Subgroups — C₅×#17893 #11940613

Order 1280.

684 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	C₅×#2989	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#2975	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×C₅×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic
4	C₅×#1594	C₂	1	2	yes	maximal, complemented
5	C₅×#1592	C₂	1	2	yes	maximal, complemented
6	C₅×#1590	C₂	1	2	yes	maximal, complemented
7	C₅×#1589	C₂	1	2	yes	maximal, complemented
8	C₅×#1565	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1476	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₅×D₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×C₈×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₅×AGL(1,ℤ/8)	C₄	1	1	yes	characteristic
13	C₄×C₅×#41	C₂²	1	1	yes	characteristic
14	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
15	C₅×#446	C₂²	1	2	yes	complemented
16	C₅×#442	C₄	1	2	yes	—
17	C₅×#440	C₄	1	2	yes	—
18	C₄×C₅×SD₁₆	C₂²	1	2	yes	—
19	C₄×C₅×D₈	C₂²	1	2	yes	—
20	C₅×#436	—	2	1	no	—
21	C₅×#436	—	2	1	no	—
22	C₅×#436	C₂²	1	2	yes	—
23	C₅×#436	C₂²	1	2	yes	—
24	C₅×#436	C₂²	1	2	yes	complemented
25	C₅×#435	—	2	2	no	—
26	C₅×#432	—	2	1	no	—
27	C₅×#431	C₂²	1	1	yes	characteristic
28	C₅×#431	C₂²	1	1	yes	characteristic
29	C₅×#428	C₄	1	1	yes	characteristic
30	C₅×#423	—	2	1	no	—
31	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
32	C₅×#418	C₄	1	1	yes	characteristic
33	C₅×#417	C₄	1	1	yes	characteristic
34	C₅×#407	—	2	2	no	—
35	C₄×C₅×M₁₆	C₂²	1	1	yes	characteristic
36	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
37	C₅×#335	C₂²	1	2	yes	complemented
38	C₅×#334	C₂²	1	2	yes	complemented
39	C₅×Q₈⋊C₈	C₂²	1	1	yes	characteristic, complemented
40	C₅×Q₈⋊C₈	C₂²	1	1	yes	characteristic, complemented
41	C₅×D₄⋊C₈	C₂²	1	2	yes	—
42	C₅×D₄⋊C₈	C₂²	1	2	yes	—
43	C₅×D₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
44	C₅×D₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
45	C₅×#322	C₂²	1	2	yes	complemented
46	C₅×C₈²	C₂²	1	2	yes	complemented
47	#17893	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
48	C₂×C₅×#41	C₂×C₄	1	1	yes	characteristic
49	C₂²×C₅×D₄	C₂×C₄	1	1	yes	characteristic
50	C₂³×C₄×C₅	—	2	1	no	—
51	C₅×AGL(1,ℤ/8)	—	2	4	no	—
52	C₂×C₅×SD₁₆	C₂×C₄	1	2	yes	—
53	C₂×C₅×D₈	C₂×C₄	1	2	yes	—
54	C₂×C₅×M₁₆	—	2	2	no	—
55	C₂×C₅×M₁₆	—	2	2	no	—
56	C₂×C₅×M₁₆	—	2	2	no	—
57	C₂×C₅×M₁₆	C₂×C₄	1	1	yes	characteristic
58	C₂×C₅×M₁₆	C₂×C₄	1	1	yes	characteristic
