Subgroups — C₅×#21527 #11944247

Order 1280.

1014 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#467	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#441	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₅×#97	C₂	1	1	yes	maximal, characteristic
4	C₄×C₅×C₂²⋊Q₈	C₂	1	2	yes	maximal
5	C₅×#1971	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#1943	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#1935	C₂	1	2	yes	maximal, complemented
8	C₅×#1892	C₂	1	2	yes	maximal
9	C₅×#1807	C₂	1	1	yes	maximal, characteristic
10	C₅×#1776	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1763	C₂	1	2	yes	maximal, complemented
12	C₂²×C₅×Q₁₆	C₂²	1	1	yes	characteristic
13	C₂³×C₅×C₈	C₂²	1	1	yes	characteristic
14	C₂³×C₅×C₈	C₂²	1	1	yes	characteristic
15	C₂×C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
16	C₂×C₄×C₅×Q₈	C₂²	1	2	yes	—
17	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
18	C₅×#467	C₄	1	8	yes	complemented
19	C₅×#441	—	2	4	no	—
20	C₂×C₅×#107	C₂²	1	1	yes	characteristic
21	C₂×C₅×#106	C₂²	1	1	yes	characteristic
22	C₂×C₅×#106	C₂²	1	1	yes	characteristic
23	C₂×C₅×#103	C₂²	1	2	yes	—
24	C₂×C₅×#103	C₂²	1	2	yes	—
25	C₂×C₅×#103	C₂²	1	2	yes	—
26	C₂×C₅×#97	—	2	4	no	—
27	C₂×C₅×#97	C₂²	1	1	yes	characteristic
28	C₂×C₅×#97	C₂²	1	1	yes	characteristic
29	C₂×C₅×#97	C₂²	1	1	yes	characteristic
30	C₂×C₅×#97	C₂²	1	1	yes	characteristic
31	C₅×#391	C₂²	1	2	yes	—
32	C₅×#389	C₂²	1	2	yes	—
33	C₅×#387	—	2	2	no	—
34	C₅×#385	—	2	2	no	—
35	C₅×#380	C₂²	1	2	yes	—
36	C₄×C₅×C₄⋊C₄	—	2	2	no	—
37	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
38	C₄×C₅×C₂²⋊C₄	—	2	2	no	—
39	C₅×#340	C₂²	1	2	yes	—
40	C₅×#340	C₂²	1	2	yes	—
41	C₅×#340	C₂²	1	2	yes	—
42	#21527	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
43	C₂²×C₅×Q₈	C₂³	1	2	yes	—
44	C₂³×C₄×C₅	D₄	1	2	yes	—
45	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
46	C₂×C₅×Q₁₆	—	2	2	no	—
47	C₂×C₅×Q₁₆	—	2	2	no	—
48	C₂×C₅×Q₁₆	C₂×C₄	1	4	yes	complemented
49	C₂²×C₅×C₈	—	2	2	no	—
50	C₂²×C₅×C₈	—	2	2	no	—
51	C₂²×C₅×C₈	—	2	2	no	—
52	C₂²×C₅×C₈	—	2	2	no	—
53	C₂²×C₅×C₈	—	2	2	no	—
54	C₂²×C₅×C₈	C₂×C₄	1	4	yes	—
55	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
56	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
57	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
58	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
59	C₅×C₂²⋊Q₈	—	2	4	no	—
60	C₅×C₂²⋊Q₈	C₂×C₄	1	8	yes	—
61	C₄×C₅×Q₈	—	2	4	no	—
62	C₄×C₅×Q₈	—	2	4	no	—
63	C₂×C₅×C₄⋊C₄	—	2	2	no	—
64	C₂×C₅×C₄⋊C₄	—	2	2	no	—
65	C₂×C₅×C₄⋊C₄	—	2	2	no	—
