×C₅×#131	C₂²	1	1	yes	characteristic
16	C₄×C₅×#41	C₂²	1	1	yes	characteristic
17	C₂×C₄×C₅×Q₈	C₂²	1	2	yes	—
18	C₅×#473	C₄	1	8	yes	complemented
19	C₅×#441	—	2	1	no	—
20	C₅×#441	—	2	1	no	—
21	C₅×#441	—	2	1	no	—
22	C₅×#441	—	2	1	no	—
23	C₅×#441	—	2	2	no	—
24	C₅×#440	—	2	2	no	—
25	C₄×C₅×Q₁₆	—	2	2	no	—
26	C₄×C₅×SD₁₆	—	2	2	no	—
27	C₂×C₅×#108	C₂²	1	1	yes	characteristic
28	C₂×C₅×#108	C₂²	1	1	yes	characteristic
29	C₅×#428	C₂²	1	2	yes	—
30	C₂×C₅×#106	C₂²	1	1	yes	characteristic
31	C₅×#419	C₂²	1	2	yes	—
32	C₅×#417	C₂²	1	2	yes	—
33	C₂×C₅×#103	C₂²	1	2	yes	—
34	C₂×C₅×#101	C₂²	1	2	yes	—
35	C₂×C₅×#101	C₂²	1	2	yes	—
36	C₅×#405	—	2	1	no	—
37	C₅×#405	—	2	1	no	—
38	C₅×#405	C₂²	1	1	yes	characteristic
39	C₅×#405	C₂²	1	1	yes	characteristic
40	C₄×C₅×M₁₆	—	2	1	no	—
41	C₄×C₅×M₁₆	C₂²	1	1	yes	characteristic
42	C₄×C₅×M₁₆	C₂²	1	2	yes	—
43	C₂×C₅×#97	—	2	1	no	—
44	C₂×C₅×#97	C₂²	1	1	yes	characteristic
45	C₅×#343	C₂²	1	2	yes	—
46	C₅×#343	C₂²	1	2	yes	—
47	C₅×#341	C₂²	1	2	yes	—
48	#21556	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
49	C₂×C₅×#41	C₂³	1	1	yes	characteristic
50	C₂²×C₅×Q₈	C₂³	1	2	yes	—
51	C₅×#137	—	2	4	no	—
52	C₅×#137	C₂×C₄	1	8	yes	—
53	C₂×C₅×Q₁₆	—	2	2	no	—
54	C₂×C₅×Q₁₆	—	2	1	no	—
55	C₂×C₅×Q₁₆	—	2	1	no	—
56	C₂×C₅×Q₁₆	—	2	2	no	—
57	C₂×C₅×Q₁₆	C₂×C₄	1	4	yes	complemented
58	C₂×C₅×SD₁₆	—	2	2	no	—
59	C₅×#131	—	2	2	no	—
60	C₅×#131	—	2	2	no	—
61	C₅×#131	—	2	2	no	—
62	C₅×#131	C₂×C₄	1	4	yes	—
63	C₂×C₅×M₁₆	—	2	1	no	—
64	C₂×C₅×M₁₆	—	2	1	no	—
65	C₂×C₅×M₁₆	C₂³	1	2	yes	—
66	C₂×C₅×M₁₆	C₂³	1	1	yes	characteristic
67	C₂×C₅×M₁₆	C₂³	1	2	yes	—
68	C₂×C₅×M₁₆	C₂³	1	1	yes	characteristic
69	C₂²×C₅×C₈	—	2	1	no	—
70	C₂²×C₅×C₈	—	2	1	no	—
71	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
72	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
73	C₄×C₅×Q₈	—	2	2	no	—
74	C₄×C₅×Q₈	—	2	2	no	—
75	C₄×C₅×Q₈	—	2	2	no	—
76	C₄×C₅×Q₈	—	2	2	no	—
77	C₄×C₅×Q₈	D₄	1	2	yes	—
78	C₄×C₅×D₄	—	2	2	no	—
79	C₄×C₅×D₄	D₄	1	2	yes	—
80	C₅×#117	—	2	1	no	—
81	C₅×#117	C₂³	1	1	yes	characteristic
82	C₂×C₅×C₄⋊C₄	—	2	2	no	—
83	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
84	C₂×C₄²×C₅	—	2	1	no	—
85	C₂×C₄²×C₅	—	2	2	no	—
86	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
87	C₅×#108	—	2	2	no	—
88	C₅×#108	C₂×C₄	1	4	yes	complemented
89	C₅×#107	—	2	2	no	—
90	C₅×#106	—	2	1	no	—
91	C₅×#106	—	2	1	no	—
92	C₅×#106	—	2	2	no	—
