Subgroups — C₅×#18011 #11940731

Order 1280.

660 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3106	C₂	1	1	yes	maximal, characteristic
2	C₅×#2971	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#2935	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#1594	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#1589	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#1588	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#1586	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1583	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1581	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×SD₁₆⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×C₈×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#1573	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#1496	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#1477	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#1453	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₅×#131	—	2	1	no	—
17	C₅×#532	C₂²	1	1	yes	characteristic
18	C₄×C₅×#41	C₂²	1	1	yes	characteristic
19	C₅×#482	C₄	1	1	yes	characteristic
20	C₅×#482	C₄	1	1	yes	characteristic
21	C₅×#477	C₄	1	1	yes	characteristic
22	C₅×#476	C₄	1	1	yes	characteristic
23	C₅×#460	C₄	1	1	yes	characteristic
24	C₅×#459	C₄	1	1	yes	characteristic
25	C₅×#449	C₄	1	1	yes	characteristic
26	C₅×#449	C₄	1	1	yes	characteristic
27	C₅×C₈×Q₈	C₂²	1	1	yes	characteristic
28	C₅×C₈×Q₈	C₂²	1	1	yes	characteristic
29	C₄×C₅×SD₁₆	C₂²	1	1	yes	characteristic
30	C₄×C₅×SD₁₆	C₂²	1	1	yes	characteristic
31	C₄×C₅×D₈	C₂²	1	1	yes	characteristic
32	C₄×C₅×D₈	C₂²	1	1	yes	characteristic
33	C₅×#436	—	2	1	no	—
34	C₅×#436	—	2	1	no	—
35	C₅×#436	C₂²	1	1	yes	characteristic
36	C₅×#436	C₂²	1	1	yes	characteristic
37	C₅×#436	C₂²	1	1	yes	characteristic
38	C₅×#436	C₂²	1	1	yes	characteristic
39	C₅×#435	—	2	1	no	—
40	C₅×#435	—	2	1	no	—
41	C₅×C₈×D₄	C₂²	1	1	yes	characteristic
42	C₅×C₈×D₄	C₂²	1	1	yes	characteristic
43	C₅×#432	—	2	1	no	—
44	C₅×#432	C₂²	1	1	yes	characteristic
45	C₅×#431	C₂²	1	1	yes	characteristic
46	C₅×#431	C₂²	1	1	yes	characteristic
47	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
48	C₅×#408	—	2	1	no	—
49	C₄×C₅×M₁₆	—	2	1	no	—
50	C₄×C₅×M₁₆	C₂²	1	1	yes	characteristic
51	C₅×#335	C₂²	1	1	yes	characteristic
52	C₅×#335	C₂²	1	1	yes	characteristic
53	C₅×#334	C₂²	1	1	yes	characteristic
54	C₅×#334	C₂²	1	1	yes	characteristic
55	C₅×Q₈⋊C₈	C₂²	1	1	yes	characteristic
56	C₅×Q₈⋊C₈	C₂²	1	1	yes	characteristic
57	C₅×D₄⋊C₈	C₂²	1	1	yes	characteristic
58	C₅×D₄⋊C₈	C₂²	1	1	yes	characteristic
59	C₅×D₄⋊C₈	C₂²	1	1	yes	characteristic
60	C₅×D₄⋊C₈	C₂²	1	1	yes	characteristic
61	C₅×D₄⋊C₈	C₂²	1	1	yes	characteristic
62	C₅×D₄⋊C₈	C₂²	1	1	yes	characteristic
63	C₅×#322	C₂²	1	1	yes	characteristic
64	C₅×#322	C₂²	1	1	yes	characteristic
65	C₅×#322	C₂²	1	1	yes	characteristic
66	C₅×C₈²	C₂²	1	1	yes	characteristic
67	#18011	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
68	C₂×C₅×#41	—	2	1	no	—
69	C₂×C₅×#41	C₂×C₄	1	1	yes	characteristic
70	C₂×C₅×SD₁₆	C₂×C₄	1	1	yes	characteristic
71	C₂×C₅×SD₁₆	C₂×C₄	1	1	yes	characteristic