59	C₂²×C₅×C₈	—	2	1	no	—
60	C₂²×C₅×C₈	—	2	1	no	—
61	C₄×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
62	C₄×C₅×Q₈	C₂³	1	1	yes	characteristic
63	C₄×C₅×D₄	—	2	1	no	—
64	C₄×C₅×D₄	—	2	1	no	—
65	C₄×C₅×D₄	—	2	1	no	—
66	C₄×C₅×D₄	—	2	1	no	—
67	C₄×C₅×D₄	C₂×C₄	1	2	yes	—
68	C₄×C₅×D₄	C₂×C₄	1	1	yes	characteristic
69	C₄×C₅×D₄	C₂³	1	2	yes	—
70	C₄×C₅×D₄	C₂³	1	1	yes	characteristic
71	C₅×#117	—	2	1	no	—
72	C₅×#117	C₂×C₄	1	1	yes	characteristic
73	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
74	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
75	C₂×C₄²×C₅	—	2	1	no	—
76	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
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	1	no	—
81	C₅×C₄⋊C₈	D₄	1	1	yes	characteristic
82	C₅×C₄⋊C₈	D₄	1	1	yes	characteristic
83	C₅×C₄⋊C₈	C₂³	1	2	yes	—
84	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
85	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
86	C₅×#103	C₂×C₄	1	2	yes	—
87	C₅×#102	C₂×C₄	1	2	yes	—
88	C₅×#102	C₂×C₄	1	2	yes	—
89	C₅×#102	C₂×C₄	1	2	yes	—
90	C₅×C₂²⋊C₈	—	2	1	no	—
91	C₅×C₂²⋊C₈	—	2	2	no	—
92	C₅×C₂²⋊C₈	—	2	2	no	—
93	C₅×C₂²⋊C₈	—	2	2	no	—
94	C₅×C₂²⋊C₈	D₄	1	2	yes	—
95	C₅×#97	—	2	2	no	—
96	C₅×#97	C₂×C₄	1	2	yes	—
97	C₄×C₅×C₈	—	2	1	no	—
98	C₄×C₅×C₈	—	2	1	no	—
99	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
100	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
101	C₄×C₅×C₈	C₂³	1	2	yes	—
102	C₄×C₅×C₈	C₂³	1	2	yes	—
103	#2989	C₂×C₅	1	1	yes	characteristic, complemented
104	#2975	C₂×C₅	1	1	yes	characteristic, complemented
105	C₄×AGL(1,ℤ/8)	C₂×C₅	1	1	yes	characteristic
106	#1594	C₂×C₅	1	2	yes	complemented
107	#1592	C₂×C₅	1	2	yes	complemented
108	#1590	C₂×C₅	1	2	yes	complemented
109	#1589	C₂×C₅	1	2	yes	complemented
110	#1565	C₂×C₅	1	1	yes	characteristic, complemented
111	#1476	C₂×C₅	1	1	yes	characteristic, complemented
112	C₂×D₄⋊C₈	C₂×C₅	1	1	yes	characteristic, complemented
113	C₈×M₁₆	C₂×C₅	1	1	yes	characteristic, complemented
114	C₂⁴×C₅	—	2	1	no	—
115	C₅×#41	—	2	2	no	—
116	C₅×#41	—	2	2	no	—
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	—	2	2	no	—
121	C₂×C₅×D₄	—	2	2	no	—
122	C₂×C₅×D₄	C₂²×C₄	1	1	yes	characteristic
123	C₂×C₅×D₄	C₂²×C₄	1	2	yes	—
124	C₂²×C₄×C₅	—	2	1	no	—
125	C₂²×C₄×C₅	—	2	1	no	—
126	C₂²×C₄×C₅	—	2	1	no	—
127	C₂²×C₄×C₅	—	2	2	no	—
128	C₂²×C₄×C₅	—	2	1	no	—
129	C₂²×C₄×C₅	—	2	2	no	—
130	C₂²×C₄×C₅	—	8	1	no	—
131	C₂²×C₄×C₅	—	8	1	no	—
132	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