93	C₅×#103	—	2	2	no	—
94	C₅×#103	—	2	2	no	—
95	C₅×#103	—	2	2	no	—
96	C₅×#103	—	2	2	no	—
97	C₅×#103	—	2	2	no	—
98	C₅×#102	—	2	2	no	—
99	C₅×#101	—	2	4	no	—
100	C₅×#101	C₂×C₄	1	8	yes	complemented
101	C₅×#97	—	2	1	no	—
102	C₅×#97	—	2	1	no	—
103	C₅×#97	—	2	1	no	—
104	C₅×#97	—	2	2	no	—
105	C₅×#97	D₄	1	1	yes	characteristic
106	C₅×#97	D₄	1	1	yes	characteristic
107	C₅×#97	D₄	1	1	yes	characteristic
108	C₅×#97	D₄	1	1	yes	characteristic
109	C₄×C₅×C₈	—	2	1	no	—
110	C₄×C₅×C₈	—	2	1	no	—
111	C₄×C₅×C₈	—	2	1	no	—
112	C₄×C₅×C₈	—	2	2	no	—
113	C₂×#473	C₂×C₅	1	1	yes	characteristic
114	C₄×#137	C₂×C₅	1	2	yes	—
115	C₂×#441	C₂×C₅	1	1	yes	characteristic, complemented
116	#2875	C₂×C₅	1	1	yes	characteristic
117	#1979	C₂×C₅	1	1	yes	characteristic, complemented
118	#1951	C₂×C₅	1	1	yes	characteristic, complemented
119	#1930	C₂×C₅	1	2	yes	complemented
120	#1908	C₂×C₅	1	2	yes	—
121	#1815	C₂×C₅	1	1	yes	characteristic
122	#1778	C₂×C₅	1	1	yes	characteristic, complemented
123	C₄×#101	C₂×C₅	1	2	yes	complemented
124	C₅×#41	—	2	1	no	—
125	C₅×#41	—	2	1	no	—
126	C₅×#41	C₂²×C₄	1	2	yes	—
127	C₅×#41	#41	1	2	yes	—
128	C₂×C₅×Q₈	—	2	2	no	—
129	C₂×C₅×Q₈	—	2	2	no	—
130	C₂×C₅×Q₈	—	2	2	no	—
131	C₂×C₅×Q₈	—	2	2	no	—
132	C₂×C₅×Q₈	—	2	2	no	—
133	C₂×C₅×Q₈	C₂²×C₄	1	4	yes	—
134	C₂×C₅×Q₈	C₂×D₄	1	1	yes	characteristic
135	C₂×C₅×D₄	—	2	1	no	—
136	C₂×C₅×D₄	C₂×D₄	1	1	yes	characteristic
137	C₂²×C₄×C₅	—	2	1	no	—
138	C₂²×C₄×C₅	—	2	2	no	—
139	C₂²×C₄×C₅	—	2	2	no	—
140	C₂²×C₄×C₅	—	2	2	no	—
141	C₂²×C₄×C₅	#41	1	2	yes	—
142	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
143	C₅×Q₁₆	—	2	8	no	—
144	C₅×Q₁₆	—	2	4	no	—
145	C₅×Q₁₆	—	2	4	no	—
146	C₅×SD₁₆	—	2	8	no	—
147	C₅×M₁₆	—	2	4	no	—
148	C₅×M₁₆	—	2	1	no	—
149	C₅×M₁₆	—	2	1	no	—
150	C₅×M₁₆	—	2	2	no	—
151	C₅×M₁₆	—	2	4	no	—
152	C₅×M₁₆	—	2	2	no	—
153	C₅×M₁₆	—	2	2	no	—
154	C₅×M₁₆	C₂²×C₄	1	2	yes	—
155	C₅×M₁₆	C₂²×C₄	1	4	yes	—
156	C₅×M₁₆	#41	1	2	yes	—
157	C₂×C₅×C₈	—	2	4	no	—
158	C₂×C₅×C₈	—	2	1	no	—
159	C₂×C₅×C₈	—	2	1	no	—
160	C₂×C₅×C₈	—	2	2	no	—
161	C₂×C₅×C₈	—	2	1	no	—
162	C₂×C₅×C₈	—	2	1	no	—
163	C₂×C₅×C₈	—	2	4	no	—
164	C₂×C₅×C₈	—	2	2	no	—
165	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
166	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
167	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
168	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
169	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
