Subgroups — C₅×#21731 #11944451

Order 1280.

802 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#501	C₂	1	1	yes	maximal, characteristic
2	C₄×C₅×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic
3	C₄×C₅×#125	C₂	1	1	yes	maximal, characteristic
4	C₅×#1993	C₂	1	1	yes	maximal, characteristic
5	C₅×#1992	C₂	1	1	yes	maximal, characteristic
6	C₅×#1942	C₂	1	2	yes	maximal
7	C₅×#1941	C₂	1	2	yes	maximal
8	C₅×#1847	C₂	1	1	yes	maximal, characteristic
9	C₅×#1776	C₂	1	2	yes	maximal
10	C₅×#1776	C₂	1	2	yes	maximal
11	C₄×C₅×#97	C₂	1	1	yes	maximal, characteristic
12	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
13	C₂×C₅×#125	C₂²	1	1	yes	characteristic
14	C₂×C₄×C₅×Q₈	—	2	1	no	—
15	C₅×#501	C₄	1	8	yes	complemented
16	C₂×C₅×#107	C₂²	1	2	yes	—
17	C₂×C₅×#107	C₂²	1	2	yes	—
18	C₂×C₅×#106	C₂²	1	2	yes	—
19	C₂×C₅×#106	C₂²	1	2	yes	—
20	C₂×C₅×#97	C₂²	1	1	yes	characteristic
21	C₂×C₅×#97	C₂²	1	1	yes	characteristic
22	C₂×C₅×#97	C₂²	1	2	yes	—
23	C₂×C₄×C₅×C₈	C₂²	1	2	yes	—
24	C₅×#391	—	2	1	no	—
25	C₅×#389	—	2	1	no	—
26	C₅×#389	C₂²	1	1	yes	characteristic
27	C₅×#389	C₂²	1	1	yes	characteristic
28	C₅×#389	C₂²	1	2	yes	—
29	C₅×#387	—	2	1	no	—
30	C₅×#387	—	2	1	no	—
31	C₅×#384	C₂²	1	1	yes	characteristic
32	C₅×#382	C₂²	1	1	yes	characteristic
33	C₄×C₅×C₄⋊C₄	—	2	1	no	—
34	C₄×C₅×C₄⋊C₄	—	2	1	no	—
35	C₄×C₅×C₄⋊C₄	—	2	1	no	—
36	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
37	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
38	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
39	C₄³×C₅	C₂²	1	1	yes	characteristic
40	C₅×#340	C₂²	1	2	yes	—
41	C₅×#340	C₂²	1	2	yes	—
42	C₅×#340	C₂²	1	2	yes	—
43	C₅×#340	C₂²	1	2	yes	—
44	#21731	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
45	C₂²×C₅×Q₈	—	2	1	no	—
46	C₂²×C₅×C₈	C₂³	1	2	yes	—
47	C₂²×C₅×C₈	C₂³	1	2	yes	—
48	C₅×C₄⋊Q₈	—	2	2	no	—
49	C₅×C₄⋊Q₈	C₂×C₄	1	4	yes	—
50	C₅×#125	—	2	2	no	—
51	C₅×#125	C₂×C₄	1	4	yes	—
52	C₄×C₅×Q₈	—	4	4	no	—
53	C₂×C₅×C₄⋊C₄	—	2	1	no	—
54	C₂×C₅×C₄⋊C₄	—	2	1	no	—
55	C₂×C₅×C₄⋊C₄	—	2	1	no	—
56	C₂×C₅×C₄⋊C₄	—	2	1	no	—
57	C₂×C₅×C₄⋊C₄	—	2	1	no	—
58	C₂×C₅×C₄⋊C₄	—	2	1	no	—
59	C₂×C₅×C₄⋊C₄	—	2	1	no	—
60	C₂×C₅×C₄⋊C₄	—	2	2	no	—
61	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
62	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
63	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
64	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