133	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₄×C₅	#41	1	1	yes	characteristic
135	C₅×SD₁₆	—	2	4	no	—
136	C₅×D₈	—	2	4	no	—
137	C₅×M₁₆	—	2	2	no	—
138	C₅×M₁₆	—	8	2	no	—
139	C₅×M₁₆	—	8	2	no	—
140	C₅×M₁₆	—	8	2	no	—
141	C₅×M₁₆	M₁₆	1	4	yes	complemented
142	C₂×C₅×C₈	—	2	1	no	—
143	C₂×C₅×C₈	—	2	2	no	—
144	C₂×C₅×C₈	—	2	1	no	—
145	C₂×C₅×C₈	—	2	1	no	—
146	C₂×C₅×C₈	—	2	1	no	—
147	C₂×C₅×C₈	—	4	2	no	—
148	C₂×C₅×C₈	—	8	1	no	—
149	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
150	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
151	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
152	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
153	C₅×C₄⋊C₄	—	2	1	no	—
154	C₅×C₄⋊C₄	—	2	1	no	—
155	C₅×C₄⋊C₄	—	2	1	no	—
156	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
157	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
158	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
159	C₅×C₂²⋊C₄	—	2	1	no	—
160	C₅×C₂²⋊C₄	—	2	2	no	—
161	C₅×C₂²⋊C₄	—	2	1	no	—
162	C₅×C₂²⋊C₄	—	2	2	no	—
163	C₅×C₂²⋊C₄	—	2	1	no	—
164	C₄²×C₅	—	2	1	no	—
165	C₄²×C₅	—	2	1	no	—
166	C₄²×C₅	—	2	1	no	—
167	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
168	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
169	C₄²×C₅	#41	1	1	yes	characteristic
170	C₄²×C₅	C₂⁴	1	1	yes	characteristic
171	C₂×AGL(1,ℤ/8)	C₄×C₅	1	1	yes	characteristic
172	C₄×#41	C₂²×C₅	1	1	yes	characteristic
173	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
174	#446	C₂²×C₅	1	2	yes	complemented
175	#442	C₄×C₅	1	2	yes	—
176	#440	C₄×C₅	1	2	yes	—
177	C₄×SD₁₆	C₂²×C₅	1	2	yes	—
178	C₄×D₈	C₂²×C₅	1	2	yes	—
179	#436	—	2	1	no	—
180	#436	—	2	1	no	—
181	#436	C₂²×C₅	1	2	yes	—
182	#436	C₂²×C₅	1	2	yes	—
183	#436	C₂²×C₅	1	2	yes	complemented
184	#435	—	2	2	no	—
185	#432	—	2	1	no	—
186	#431	C₂²×C₅	1	1	yes	characteristic
187	#431	C₂²×C₅	1	1	yes	characteristic
188	#428	C₄×C₅	1	1	yes	characteristic
189	#423	—	2	1	no	—
190	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
191	#418	C₄×C₅	1	1	yes	characteristic
192	#417	C₄×C₅	1	1	yes	characteristic
193	#407	—	2	2	no	—
194	C₄×M₁₆	C₂²×C₅	1	1	yes	characteristic
195	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
196	#335	C₂²×C₅	1	2	yes	complemented
197	#334	C₂²×C₅	1	2	yes	complemented
198	Q₈⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
199	Q₈⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