66	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
67	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
68	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
69	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
70	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
71	C₂×C₄²×C₅	—	2	2	no	—
72	C₂×C₄²×C₅	—	2	2	no	—
73	C₂×C₄²×C₅	—	2	2	no	—
74	C₂×C₄²×C₅	—	2	2	no	—
75	C₂×C₄²×C₅	D₄	1	2	yes	—
76	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
77	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
78	C₅×#107	C₂×C₄	1	4	yes	complemented
79	C₅×#106	—	2	2	no	—
80	C₅×#106	—	2	2	no	—
81	C₅×#103	—	2	4	no	—
82	C₅×#103	—	2	4	no	—
83	C₅×#103	C₂×C₄	1	8	yes	complemented
84	C₅×#97	—	2	2	no	—
85	C₅×#97	—	2	2	no	—
86	C₅×#97	—	2	2	no	—
87	C₅×#97	D₄	1	4	yes	—
88	C₅×#95	—	2	2	no	—
89	C₅×#95	—	2	2	no	—
90	C₅×#95	—	2	2	no	—
91	C₅×#95	—	2	2	no	—
92	C₅×#95	—	2	2	no	—
93	C₂×#467	C₂×C₅	1	1	yes	characteristic
94	C₂×#441	C₂×C₅	1	1	yes	characteristic, complemented
95	C₂²×#97	C₂×C₅	1	1	yes	characteristic
96	C₄×C₂²⋊Q₈	C₂×C₅	1	2	yes	—
97	#1971	C₂×C₅	1	1	yes	characteristic, complemented
98	#1943	C₂×C₅	1	1	yes	characteristic, complemented
99	#1935	C₂×C₅	1	2	yes	complemented
100	#1892	C₂×C₅	1	2	yes	—
101	#1807	C₂×C₅	1	1	yes	characteristic
102	#1776	C₂×C₅	1	1	yes	characteristic, complemented
103	#1763	C₂×C₅	1	2	yes	complemented
104	C₂⁴×C₅	C₂×D₄	1	1	yes	characteristic
105	C₂×C₅×Q₈	—	2	2	no	—
106	C₂×C₅×Q₈	—	2	2	no	—
107	C₂×C₅×Q₈	—	2	2	no	—
108	C₂×C₅×Q₈	—	2	2	no	—
109	C₂×C₅×Q₈	—	2	2	no	—
110	C₂×C₅×Q₈	C₂²×C₄	1	4	yes	—
111	C₂²×C₄×C₅	—	2	1	no	—
112	C₂²×C₄×C₅	—	2	1	no	—
113	C₂²×C₄×C₅	—	2	1	no	—
114	C₂²×C₄×C₅	—	2	1	no	—
115	C₂²×C₄×C₅	—	2	4	no	—
116	C₂²×C₄×C₅	—	2	2	no	—
117	C₂²×C₄×C₅	—	2	2	no	—
118	C₂²×C₄×C₅	—	2	4	no	—
119	C₂²×C₄×C₅	—	2	2	no	—
120	C₂²×C₄×C₅	—	2	2	no	—
121	C₂²×C₄×C₅	—	4	2	no	—
122	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
123	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
124	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
125	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
126	C₂²×C₄×C₅	#41	1	2	yes	—
127	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
128	C₅×Q₁₆	—	2	8	no	—
129	C₂×C₅×C₈	—	2	8	no	—
130	C₂×C₅×C₈	—	2	1	no	—
131	C₂×C₅×C₈	—	2	1	no	—
132	C₂×C₅×C₈	—	2	1	no	—
133	C₂×C₅×C₈	—	2	1	no	—
134	C₂×C₅×C₈	—	2	1	no	—
135	C₂×C₅×C₈	—	2	1	no	—
136	C₂×C₅×C₈	—	2	8	no	—
137	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
138	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