65	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
66	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
67	C₂×C₄²×C₅	—	2	1	no	—
68	C₂×C₄²×C₅	—	2	1	no	—
69	C₂×C₄²×C₅	—	2	2	no	—
70	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
71	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
72	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
73	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
74	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
75	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
76	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
77	C₅×#107	—	2	4	no	—
78	C₅×#107	C₂×C₄	1	8	yes	—
79	C₅×#106	—	2	4	no	—
80	C₅×#106	C₂×C₄	1	8	yes	—
81	C₅×#97	—	2	2	no	—
82	C₅×#97	C₂×C₄	1	4	yes	—
83	C₅×#97	Q₈	1	8	yes	complemented
84	C₄×C₅×C₈	—	2	4	no	—
85	C₅×#95	—	2	1	no	—
86	C₅×#95	—	2	1	no	—
87	C₅×#95	—	2	1	no	—
88	C₅×#95	—	2	1	no	—
89	C₅×#95	—	2	2	no	—
90	C₅×#95	—	2	1	no	—
91	C₅×#95	—	2	1	no	—
92	C₅×#95	—	2	2	no	—
93	C₂×#501	C₂×C₅	1	1	yes	characteristic
94	C₄×C₄⋊Q₈	C₂×C₅	1	1	yes	characteristic
95	C₄×#125	C₂×C₅	1	1	yes	characteristic
96	#1993	C₂×C₅	1	1	yes	characteristic
97	#1992	C₂×C₅	1	1	yes	characteristic
98	#1942	C₂×C₅	1	2	yes	—
99	#1941	C₂×C₅	1	2	yes	—
100	#1847	C₂×C₅	1	1	yes	characteristic
101	#1776	C₂×C₅	1	2	yes	—
102	#1776	C₂×C₅	1	2	yes	—
103	C₄×#97	C₂×C₅	1	1	yes	characteristic
104	C₂×C₅×Q₈	—	2	4	no	—
105	C₂×C₅×Q₈	—	4	2	no	—
106	C₂×C₅×Q₈	—	4	2	no	—
107	C₂²×C₄×C₅	—	2	1	no	—
108	C₂²×C₄×C₅	—	2	1	no	—
109	C₂²×C₄×C₅	—	2	2	no	—
110	C₂²×C₄×C₅	—	2	2	no	—
111	C₂²×C₄×C₅	—	2	1	no	—
112	C₂²×C₄×C₅	—	2	1	no	—
113	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
120	C₂×C₅×C₈	—	2	2	no	—
121	C₂×C₅×C₈	—	2	2	no	—
122	C₂×C₅×C₈	C₂²×C₄	1	4	yes	—
123	C₂×C₅×C₈	C₂×Q₈	1	4	yes	—
124	C₂×C₅×C₈	C₂×Q₈	1	4	yes	—
125	C₂×C₅×C₈	#41	1	4	yes	—
126	C₅×C₄⋊C₄	—	2	4	no	—
127	C₅×C₄⋊C₄	—	2	4	no	—
128	C₅×C₄⋊C₄	—	2	4	no	—
129	C₅×C₄⋊C₄	—	2	1	no	—
130	C₅×C₄⋊C₄	—	2	1	no	—
131	C₅×C₄⋊C₄	—	2	2	no	—
132	C₅×C₄⋊C₄	—	2	2	no	—
133	C₅×C₄⋊C₄	—	2	2	no	—
134	C₅×C₄⋊C₄	—	2	2	no	—
135	C₅×C₄⋊C₄	—	2	2	no	—
136	C₅×C₄⋊C₄	—	4	2	no	—
137	C₅×C₄⋊C₄	—	4	2	no	—
138	C₅×C₄⋊C₄	—	4	2	no	—
139	C₅×C₄⋊C₄	—	4	4	no	—
140	C₅×C₄⋊C₄	—	4	2	no	—
141	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
142	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
143	C₅×C₄⋊C₄	C₂²×C₄	1	4	yes	—
144	C₄²×C₅	—	2	2	no	—
145	C₄²×C₅	—	2	2	no	—
146	C₄²×C₅	—	2	2	no	—