200	D₄⋊C₈	C₂²×C₅	1	2	yes	—
201	D₄⋊C₈	C₂²×C₅	1	2	yes	—
202	D₄⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
203	D₄⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
204	#322	C₂²×C₅	1	2	yes	complemented
205	C₈²	C₂²×C₅	1	2	yes	complemented
206	C₂³×C₅	—	2	1	no	—
207	C₂³×C₅	—	2	2	no	—
208	C₂³×C₅	—	4	2	no	—
209	C₂³×C₅	—	8	1	no	—
210	C₂³×C₅	—	8	1	no	—
211	C₂³×C₅	C₄×D₄	1	1	yes	characteristic
212	C₅×Q₈	—	2	1	no	—
213	C₅×Q₈	—	2	1	no	—
214	C₅×D₄	—	2	1	no	—
215	C₅×D₄	—	2	2	no	—
216	C₅×D₄	—	2	2	no	—
217	C₅×D₄	—	2	1	no	—
218	C₅×D₄	—	4	2	no	—
219	C₅×D₄	—	4	2	no	—
220	C₂×C₄×C₅	—	2	1	no	—
221	C₂×C₄×C₅	—	2	1	no	—
222	C₂×C₄×C₅	—	2	1	no	—
223	C₂×C₄×C₅	—	2	1	no	—
224	C₂×C₄×C₅	—	2	1	no	—
225	C₂×C₄×C₅	—	2	2	no	—
226	C₂×C₄×C₅	—	4	1	no	—
227	C₂×C₄×C₅	—	4	1	no	—
228	C₂×C₄×C₅	—	4	2	no	—
229	C₂×C₄×C₅	—	4	2	no	—
230	C₂×C₄×C₅	—	4	1	no	—
231	C₂×C₄×C₅	—	4	2	no	—
232	C₂×C₄×C₅	—	8	1	no	—
233	C₂×C₄×C₅	—	8	2	no	—
234	C₂×C₄×C₅	—	8	1	no	—
235	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
236	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
237	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
238	C₂×C₄×C₅	C₂×M₁₆	1	2	yes	—
239	C₂×C₄×C₅	#131	1	2	yes	—
240	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
241	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
242	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
243	C₅×C₈	—	2	2	no	—
244	C₅×C₈	—	2	2	no	—
245	C₅×C₈	—	2	2	no	—
246	C₅×C₈	—	2	2	no	—
247	C₅×C₈	—	4	1	no	—
248	C₅×C₈	—	4	2	no	—
249	C₅×C₈	—	4	1	no	—
250	C₅×C₈	—	4	1	no	—
251	C₅×C₈	C₂×M₁₆	1	4	yes	—
252	C₂×#41	C₂×C₄×C₅	1	1	yes	characteristic
253	C₂²×D₄	C₂×C₄×C₅	1	1	yes	characteristic
254	C₂³×C₄	—	2	1	no	—
255	AGL(1,ℤ/8)	—	2	4	no	—
256	C₂×SD₁₆	C₂×C₄×C₅	1	2	yes	—
257	C₂×D₈	C₂×C₄×C₅	1	2	yes	—
258	C₂×M₁₆	—	2	2	no	—
259	C₂×M₁₆	—	2	2	no	—
260	C₂×M₁₆	—	2	2	no	—
261	C₂×M₁₆	C₂×C₄×C₅	1	1	yes	characteristic
262	C₂×M₁₆	C₂×C₄×C₅	1	1	yes	characteristic
263	C₂²×C₈	—	2	1	no	—
264	C₂²×C₈	—	2	1	no	—
265	C₄×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
266	C₄×Q₈	C₂³×C₅	1	1	yes	characteristic
267	C₄×D₄	—	2	1	no	—
268	C₄×D₄	—	2	1	no	—
269	C₄×D₄	—	2	1	no	—
270	C₄×D₄	—	2	1	no	—
271	C₄×D₄	C₂×C₄×C₅	1	2	yes	—
272	C₄×D₄	C₂×C₄×C₅	1	1	yes	characteristic
273	C₄×D₄	C₂³×C₅	1	2	yes	—
274	C₄×D₄	C₂³×C₅	1	1	yes	characteristic
275	#117	—	2	1	no	—
276	#117	C₂×C₄×C₅	1	1	yes	characteristic
277	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
278	C₂×C₂²⋊C₄	—	2	1	no	—