170	C₂×C₅×C₈	#41	1	2	yes	—
171	C₅×C₄⋊C₄	—	2	2	no	—
172	C₅×C₄⋊C₄	—	2	2	no	—
173	C₅×C₄⋊C₄	—	2	2	no	—
174	C₅×C₄⋊C₄	—	4	2	no	—
175	C₅×C₄⋊C₄	—	4	2	no	—
176	C₅×C₄⋊C₄	C₂×D₄	1	2	yes	—
177	C₅×C₂²⋊C₄	—	2	1	no	—
178	C₅×C₂²⋊C₄	—	2	2	no	—
179	C₄²×C₅	—	2	2	no	—
180	C₄²×C₅	—	2	1	no	—
181	C₄²×C₅	—	4	2	no	—
182	C₄²×C₅	—	4	2	no	—
183	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
184	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
185	C₄²×C₅	C₂×D₄	1	2	yes	—
186	C₂×#137	C₂²×C₅	1	2	yes	—
187	C₂²×Q₁₆	C₂²×C₅	1	1	yes	characteristic
188	C₂×#131	C₂²×C₅	1	1	yes	characteristic
189	C₂×#131	C₂²×C₅	1	1	yes	characteristic
190	C₄×#41	C₂²×C₅	1	1	yes	characteristic
191	C₂×C₄×Q₈	C₂²×C₅	1	2	yes	—
192	#473	C₄×C₅	1	8	yes	complemented
193	#441	—	2	2	no	—
194	#441	—	2	1	no	—
195	#441	—	2	1	no	—
196	#441	—	2	1	no	—
197	#441	—	2	1	no	—
198	#440	—	2	2	no	—
199	C₄×Q₁₆	—	2	2	no	—
200	C₄×SD₁₆	—	2	2	no	—
201	C₂×#108	C₂²×C₅	1	1	yes	characteristic
202	C₂×#108	C₂²×C₅	1	1	yes	characteristic
203	#428	C₂²×C₅	1	2	yes	—
204	C₂×#106	C₂²×C₅	1	1	yes	characteristic
205	#419	C₂²×C₅	1	2	yes	—
206	#417	C₂²×C₅	1	2	yes	—
207	C₂×#103	C₂²×C₅	1	2	yes	—
208	C₂×#101	C₂²×C₅	1	2	yes	—
209	C₂×#101	C₂²×C₅	1	2	yes	—
210	#405	—	2	1	no	—
211	#405	—	2	1	no	—
212	#405	C₂²×C₅	1	1	yes	characteristic
213	#405	C₂²×C₅	1	1	yes	characteristic
214	C₄×M₁₆	—	2	1	no	—
215	C₄×M₁₆	C₂²×C₅	1	1	yes	characteristic
216	C₄×M₁₆	C₂²×C₅	1	2	yes	—
217	C₂×#97	—	2	1	no	—
218	C₂×#97	C₂²×C₅	1	1	yes	characteristic
219	#343	C₂²×C₅	1	2	yes	—
220	#343	C₂²×C₅	1	2	yes	—
221	#341	C₂²×C₅	1	2	yes	—
222	C₂³×C₅	—	2	1	no	—
223	C₂³×C₅	C₂×#41	1	1	yes	characteristic
224	C₅×Q₈	—	2	1	no	—
225	C₅×Q₈	—	2	4	no	—
226	C₅×Q₈	—	2	4	no	—
227	C₅×Q₈	—	4	2	no	—
228	C₅×Q₈	—	4	2	no	—
229	C₅×Q₈	C₄×D₄	1	2	yes	—
230	C₅×D₄	—	2	2	no	—
231	C₅×D₄	—	2	2	no	—
232	C₅×D₄	—	2	1	no	—
233	C₅×D₄	C₄×D₄	1	2	yes	—
234	C₂×C₄×C₅	—	2	1	no	—
235	C₂×C₄×C₅	—	2	2	no	—
236	C₂×C₄×C₅	—	2	2	no	—
237	C₂×C₄×C₅	—	2	4	no	—
238	C₂×C₄×C₅	—	2	2	no	—
239	C₂×C₄×C₅	—	4	2	no	—
240	C₂×C₄×C₅	—	4	2	no	—
241	C₂×C₄×C₅	—	4	2	no	—
242	C₂×C₄×C₅	—	4	2	no	—
243	C₂×C₄×C₅	—	8	2	no	—
244	C₂×C₄×C₅	—	8	2	no	—
245	C₂×C₄×C₅	#121	1	2	yes	—
246	C₂×C₄×C₅	#121	1	2	yes	—
247	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
248	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
249	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