147	C₄²×C₅	—	4	1	no	—
148	C₄²×C₅	—	4	1	no	—
149	C₄²×C₅	—	4	2	no	—
150	C₄²×C₅	—	4	2	no	—
151	C₄²×C₅	—	4	4	no	—
152	C₄²×C₅	C₂²×C₄	1	2	yes	—
153	C₄²×C₅	C₂×Q₈	1	4	yes	—
154	C₄²×C₅	#41	1	2	yes	—
155	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
156	C₂×#125	C₂²×C₅	1	1	yes	characteristic
157	C₂×C₄×Q₈	—	2	1	no	—
158	#501	C₄×C₅	1	8	yes	complemented
159	C₂×#107	C₂²×C₅	1	2	yes	—
160	C₂×#107	C₂²×C₅	1	2	yes	—
161	C₂×#106	C₂²×C₅	1	2	yes	—
162	C₂×#106	C₂²×C₅	1	2	yes	—
163	C₂×#97	C₂²×C₅	1	1	yes	characteristic
164	C₂×#97	C₂²×C₅	1	1	yes	characteristic
165	C₂×#97	C₂²×C₅	1	2	yes	—
166	C₂×C₄×C₈	C₂²×C₅	1	2	yes	—
167	#391	—	2	1	no	—
168	#389	—	2	1	no	—
169	#389	C₂²×C₅	1	1	yes	characteristic
170	#389	C₂²×C₅	1	1	yes	characteristic
171	#389	C₂²×C₅	1	2	yes	—
172	#387	—	2	1	no	—
173	#387	—	2	1	no	—
174	#384	C₂²×C₅	1	1	yes	characteristic
175	#382	C₂²×C₅	1	1	yes	characteristic
176	C₄×C₄⋊C₄	—	2	1	no	—
177	C₄×C₄⋊C₄	—	2	1	no	—
178	C₄×C₄⋊C₄	—	2	1	no	—
179	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
180	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
181	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
182	C₄³	C₂²×C₅	1	1	yes	characteristic
183	#340	C₂²×C₅	1	2	yes	—
184	#340	C₂²×C₅	1	2	yes	—
185	#340	C₂²×C₅	1	2	yes	—
186	#340	C₂²×C₅	1	2	yes	—
187	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
188	C₅×Q₈	—	4	8	no	—
189	C₂×C₄×C₅	—	2	1	no	—
190	C₂×C₄×C₅	—	2	1	no	—
191	C₂×C₄×C₅	—	2	1	no	—
192	C₂×C₄×C₅	—	2	1	no	—
193	C₂×C₄×C₅	—	2	1	no	—
194	C₂×C₄×C₅	—	2	1	no	—
195	C₂×C₄×C₅	—	2	1	no	—
196	C₂×C₄×C₅	—	2	1	no	—
197	C₂×C₄×C₅	—	2	1	no	—
198	C₂×C₄×C₅	—	2	1	no	—
199	C₂×C₄×C₅	—	2	1	no	—
200	C₂×C₄×C₅	—	2	1	no	—
201	C₂×C₄×C₅	—	2	2	no	—
202	C₂×C₄×C₅	—	2	2	no	—
203	C₂×C₄×C₅	—	2	4	no	—
204	C₂×C₄×C₅	—	4	2	no	—
205	C₂×C₄×C₅	—	4	1	no	—
206	C₂×C₄×C₅	—	4	1	no	—
207	C₂×C₄×C₅	—	4	1	no	—
208	C₂×C₄×C₅	—	4	1	no	—
209	C₂×C₄×C₅	—	4	2	no	—
210	C₂×C₄×C₅	—	4	2	no	—
211	C₂×C₄×C₅	—	4	1	no	—
212	C₂×C₄×C₅	—	4	1	no	—
213	C₂×C₄×C₅	—	4	2	no	—
214	C₂×C₄×C₅	—	4	1	no	—
215	C₂×C₄×C₅	—	4	1	no	—
216	C₂×C₄×C₅	—	4	1	no	—
217	C₂×C₄×C₅	—	4	1	no	—
218	C₂×C₄×C₅	—	4	2	no	—
219	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
220	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
221	C₂×C₄×C₅	C₄⋊Q₈	1	2	yes	—
222	C₂×C₄×C₅	C₄⋊Q₈	1	2	yes	—
223	C₂×C₄×C₅	AGL(1,ℤ/8)	1	2	yes	—
224	C₂×C₄×C₅	#137	1	2	yes	—
225	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