279	C₂×C₄²	—	2	1	no	—
280	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
281	#107	C₂×C₄×C₅	1	2	yes	—
282	#106	C₂×C₄×C₅	1	2	yes	—
283	C₄⋊C₈	—	2	2	no	—
284	C₄⋊C₈	—	2	1	no	—
285	C₄⋊C₈	C₅×D₄	1	1	yes	characteristic
286	C₄⋊C₈	C₅×D₄	1	1	yes	characteristic
287	C₄⋊C₈	C₂³×C₅	1	2	yes	—
288	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
289	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
290	#103	C₂×C₄×C₅	1	2	yes	—
291	#102	C₂×C₄×C₅	1	2	yes	—
292	#102	C₂×C₄×C₅	1	2	yes	—
293	#102	C₂×C₄×C₅	1	2	yes	—
294	C₂²⋊C₈	—	2	1	no	—
295	C₂²⋊C₈	—	2	2	no	—
296	C₂²⋊C₈	—	2	2	no	—
297	C₂²⋊C₈	—	2	2	no	—
298	C₂²⋊C₈	C₅×D₄	1	2	yes	—
299	#97	—	2	2	no	—
300	#97	C₂×C₄×C₅	1	2	yes	—
301	C₄×C₈	—	2	1	no	—
302	C₄×C₈	—	2	1	no	—
303	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
304	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
305	C₄×C₈	C₂³×C₅	1	2	yes	—
306	C₄×C₈	C₂³×C₅	1	2	yes	—
307	C₂²×C₅	—	2	1	no	—
308	C₂²×C₅	—	2	1	no	—
309	C₂²×C₅	—	4	1	no	—
310	C₂²×C₅	—	4	2	no	—
311	C₂²×C₅	—	4	2	no	—
312	C₂²×C₅	—	4	1	no	—
313	C₂²×C₅	—	4	1	no	—
314	C₂²×C₅	—	4	2	no	—
315	C₂²×C₅	—	8	4	no	—
316	C₂²×C₅	#436	1	2	yes	—
317	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
318	C₄×C₅	—	2	1	no	—
319	C₄×C₅	—	2	1	no	—
320	C₄×C₅	—	2	1	no	—
321	C₄×C₅	—	4	1	no	—
322	C₄×C₅	—	4	1	no	—
323	C₄×C₅	—	4	2	no	—
324	C₄×C₅	—	4	1	no	—
325	C₄×C₅	#436	1	2	yes	—
326	C₄×C₅	C₂²×M₁₆	1	1	yes	characteristic
327	C₄×C₅	C₂×#131	1	1	yes	characteristic
328	C₄×C₅	#576	1	1	yes	characteristic
329	C₄×C₅	#577	1	1	yes	characteristic
330	C₂⁴	—	2	1	no	—
331	#41	—	2	2	no	—
332	#41	—	2	2	no	—
333	C₂×Q₈	C₂²×C₄×C₅	1	1	yes	characteristic
334	C₂×D₄	—	2	1	no	—
335	C₂×D₄	—	2	1	no	—
336	C₂×D₄	—	2	2	no	—
337	C₂×D₄	—	2	2	no	—
338	C₂×D₄	C₂²×C₄×C₅	1	1	yes	characteristic
339	C₂×D₄	C₂²×C₄×C₅	1	2	yes	—
340	C₂²×C₄	—	2	1	no	—
341	C₂²×C₄	—	2	1	no	—
342	C₂²×C₄	—	2	1	no	—
343	C₂²×C₄	—	2	2	no	—
344	C₂²×C₄	—	2	1	no	—
345	C₂²×C₄	—	2	2	no	—
346	C₂²×C₄	—	8	1	no	—
347	C₂²×C₄	—	8	1	no	—
348	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
349	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
350	C₂²×C₄	C₅×#41	1	1	yes	characteristic
351	SD₁₆	—	2	4	no	—
352	D₈	—	2	4	no	—
353	M₁₆	—	2	2	no	—
354	M₁₆	—	8	2	no	—
355	M₁₆	—	8	2	no	—
356	M₁₆	—	8	2	no	—
357	M₁₆	C₅×M₁₆	1	4	yes	complemented
358	C₂×C₈	—	2	1	no	—
359	C₂×C₈	—	2	1	no	—
360	C₂×C₈	—	2	1	no	—
361	C₂×C₈	—	2	2	no	—
362	C₂×C₈	—	2	1	no	—
363	C₂×C₈	—	4	2	no	—