250	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
251	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
252	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
253	C₅×C₈	—	2	2	no	—
254	C₅×C₈	—	2	4	no	—
255	C₅×C₈	—	2	1	no	—
256	C₅×C₈	—	2	2	no	—
257	C₅×C₈	—	2	1	no	—
258	C₅×C₈	—	4	2	no	—
259	C₅×C₈	C₄×D₄	1	2	yes	—
260	C₅×C₈	C₄×D₄	1	2	yes	—
261	C₂×#41	C₂³×C₅	1	1	yes	characteristic
262	C₂²×Q₈	C₂³×C₅	1	2	yes	—
263	#137	—	2	4	no	—
264	#137	C₂×C₄×C₅	1	8	yes	—
265	C₂×Q₁₆	—	2	2	no	—
266	C₂×Q₁₆	—	2	1	no	—
267	C₂×Q₁₆	—	2	1	no	—
268	C₂×Q₁₆	—	2	2	no	—
269	C₂×Q₁₆	C₂×C₄×C₅	1	4	yes	complemented
270	C₂×SD₁₆	—	2	2	no	—
271	#131	—	2	2	no	—
272	#131	—	2	2	no	—
273	#131	—	2	2	no	—
274	#131	C₂×C₄×C₅	1	4	yes	—
275	C₂×M₁₆	—	2	1	no	—
276	C₂×M₁₆	—	2	1	no	—
277	C₂×M₁₆	C₂³×C₅	1	2	yes	—
278	C₂×M₁₆	C₂³×C₅	1	1	yes	characteristic
279	C₂×M₁₆	C₂³×C₅	1	2	yes	—
280	C₂×M₁₆	C₂³×C₅	1	1	yes	characteristic
281	C₂²×C₈	—	2	1	no	—
282	C₂²×C₈	—	2	1	no	—
283	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
284	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
285	C₄×Q₈	—	2	2	no	—
286	C₄×Q₈	—	2	2	no	—
287	C₄×Q₈	—	2	2	no	—
288	C₄×Q₈	—	2	2	no	—
289	C₄×Q₈	C₅×D₄	1	2	yes	—
290	C₄×D₄	—	2	2	no	—
291	C₄×D₄	C₅×D₄	1	2	yes	—
292	#117	—	2	1	no	—
293	#117	C₂³×C₅	1	1	yes	characteristic
294	C₂×C₄⋊C₄	—	2	2	no	—
295	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
296	C₂×C₄²	—	2	1	no	—
297	C₂×C₄²	—	2	2	no	—
298	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
299	#108	—	2	2	no	—
300	#108	C₂×C₄×C₅	1	4	yes	complemented
301	#107	—	2	2	no	—
302	#106	—	2	1	no	—
303	#106	—	2	1	no	—
304	#106	—	2	2	no	—
305	#103	—	2	2	no	—
306	#103	—	2	2	no	—
307	#103	—	2	2	no	—
308	#103	—	2	2	no	—
309	#103	—	2	2	no	—
310	#102	—	2	2	no	—
311	#101	—	2	4	no	—
312	#101	C₂×C₄×C₅	1	8	yes	complemented
313	#97	—	2	1	no	—
314	#97	—	2	1	no	—
315	#97	—	2	1	no	—
316	#97	—	2	2	no	—
317	#97	C₅×D₄	1	1	yes	characteristic
318	#97	C₅×D₄	1	1	yes	characteristic
319	#97	C₅×D₄	1	1	yes	characteristic
320	#97	C₅×D₄	1	1	yes	characteristic
321	C₄×C₈	—	2	1	no	—
322	C₄×C₈	—	2	1	no	—
323	C₄×C₈	—	2	1	no	—
324	C₄×C₈	—	2	2	no	—
325	C₂²×C₅	—	2	2	no	—
326	C₂²×C₅	—	2	2	no	—
327	C₂²×C₅	—	4	2	no	—
328	C₂²×C₅	C₄×#41	1	1	yes	characteristic
329	C₂²×C₅	C₂×#121	1	1	yes	characteristic
330	C₂²×C₅	#529	1	1	yes	characteristic
331	C₄×C₅	—	2	2	no	—