226	C₂×C₄×C₅	C₂²×Q₈	1	2	yes	—
227	C₂×C₄×C₅	C₂×#41	1	2	yes	—
228	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
229	C₅×C₈	—	2	4	no	—
230	C₅×C₈	C₄×Q₈	1	8	yes	complemented
231	C₂²×Q₈	—	2	1	no	—
232	C₂²×C₈	C₂³×C₅	1	2	yes	—
233	C₂²×C₈	C₂³×C₅	1	2	yes	—
234	C₄⋊Q₈	—	2	2	no	—
235	C₄⋊Q₈	C₂×C₄×C₅	1	4	yes	—
236	#125	—	2	2	no	—
237	#125	C₂×C₄×C₅	1	4	yes	—
238	C₄×Q₈	—	4	4	no	—
239	C₂×C₄⋊C₄	—	2	1	no	—
240	C₂×C₄⋊C₄	—	2	1	no	—
241	C₂×C₄⋊C₄	—	2	1	no	—
242	C₂×C₄⋊C₄	—	2	1	no	—
243	C₂×C₄⋊C₄	—	2	2	no	—
244	C₂×C₄⋊C₄	—	2	1	no	—
245	C₂×C₄⋊C₄	—	2	1	no	—
246	C₂×C₄⋊C₄	—	2	1	no	—
247	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
248	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
249	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
250	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
251	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
252	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
253	C₂×C₄²	—	2	2	no	—
254	C₂×C₄²	—	2	1	no	—
255	C₂×C₄²	—	2	1	no	—
256	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
257	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
258	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
259	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
260	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
261	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
262	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
263	#107	—	2	4	no	—
264	#107	C₂×C₄×C₅	1	8	yes	—
265	#106	—	2	4	no	—
266	#106	C₂×C₄×C₅	1	8	yes	—
267	#97	—	2	2	no	—
268	#97	C₂×C₄×C₅	1	4	yes	—
269	#97	C₅×Q₈	1	8	yes	complemented
270	C₄×C₈	—	2	4	no	—
271	#95	—	2	1	no	—
272	#95	—	2	1	no	—
273	#95	—	2	1	no	—
274	#95	—	2	1	no	—
275	#95	—	2	2	no	—
276	#95	—	2	1	no	—
277	#95	—	2	1	no	—
278	#95	—	2	2	no	—
279	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
280	C₂²×C₅	C₂×C₄⋊Q₈	1	1	yes	characteristic
281	C₂²×C₅	#532	1	1	yes	characteristic
282	C₂²×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
283	C₂²×C₅	C₂×#137	1	1	yes	characteristic
284	C₂²×C₅	#575	1	1	yes	characteristic
285	C₂²×C₅	#575	1	1	yes	characteristic
286	C₄×C₅	—	2	2	no	—
287	C₄×C₅	—	2	2	no	—
288	C₄×C₅	—	2	2	no	—
289	C₄×C₅	—	2	2	no	—
290	C₄×C₅	—	2	2	no	—
291	C₄×C₅	—	2	2	no	—
292	C₄×C₅	—	4	2	no	—
293	C₄×C₅	—	4	4	no	—
294	C₄×C₅	—	4	2	no	—
295	C₄×C₅	—	8	2	no	—
296	C₄×C₅	—	8	1	no	—
297	C₄×C₅	—	8	1	no	—