139	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
140	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
141	C₂×C₅×C₈	#41	1	2	yes	—
142	C₂×C₅×C₈	#41	1	2	yes	—
143	C₅×C₄⋊C₄	—	2	8	no	—
144	C₅×C₄⋊C₄	—	2	2	no	—
145	C₅×C₄⋊C₄	—	2	2	no	—
146	C₅×C₄⋊C₄	—	2	2	no	—
147	C₅×C₄⋊C₄	—	2	2	no	—
148	C₅×C₄⋊C₄	—	2	2	no	—
149	C₅×C₄⋊C₄	—	4	4	no	—
150	C₅×C₄⋊C₄	—	4	4	no	—
151	C₅×C₄⋊C₄	C₂²×C₄	1	4	yes	—
152	C₅×C₂²⋊C₄	—	2	8	no	—
153	C₅×C₂²⋊C₄	—	4	4	no	—
154	C₄²×C₅	—	2	4	no	—
155	C₄²×C₅	—	2	1	no	—
156	C₄²×C₅	—	2	1	no	—
157	C₄²×C₅	—	4	4	no	—
158	C₄²×C₅	—	4	4	no	—
159	C₄²×C₅	C₂×D₄	1	2	yes	—
160	C₄²×C₅	#41	1	2	yes	—
161	C₂²×Q₁₆	C₂²×C₅	1	1	yes	characteristic
162	C₂³×C₈	C₂²×C₅	1	1	yes	characteristic
163	C₂³×C₈	C₂²×C₅	1	1	yes	characteristic
164	C₂×C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
165	C₂×C₄×Q₈	C₂²×C₅	1	2	yes	—
166	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
167	#467	C₄×C₅	1	8	yes	complemented
168	#441	—	2	4	no	—
169	C₂×#107	C₂²×C₅	1	1	yes	characteristic
170	C₂×#106	C₂²×C₅	1	1	yes	characteristic
171	C₂×#106	C₂²×C₅	1	1	yes	characteristic
172	C₂×#103	C₂²×C₅	1	2	yes	—
173	C₂×#103	C₂²×C₅	1	2	yes	—
174	C₂×#103	C₂²×C₅	1	2	yes	—
175	C₂×#97	—	2	4	no	—
176	C₂×#97	C₂²×C₅	1	1	yes	characteristic
177	C₂×#97	C₂²×C₅	1	1	yes	characteristic
178	C₂×#97	C₂²×C₅	1	1	yes	characteristic
179	C₂×#97	C₂²×C₅	1	1	yes	characteristic
180	#391	C₂²×C₅	1	2	yes	—
181	#389	C₂²×C₅	1	2	yes	—
182	#387	—	2	2	no	—
183	#385	—	2	2	no	—
184	#380	C₂²×C₅	1	2	yes	—
185	C₄×C₄⋊C₄	—	2	2	no	—
186	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
187	C₄×C₂²⋊C₄	—	2	2	no	—
188	#340	C₂²×C₅	1	2	yes	—
189	#340	C₂²×C₅	1	2	yes	—
190	#340	C₂²×C₅	1	2	yes	—
191	C₂³×C₅	—	2	1	no	—
192	C₂³×C₅	—	2	1	no	—
193	C₂³×C₅	—	2	2	no	—
194	C₂³×C₅	C₄×D₄	1	2	yes	—
195	C₂³×C₅	#137	1	4	yes	—
196	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
197	C₅×Q₈	—	2	4	no	—
198	C₅×Q₈	—	2	4	no	—
199	C₅×Q₈	—	4	2	no	—
200	C₅×Q₈	—	4	2	no	—
201	C₂×C₄×C₅	—	2	1	no	—
202	C₂×C₄×C₅	—	2	1	no	—
203	C₂×C₄×C₅	—	2	2	no	—
204	C₂×C₄×C₅	—	2	2	no	—
205	C₂×C₄×C₅	—	2	2	no	—
206	C₂×C₄×C₅	—	2	2	no	—
207	C₂×C₄×C₅	—	2	2	no	—
208	C₂×C₄×C₅	—	2	2	no	—
209	C₂×C₄×C₅	—	2	4	no	—
210	C₂×C₄×C₅	—	2	4	no	—
211	C₂×C₄×C₅	—	2	2	no	—
212	C₂×C₄×C₅	—	2	2	no	—
213	C₂×C₄×C₅	—	2	2	no	—
214	C₂×C₄×C₅	—	4	8	no	—
215	C₂×C₄×C₅	—	4	2	no	—
216	C₂×C₄×C₅	—	4	2	no	—
217	C₂×C₄×C₅	—	4	2	no	—
218	C₂×C₄×C₅	—	4	2	no	—
219	C₂×C₄×C₅	—	4	2	no	—
220	C₂×C₄×C₅	—	4	2	no	—
221	C₂×C₄×C₅	—	4	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	C₄×D₄	1	2	yes	—