332	C₄×C₅	—	2	2	no	—
333	C₄×C₅	—	2	2	no	—
334	C₄×C₅	—	4	4	no	—
335	C₄×C₅	—	4	2	no	—
336	C₄×C₅	—	8	2	no	—
337	C₄×C₅	C₂×C₄×D₄	1	1	yes	characteristic
338	C₄×C₅	C₂×C₄×D₄	1	1	yes	characteristic
339	C₄×C₅	#525	1	1	yes	characteristic
340	C₄×C₅	#532	1	1	yes	characteristic
341	#41	—	2	1	no	—
342	#41	—	2	1	no	—
343	#41	C₂²×C₄×C₅	1	2	yes	—
344	#41	C₅×#41	1	2	yes	—
345	C₂×Q₈	—	2	2	no	—
346	C₂×Q₈	—	2	2	no	—
347	C₂×Q₈	—	2	2	no	—
348	C₂×Q₈	—	2	2	no	—
349	C₂×Q₈	—	2	2	no	—
350	C₂×Q₈	C₂²×C₄×C₅	1	4	yes	—
351	C₂×Q₈	C₂×C₅×D₄	1	1	yes	characteristic
352	C₂×D₄	—	2	1	no	—
353	C₂×D₄	C₂×C₅×D₄	1	1	yes	characteristic
354	C₂²×C₄	—	2	1	no	—
355	C₂²×C₄	—	2	2	no	—
356	C₂²×C₄	—	2	2	no	—
357	C₂²×C₄	—	2	2	no	—
358	C₂²×C₄	C₅×#41	1	2	yes	—
359	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
360	Q₁₆	—	2	8	no	—
361	Q₁₆	—	2	4	no	—
362	Q₁₆	—	2	4	no	—
363	SD₁₆	—	2	8	no	—
364	M₁₆	—	2	4	no	—
365	M₁₆	—	2	1	no	—
366	M₁₆	—	2	1	no	—
367	M₁₆	—	2	2	no	—
368	M₁₆	—	2	4	no	—
369	M₁₆	—	2	2	no	—
370	M₁₆	—	2	2	no	—
371	M₁₆	C₂²×C₄×C₅	1	2	yes	—
372	M₁₆	C₂²×C₄×C₅	1	4	yes	—
373	M₁₆	C₅×#41	1	2	yes	—
374	C₂×C₈	—	2	4	no	—
375	C₂×C₈	—	2	1	no	—
376	C₂×C₈	—	2	1	no	—
377	C₂×C₈	—	2	2	no	—
378	C₂×C₈	—	2	1	no	—
379	C₂×C₈	—	2	1	no	—
380	C₂×C₈	—	2	4	no	—
381	C₂×C₈	—	2	2	no	—
382	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
383	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
384	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
385	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
386	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
387	C₂×C₈	C₅×#41	1	2	yes	—
388	C₄⋊C₄	—	2	2	no	—
389	C₄⋊C₄	—	2	2	no	—
390	C₄⋊C₄	—	2	2	no	—
391	C₄⋊C₄	—	4	2	no	—
392	C₄⋊C₄	—	4	2	no	—
393	C₄⋊C₄	C₂×C₅×D₄	1	2	yes	—
394	C₂²⋊C₄	—	2	1	no	—
395	C₂²⋊C₄	—	2	2	no	—
396	C₄²	—	2	2	no	—
397	C₄²	—	2	1	no	—
398	C₄²	—	4	2	no	—
399	C₄²	—	4	2	no	—
400	C₄²	C₂×C₅×D₄	1	2	yes	—
401	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
402	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
403	C₂×C₅	—	2	1	no	—
404	C₂×C₅	—	2	1	no	—
405	C₂×C₅	—	4	2	no	—
406	C₂×C₅	C₄×#121	1	1	yes	characteristic
407	C₂×C₅	#3069	1	2	yes	—
408	C₂³	—	2	1	no	—
409	C₂³	C₂×C₅×#41	1	1	yes	characteristic
410	Q₈	—	2	1	no	—
411	Q₈	—	2	4	no	—
412	Q₈	—	2	4	no	—
413	Q₈	—	4	2	no	—
414	Q₈	—	4	2	no	—
415	Q₈	C₄×C₅×D₄	1	2	yes	—
416	D₄	—	2	2	no	—
417	D₄	—	2	2	no	—