298	C₄×C₅	C₂×C₄×Q₈	1	2	yes	—
299	C₄×C₅	#533	1	2	yes	—
300	C₂×Q₈	—	2	4	no	—
301	C₂×Q₈	—	4	2	no	—
302	C₂×Q₈	—	4	2	no	—
303	C₂²×C₄	—	2	1	no	—
304	C₂²×C₄	—	2	1	no	—
305	C₂²×C₄	—	2	2	no	—
306	C₂²×C₄	—	2	1	no	—
307	C₂²×C₄	—	2	1	no	—
308	C₂²×C₄	—	2	2	no	—
309	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
310	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
311	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
312	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
313	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
314	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
315	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
316	C₂×C₈	—	2	2	no	—
317	C₂×C₈	—	2	2	no	—
318	C₂×C₈	C₂²×C₄×C₅	1	4	yes	—
319	C₂×C₈	C₂×C₅×Q₈	1	4	yes	—
320	C₂×C₈	C₂×C₅×Q₈	1	4	yes	—
321	C₂×C₈	C₅×#41	1	4	yes	—
322	C₄⋊C₄	—	2	4	no	—
323	C₄⋊C₄	—	2	4	no	—
324	C₄⋊C₄	—	2	4	no	—
325	C₄⋊C₄	—	2	1	no	—
326	C₄⋊C₄	—	2	1	no	—
327	C₄⋊C₄	—	2	2	no	—
328	C₄⋊C₄	—	2	2	no	—
329	C₄⋊C₄	—	2	2	no	—
330	C₄⋊C₄	—	2	2	no	—
331	C₄⋊C₄	—	2	2	no	—
332	C₄⋊C₄	—	4	2	no	—
333	C₄⋊C₄	—	4	2	no	—
334	C₄⋊C₄	—	4	4	no	—
335	C₄⋊C₄	—	4	2	no	—
336	C₄⋊C₄	—	4	2	no	—
337	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
338	C₄⋊C₄	C₂²×C₄×C₅	1	4	yes	—
339	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
340	C₄²	—	2	2	no	—
341	C₄²	—	2	2	no	—
342	C₄²	—	2	2	no	—
343	C₄²	—	4	1	no	—
344	C₄²	—	4	1	no	—
345	C₄²	—	4	4	no	—
346	C₄²	—	4	2	no	—
347	C₄²	—	4	2	no	—
348	C₄²	C₂²×C₄×C₅	1	2	yes	—
349	C₄²	C₂×C₅×Q₈	1	4	yes	—
350	C₄²	C₅×#41	1	2	yes	—
351	C₂×C₅	C₄×C₄⋊Q₈	1	1	yes	characteristic
352	C₂×C₅	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic
353	C₂×C₅	C₄×#137	1	1	yes	characteristic
354	C₂×C₅	#3165	1	1	yes	characteristic
355	C₂×C₅	#3166	1	1	yes	characteristic
356	C₂×C₅	#3180	1	1	yes	characteristic
357	C₂×C₅	#3181	1	1	yes	characteristic
358	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
359	Q₈	—	4	8	no	—
360	C₂×C₄	—	2	1	no	—
361	C₂×C₄	—	2	1	no	—
362	C₂×C₄	—	2	1	no	—
363	C₂×C₄	—	2	1	no	—
364	C₂×C₄	—	2	1	no	—
365	C₂×C₄	—	2	1	no	—
366	C₂×C₄	—	2	1	no	—
367	C₂×C₄	—	2	1	no	—
368	C₂×C₄	—	2	1	no	—
369	C₂×C₄	—	2	1	no	—
370	C₂×C₄	—	2	1	no	—
371	C₂×C₄	—	2	1	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	2	4	no	—
375	C₂×C₄	—	4	2	no	—
376	C₂×C₄	—	4	1	no	—
377	C₂×C₄	—	4	1	no	—
378	C₂×C₄	—	4	1	no	—
379	C₂×C₄	—	4	1	no	—
380	C₂×C₄	—	4	2	no	—