226	C₂×C₄×C₅	#121	1	4	yes	—
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	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	C₅×C₈	—	2	2	no	—
234	C₅×C₈	—	2	2	no	—
235	C₅×C₈	—	2	2	no	—
236	C₅×C₈	C₄×D₄	1	4	yes	—
237	C₂²×Q₈	C₂³×C₅	1	2	yes	—
238	C₂³×C₄	C₅×D₄	1	2	yes	—
239	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
240	C₂×Q₁₆	—	2	2	no	—
241	C₂×Q₁₆	—	2	2	no	—
242	C₂×Q₁₆	C₂×C₄×C₅	1	4	yes	complemented
243	C₂²×C₈	—	2	2	no	—
244	C₂²×C₈	—	2	2	no	—
245	C₂²×C₈	—	2	2	no	—
246	C₂²×C₈	—	2	2	no	—
247	C₂²×C₈	—	2	2	no	—
248	C₂²×C₈	C₂×C₄×C₅	1	4	yes	—
249	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
250	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
251	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
252	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
253	C₂²⋊Q₈	—	2	4	no	—
254	C₂²⋊Q₈	C₂×C₄×C₅	1	8	yes	—
255	C₄×Q₈	—	2	4	no	—
256	C₄×Q₈	—	2	4	no	—
257	C₂×C₄⋊C₄	—	2	2	no	—
258	C₂×C₄⋊C₄	—	2	2	no	—
259	C₂×C₄⋊C₄	—	2	2	no	—
260	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
261	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
262	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
263	C₂×C₂²⋊C₄	—	2	2	no	—
264	C₂×C₂²⋊C₄	—	2	2	no	—
265	C₂×C₄²	—	2	2	no	—
266	C₂×C₄²	—	2	2	no	—
267	C₂×C₄²	—	2	2	no	—
268	C₂×C₄²	—	2	2	no	—
269	C₂×C₄²	C₅×D₄	1	2	yes	—
270	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
271	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
272	#107	C₂×C₄×C₅	1	4	yes	complemented
273	#106	—	2	2	no	—
274	#106	—	2	2	no	—
275	#103	—	2	4	no	—
276	#103	—	2	4	no	—
277	#103	C₂×C₄×C₅	1	8	yes	complemented
278	#97	—	2	2	no	—
279	#97	—	2	2	no	—
280	#97	—	2	2	no	—
281	#97	C₅×D₄	1	4	yes	—
282	#95	—	2	2	no	—
283	#95	—	2	2	no	—
284	#95	—	2	2	no	—
285	#95	—	2	2	no	—
286	#95	—	2	2	no	—
287	C₂²×C₅	—	2	4	no	—
288	C₂²×C₅	—	2	2	no	—
289	C₂²×C₅	—	2	4	no	—
290	C₂²×C₅	—	2	2	no	—
291	C₂²×C₅	#441	1	4	yes	complemented
292	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
293	C₂²×C₅	C₂×#121	1	1	yes	characteristic
294	C₂²×C₅	#532	1	1	yes	characteristic
295	C₂²×C₅	C₂×#137	1	2	yes	—
296	C₂²×C₅	#575	1	2	yes	—
297	C₄×C₅	—	2	4	no	—
298	C₄×C₅	—	2	2	no	—
299	C₄×C₅	—	4	4	no	—
300	C₄×C₅	—	4	2	no	—
301	C₄×C₅	—	4	4	no	—
302	C₄×C₅	—	8	2	no	—
303	C₄×C₅	—	8	2	no	—
304	C₄×C₅	C₂×C₄×D₄	1	1	yes	characteristic
305	C₄×C₅	C₄×#41	1	1	yes	characteristic
306	C₄×C₅	#525	1	1	yes	characteristic
307	C₄×C₅	#529	1	1	yes	characteristic
308	C₂⁴	C₂×C₅×D₄	1	1	yes	characteristic
309	C₂×Q₈	—	2	2	no	—
310	C₂×Q₈	—	2	2	no	—
311	C₂×Q₈	—	2	2	no	—