418	D₄	—	2	1	no	—
419	D₄	C₄×C₅×D₄	1	2	yes	—
420	C₂×C₄	—	2	1	no	—
421	C₂×C₄	—	2	2	no	—
422	C₂×C₄	—	2	2	no	—
423	C₂×C₄	—	2	4	no	—
424	C₂×C₄	—	2	2	no	—
425	C₂×C₄	—	4	2	no	—
426	C₂×C₄	—	4	2	no	—
427	C₂×C₄	—	4	2	no	—
428	C₂×C₄	—	4	2	no	—
429	C₂×C₄	—	8	2	no	—
430	C₂×C₄	—	8	2	no	—
431	C₂×C₄	C₅×#121	1	2	yes	—
432	C₂×C₄	C₅×#121	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	2	no	—
440	C₈	—	2	4	no	—
441	C₈	—	2	1	no	—
442	C₈	—	2	2	no	—
443	C₈	—	2	1	no	—
444	C₈	—	4	2	no	—
445	C₈	C₄×C₅×D₄	1	2	yes	—
446	C₈	C₄×C₅×D₄	1	2	yes	—
447	C₅	#21556	1	1	yes	characteristic, direct product factor, Sylow
448	C₂²	—	2	2	no	—
449	C₂²	—	2	2	no	—
450	C₂²	—	4	2	no	—
451	C₂²	C₄×C₅×#41	1	1	yes	characteristic
452	C₂²	C₂×C₅×#121	1	1	yes	characteristic
453	C₂²	C₅×#529	1	1	yes	characteristic
454	C₄	—	2	2	no	—
455	C₄	—	2	2	no	—
456	C₄	—	2	2	no	—
457	C₄	—	4	4	no	—
458	C₄	—	4	2	no	—
459	C₄	—	8	2	no	—
460	C₄	C₂×C₄×C₅×D₄	1	1	yes	characteristic
461	C₄	C₂×C₄×C₅×D₄	1	1	yes	characteristic
462	C₄	C₅×#525	1	1	yes	characteristic
463	C₄	C₅×#532	1	1	yes	characteristic
464	C₂	—	2	1	no	—
465	C₂	—	2	1	no	—
466	C₂	—	4	2	no	—
467	C₂	C₄×C₅×#121	1	1	yes	characteristic
468	C₂	C₅×#3069	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₅	C₂×#121
commutator	C₂×C₄	C₂³×C₄×C₅
Frattini, cosocle	C₂²×C₄	C₂⁴×C₅
prime radical	C₂×C₅×#41	C₂³
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ 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
3. C₂×C₅×#441	C₂	semidirect
5. C₅×#1979	C₂	semidirect
6. C₅×#1951	C₂	semidirect
7. C₅×#1930	C₂	semidirect
10. C₅×#1778	C₂	semidirect
11. C₄×C₅×#101	C₂	semidirect
18. C₅×#473	C₄	semidirect
48. #21556	C₅	direct (N × H)
57. C₂×C₅×Q₁₆	C₂×C₄	semidirect
88. C₅×#108	C₂×C₄	semidirect
100. C₅×#101	C₂×C₄	semidirect
115. C₂×#441	C₂×C₅	semidirect
117. #1979	C₂×C₅	semidirect
118. #1951	C₂×C₅	semidirect
119. #1930	C₂×C₅	semidirect
122. #1778	C₂×C₅	semidirect
123. C₄×#101	C₂×C₅	semidirect
192. #473	C₄×C₅	semidirect
269. C₂×Q₁₆	C₂×C₄×C₅	semidirect
300. #108	C₂×C₄×C₅	semidirect
312. #101	C₂×C₄×C₅	semidirect
447. C₅	#21556	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×#473	2
C₄×C₅×#137	2
C₂×C₅×#441	2
C₅×#2875	2
C₅×#1979	2
C₅×#1951	2
C₅×#1930	2
C₅×#1908	2
C₅×#1815	2
C₅×#1778	2
C₄×C₅×#101	2
#21556	5

Subgroups — C5×#21556 #11944276

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#21556 #11944276