381	C₂×C₄	—	4	2	no	—
382	C₂×C₄	—	4	1	no	—
383	C₂×C₄	—	4	1	no	—
384	C₂×C₄	—	4	2	no	—
385	C₂×C₄	—	4	1	no	—
386	C₂×C₄	—	4	1	no	—
387	C₂×C₄	—	4	1	no	—
388	C₂×C₄	—	4	1	no	—
389	C₂×C₄	—	4	2	no	—
390	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
391	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
392	C₂×C₄	C₅×C₄⋊Q₈	1	2	yes	—
393	C₂×C₄	C₅×C₄⋊Q₈	1	2	yes	—
394	C₂×C₄	C₅×AGL(1,ℤ/8)	1	2	yes	—
395	C₂×C₄	C₅×#137	1	2	yes	—
396	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
397	C₂×C₄	C₂²×C₅×Q₈	1	2	yes	—
398	C₂×C₄	C₂×C₅×#41	1	2	yes	—
399	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
400	C₈	—	2	4	no	—
401	C₈	C₄×C₅×Q₈	1	8	yes	complemented
402	C₅	#21731	1	1	yes	characteristic, direct product factor, Sylow
403	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
404	C₂²	C₂×C₅×C₄⋊Q₈	1	1	yes	characteristic
405	C₂²	C₅×#532	1	1	yes	characteristic
406	C₂²	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
407	C₂²	C₂×C₅×#137	1	1	yes	characteristic
408	C₂²	C₅×#575	1	1	yes	characteristic
409	C₂²	C₅×#575	1	1	yes	characteristic
410	C₄	—	2	2	no	—
411	C₄	—	2	2	no	—
412	C₄	—	2	2	no	—
413	C₄	—	2	2	no	—
414	C₄	—	2	2	no	—
415	C₄	—	2	2	no	—
416	C₄	—	4	4	no	—
417	C₄	—	4	2	no	—
418	C₄	—	4	2	no	—
419	C₄	—	8	2	no	—
420	C₄	—	8	1	no	—
421	C₄	—	8	1	no	—
422	C₄	C₂×C₄×C₅×Q₈	1	2	yes	—
423	C₄	C₅×#533	1	2	yes	—
424	C₂	C₄×C₅×C₄⋊Q₈	1	1	yes	characteristic
425	C₂	C₄×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
426	C₂	C₄×C₅×#137	1	1	yes	characteristic
427	C₂	C₅×#3165	1	1	yes	characteristic
428	C₂	C₅×#3166	1	1	yes	characteristic
429	C₂	C₅×#3180	1	1	yes	characteristic
430	C₂	C₅×#3181	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂³×C₅	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₅
Frattini, cosocle	C₂²×C₄	C₂⁴×C₅
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₅ ◁ C₄³×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
15. C₅×#501	C₄	semidirect
44. #21731	C₅	direct (N × H)
83. C₅×#97	Q₈	semidirect
158. #501	C₄×C₅	semidirect
230. C₅×C₈	C₄×Q₈	semidirect
269. #97	C₅×Q₈	semidirect
401. C₈	C₄×C₅×Q₈	semidirect
402. C₅	#21731	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×#501	2
C₄×C₅×C₄⋊Q₈	2
C₄×C₅×#125	2
C₅×#1993	2
C₅×#1992	2
C₅×#1942	2
C₅×#1941	2
C₅×#1847	2
C₅×#1776	2
C₄×C₅×#97	2
#21731	5

Subgroups — C5×#21731 #11944451

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#21731 #11944451