312	C₂×Q₈	—	2	2	no	—
313	C₂×Q₈	—	2	2	no	—
314	C₂×Q₈	C₂²×C₄×C₅	1	4	yes	—
315	C₂²×C₄	—	2	1	no	—
316	C₂²×C₄	—	2	1	no	—
317	C₂²×C₄	—	2	1	no	—
318	C₂²×C₄	—	2	1	no	—
319	C₂²×C₄	—	2	4	no	—
320	C₂²×C₄	—	2	2	no	—
321	C₂²×C₄	—	2	2	no	—
322	C₂²×C₄	—	2	4	no	—
323	C₂²×C₄	—	2	2	no	—
324	C₂²×C₄	—	2	2	no	—
325	C₂²×C₄	—	4	2	no	—
326	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
327	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
328	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
329	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
330	C₂²×C₄	C₅×#41	1	2	yes	—
331	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
332	Q₁₆	—	2	8	no	—
333	C₂×C₈	—	2	8	no	—
334	C₂×C₈	—	2	1	no	—
335	C₂×C₈	—	2	1	no	—
336	C₂×C₈	—	2	1	no	—
337	C₂×C₈	—	2	1	no	—
338	C₂×C₈	—	2	1	no	—
339	C₂×C₈	—	2	1	no	—
340	C₂×C₈	—	2	8	no	—
341	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
342	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
343	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
344	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
345	C₂×C₈	C₅×#41	1	2	yes	—
346	C₂×C₈	C₅×#41	1	2	yes	—
347	C₄⋊C₄	—	2	8	no	—
348	C₄⋊C₄	—	2	2	no	—
349	C₄⋊C₄	—	2	2	no	—
350	C₄⋊C₄	—	2	2	no	—
351	C₄⋊C₄	—	2	2	no	—
352	C₄⋊C₄	—	2	2	no	—
353	C₄⋊C₄	—	4	4	no	—
354	C₄⋊C₄	—	4	4	no	—
355	C₄⋊C₄	C₂²×C₄×C₅	1	4	yes	—
356	C₂²⋊C₄	—	2	8	no	—
357	C₂²⋊C₄	—	4	4	no	—
358	C₄²	—	2	4	no	—
359	C₄²	—	2	1	no	—
360	C₄²	—	2	1	no	—
361	C₄²	—	4	4	no	—
362	C₄²	—	4	4	no	—
363	C₄²	C₂×C₅×D₄	1	2	yes	—
364	C₄²	C₅×#41	1	2	yes	—
365	C₂×C₅	—	2	4	no	—
366	C₂×C₅	C₄×#121	1	1	yes	characteristic
367	C₂×C₅	C₂×#441	1	1	yes	characteristic
368	C₂×C₅	#2943	1	1	yes	characteristic
369	C₂×C₅	#3056	1	2	yes	—
370	C₂×C₅	#3181	1	2	yes	—
371	C₂³	—	2	1	no	—
372	C₂³	—	2	1	no	—
373	C₂³	—	2	2	no	—
374	C₂³	C₄×C₅×D₄	1	2	yes	—
375	C₂³	C₅×#137	1	4	yes	—
376	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
377	Q₈	—	2	4	no	—
378	Q₈	—	2	4	no	—
379	Q₈	—	4	2	no	—
380	Q₈	—	4	2	no	—
381	C₂×C₄	—	2	1	no	—
382	C₂×C₄	—	2	1	no	—
383	C₂×C₄	—	2	2	no	—
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	2	4	no	—
390	C₂×C₄	—	2	4	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	4	8	no	—
395	C₂×C₄	—	4	2	no	—
396	C₂×C₄	—	4	2	no	—
397	C₂×C₄	—	4	2	no	—
398	C₂×C₄	—	4	2	no	—
399	C₂×C₄	—	4	2	no	—
400	C₂×C₄	—	4	2	no	—
401	C₂×C₄	—	4	2	no	—
402	C₂×C₄	—	4	2	no	—
403	C₂×C₄	—	4	2	no	—
404	C₂×C₄	—	4	2	no	—
405	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
406	C₂×C₄	C₅×#121	1	4	yes	—
407	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