364	C₂×C₈	—	8	1	no	—
365	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
366	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
367	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
368	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
369	C₄⋊C₄	—	2	1	no	—
370	C₄⋊C₄	—	2	1	no	—
371	C₄⋊C₄	—	2	1	no	—
372	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
373	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
374	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
375	C₂²⋊C₄	—	2	1	no	—
376	C₂²⋊C₄	—	2	2	no	—
377	C₂²⋊C₄	—	2	1	no	—
378	C₂²⋊C₄	—	2	2	no	—
379	C₂²⋊C₄	—	2	1	no	—
380	C₄²	—	2	1	no	—
381	C₄²	—	2	1	no	—
382	C₄²	—	2	1	no	—
383	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
384	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
385	C₄²	C₅×#41	1	1	yes	characteristic
386	C₄²	C₂⁴×C₅	1	1	yes	characteristic
387	C₂×C₅	—	2	2	no	—
388	C₂×C₅	—	8	1	no	—
389	C₂×C₅	—	8	2	no	—
390	C₂×C₅	C₂×#436	1	1	yes	characteristic
391	C₂×C₅	#2946	1	1	yes	characteristic
392	C₂×C₅	#2956	1	1	yes	characteristic
393	C₂³	—	2	1	no	—
394	C₂³	—	2	2	no	—
395	C₂³	—	4	2	no	—
396	C₂³	—	8	1	no	—
397	C₂³	—	8	1	no	—
398	C₂³	C₄×C₅×D₄	1	1	yes	characteristic
399	Q₈	—	2	1	no	—
400	Q₈	—	2	1	no	—
401	D₄	—	2	1	no	—
402	D₄	—	2	2	no	—
403	D₄	—	2	2	no	—
404	D₄	—	2	1	no	—
405	D₄	—	4	2	no	—
406	D₄	—	4	2	no	—
407	C₂×C₄	—	2	1	no	—
408	C₂×C₄	—	2	1	no	—
409	C₂×C₄	—	2	1	no	—
410	C₂×C₄	—	2	1	no	—
411	C₂×C₄	—	2	1	no	—
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	4	1	no	—
414	C₂×C₄	—	4	2	no	—
415	C₂×C₄	—	4	1	no	—
416	C₂×C₄	—	4	2	no	—
417	C₂×C₄	—	4	2	no	—
418	C₂×C₄	—	4	1	no	—
419	C₂×C₄	—	8	2	no	—
420	C₂×C₄	—	8	1	no	—
421	C₂×C₄	—	8	1	no	—
422	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
423	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
424	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
425	C₂×C₄	C₂×C₅×M₁₆	1	2	yes	—
426	C₂×C₄	C₅×#131	1	2	yes	—
427	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
428	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
429	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
430	C₈	—	2	2	no	—
431	C₈	—	2	2	no	—
432	C₈	—	2	2	no	—
433	C₈	—	2	2	no	—
434	C₈	—	4	1	no	—
435	C₈	—	4	2	no	—
436	C₈	—	4	1	no	—
437	C₈	—	4	1	no	—
438	C₈	C₂×C₅×M₁₆	1	4	yes	—
439	C₅	#17893	1	1	yes	characteristic, direct product factor, Sylow
440	C₂²	—	2	1	no	—
441	C₂²	—	2	1	no	—
442	C₂²	—	4	1	no	—
443	C₂²	—	4	2	no	—
444	C₂²	—	4	2	no	—