408	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
409	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
410	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
411	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
412	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
413	C₈	—	2	2	no	—
414	C₈	—	2	2	no	—
415	C₈	—	2	2	no	—
416	C₈	C₄×C₅×D₄	1	4	yes	—
417	C₅	#21527	1	1	yes	characteristic, direct product factor, Sylow
418	C₂²	—	2	4	no	—
419	C₂²	—	2	2	no	—
420	C₂²	—	2	4	no	—
421	C₂²	—	2	2	no	—
422	C₂²	C₅×#441	1	4	yes	complemented
423	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
424	C₂²	C₂×C₅×#121	1	1	yes	characteristic
425	C₂²	C₅×#532	1	1	yes	characteristic
426	C₂²	C₂×C₅×#137	1	2	yes	—
427	C₂²	C₅×#575	1	2	yes	—
428	C₄	—	2	4	no	—
429	C₄	—	2	2	no	—
430	C₄	—	4	2	no	—
431	C₄	—	4	4	no	—
432	C₄	—	4	4	no	—
433	C₄	—	8	2	no	—
434	C₄	—	8	2	no	—
435	C₄	C₂×C₄×C₅×D₄	1	1	yes	characteristic
436	C₄	C₄×C₅×#41	1	1	yes	characteristic
437	C₄	C₅×#525	1	1	yes	characteristic
438	C₄	C₅×#529	1	1	yes	characteristic
439	C₂	—	2	4	no	—
440	C₂	C₄×C₅×#121	1	1	yes	characteristic
441	C₂	C₂×C₅×#441	1	1	yes	characteristic
442	C₂	C₅×#2943	1	1	yes	characteristic
443	C₂	C₅×#3056	1	2	yes	—
444	C₂	C₅×#3181	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₅	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₅
Frattini, cosocle	C₂²×C₄	C₂⁴×C₅
prime radical	C₂⁴×C₅	C₂×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₅ ◁ C₂²×C₄²×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₅×#441	C₂	semidirect
5. C₅×#1971	C₂	semidirect
6. C₅×#1943	C₂	semidirect
7. C₅×#1935	C₂	semidirect
10. C₅×#1776	C₂	semidirect
11. C₅×#1763	C₂	semidirect
18. C₅×#467	C₄	semidirect
42. #21527	C₅	direct (N × H)
48. C₂×C₅×Q₁₆	C₂×C₄	semidirect
78. C₅×#107	C₂×C₄	semidirect
83. C₅×#103	C₂×C₄	semidirect
94. C₂×#441	C₂×C₅	semidirect
97. #1971	C₂×C₅	semidirect
98. #1943	C₂×C₅	semidirect
99. #1935	C₂×C₅	semidirect
102. #1776	C₂×C₅	semidirect
103. #1763	C₂×C₅	semidirect
167. #467	C₄×C₅	semidirect
242. C₂×Q₁₆	C₂×C₄×C₅	semidirect
272. #107	C₂×C₄×C₅	semidirect
277. #103	C₂×C₄×C₅	semidirect
291. C₂²×C₅	#441	semidirect
417. C₅	#21527	direct (N × H)
422. C₂²	C₅×#441	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×#467	2
C₂×C₅×#441	2
C₂²×C₅×#97	2
C₄×C₅×C₂²⋊Q₈	2
C₅×#1971	2
C₅×#1943	2
C₅×#1935	2
C₅×#1892	2
C₅×#1807	2
C₅×#1776	2
C₅×#1763	2
#21527	5

Subgroups — C5×#21527 #11944247

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#21527 #11944247