445	C₂²	—	4	1	no	—
446	C₂²	—	4	1	no	—
447	C₂²	—	4	2	no	—
448	C₂²	—	8	4	no	—
449	C₂²	C₅×#436	1	2	yes	—
450	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
451	C₄	—	2	1	no	—
452	C₄	—	2	1	no	—
453	C₄	—	2	1	no	—
454	C₄	—	4	1	no	—
455	C₄	—	4	2	no	—
456	C₄	—	4	1	no	—
457	C₄	—	4	1	no	—
458	C₄	C₅×#436	1	2	yes	—
459	C₄	C₂²×C₅×M₁₆	1	1	yes	characteristic
460	C₄	C₂×C₅×#131	1	1	yes	characteristic
461	C₄	C₅×#576	1	1	yes	characteristic
462	C₄	C₅×#577	1	1	yes	characteristic
463	C₂	—	2	2	no	—
464	C₂	—	8	2	no	—
465	C₂	—	8	1	no	—
466	C₂	C₂×C₅×#436	1	1	yes	characteristic
467	C₂	C₅×#2946	1	1	yes	characteristic
468	C₂	C₅×#2956	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₅
Frattini, cosocle	C₄²	C₂⁴×C₅
socle	C₂²×C₅	C₂×C₄×D₄
prime radical	C₂×C₅×AGL(1,ℤ/8)	C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₅×#431 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅×#2989	C₂	semidirect
2. C₅×#2975	C₂	semidirect
4. C₅×#1594	C₂	semidirect
5. C₅×#1592	C₂	semidirect
6. C₅×#1590	C₂	semidirect
7. C₅×#1589	C₂	semidirect
8. C₅×#1565	C₂	semidirect
9. C₅×#1476	C₂	semidirect
10. C₂×C₅×D₄⋊C₈	C₂	semidirect
11. C₅×C₈×M₁₆	C₂	semidirect
15. C₅×#446	C₂²	semidirect
24. C₅×#436	C₂²	semidirect
37. C₅×#335	C₂²	semidirect
38. C₅×#334	C₂²	semidirect
39. C₅×Q₈⋊C₈	C₂²	semidirect
40. C₅×Q₈⋊C₈	C₂²	semidirect
43. C₅×D₄⋊C₈	C₂²	semidirect
44. C₅×D₄⋊C₈	C₂²	semidirect
45. C₅×#322	C₂²	semidirect
46. C₅×C₈²	C₂²	semidirect
47. #17893	C₅	direct (N × H)
103. #2989	C₂×C₅	semidirect
104. #2975	C₂×C₅	semidirect
106. #1594	C₂×C₅	semidirect
107. #1592	C₂×C₅	semidirect
108. #1590	C₂×C₅	semidirect
109. #1589	C₂×C₅	semidirect
110. #1565	C₂×C₅	semidirect
111. #1476	C₂×C₅	semidirect
112. C₂×D₄⋊C₈	C₂×C₅	semidirect
113. C₈×M₁₆	C₂×C₅	semidirect
141. C₅×M₁₆	M₁₆	semidirect
174. #446	C₂²×C₅	semidirect
183. #436	C₂²×C₅	semidirect
196. #335	C₂²×C₅	semidirect
197. #334	C₂²×C₅	semidirect
198. Q₈⋊C₈	C₂²×C₅	semidirect
199. Q₈⋊C₈	C₂²×C₅	semidirect
202. D₄⋊C₈	C₂²×C₅	semidirect
203. D₄⋊C₈	C₂²×C₅	semidirect
204. #322	C₂²×C₅	semidirect
205. C₈²	C₂²×C₅	semidirect
357. M₁₆	C₅×M₁₆	semidirect
439. C₅	#17893	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×#2989	2
C₅×#2975	2
C₄×C₅×AGL(1,ℤ/8)	2
C₅×#1594	2
C₅×#1592	2
C₅×#1590	2
C₅×#1589	2
C₅×#1565	2
C₅×#1476	2
C₂×C₅×D₄⋊C₈	2
C₅×C₈×M₁₆	2
#17893	5

Subgroups — C5×#17893 #11940613

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#17893 #11940613