72	C₂×C₅×D₈	C₂×C₄	1	1	yes	characteristic
73	C₂×C₅×D₈	C₂×C₄	1	1	yes	characteristic
74	C₅×#131	—	4	4	no	—
75	C₂×C₅×M₁₆	—	2	1	no	—
76	C₂×C₅×M₁₆	—	2	1	no	—
77	C₂×C₅×M₁₆	—	2	1	no	—
78	C₂×C₅×M₁₆	—	2	1	no	—
79	C₂×C₅×M₁₆	D₄	1	1	yes	characteristic
80	C₂×C₅×M₁₆	D₄	1	1	yes	characteristic
81	C₂²×C₅×C₈	—	2	1	no	—
82	C₂²×C₅×C₈	—	2	1	no	—
83	C₂²×C₅×C₈	—	2	1	no	—
84	C₅×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
85	C₅×#127	C₂×C₄	1	1	yes	characteristic
86	C₅×#124	—	2	1	no	—
87	C₅×#121	—	2	1	no	—
88	C₅×#121	C₂×C₄	1	1	yes	characteristic
89	C₅×#121	C₂×C₄	1	1	yes	characteristic
90	C₄×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
91	C₄×C₅×Q₈	C₂³	1	1	yes	characteristic
92	C₄×C₅×D₄	—	2	1	no	—
93	C₄×C₅×D₄	—	2	1	no	—
94	C₄×C₅×D₄	—	2	1	no	—
95	C₄×C₅×D₄	C₂×C₄	1	1	yes	characteristic
96	C₄×C₅×D₄	C₂³	1	1	yes	characteristic
97	C₄×C₅×D₄	C₂³	1	1	yes	characteristic
98	C₄×C₅×D₄	C₂³	1	1	yes	characteristic
99	C₅×#117	—	2	1	no	—
100	C₅×#117	C₂×C₄	1	1	yes	characteristic
101	C₂×C₄²×C₅	—	2	1	no	—
102	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
103	C₅×#107	C₂×C₄	1	1	yes	characteristic
104	C₅×#107	C₂×C₄	1	1	yes	characteristic
105	C₅×#106	C₂×C₄	1	1	yes	characteristic
106	C₅×#106	C₂×C₄	1	1	yes	characteristic
107	C₅×C₄⋊C₈	—	2	1	no	—
108	C₅×C₄⋊C₈	—	2	1	no	—
109	C₅×C₄⋊C₈	—	2	1	no	—
110	C₅×C₄⋊C₈	—	2	1	no	—
111	C₅×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
112	C₅×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
113	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
114	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
115	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
116	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
117	C₅×#103	C₂×C₄	1	1	yes	characteristic
118	C₅×#103	C₂×C₄	1	1	yes	characteristic
119	C₅×#102	C₂×C₄	1	1	yes	characteristic
120	C₅×#102	C₂×C₄	1	1	yes	characteristic
121	C₅×#102	C₂×C₄	1	1	yes	characteristic
122	C₅×#102	C₂×C₄	1	1	yes	characteristic
123	C₅×#102	C₂×C₄	1	1	yes	characteristic
124	C₅×#102	C₂×C₄	1	1	yes	characteristic
125	C₅×C₂²⋊C₈	—	2	1	no	—
126	C₅×C₂²⋊C₈	—	2	1	no	—
127	C₅×C₂²⋊C₈	—	2	1	no	—
128	C₅×C₂²⋊C₈	—	2	1	no	—
129	C₅×C₂²⋊C₈	—	2	1	no	—
130	C₅×C₂²⋊C₈	—	2	1	no	—
131	C₅×C₂²⋊C₈	—	2	1	no	—
132	C₅×C₂²⋊C₈	—	2	1	no	—
133	C₅×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
134	C₅×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
135	C₅×#97	—	2	1	no	—
136	C₅×#97	D₄	1	1	yes	characteristic
137	C₅×#97	D₄	1	1	yes	characteristic
138	C₄×C₅×C₈	—	2	1	no	—
139	C₄×C₅×C₈	—	2	1	no	—
140	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
141	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
142	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
143	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
144	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
145	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
146	#3106	C₂×C₅	1	1	yes	characteristic
147	#2971	C₂×C₅	1	1	yes	characteristic, complemented
148	#2935	C₂×C₅	1	1	yes	characteristic, complemented
149	#1594	C₂×C₅	1	1	yes	characteristic, complemented
150	#1589	C₂×C₅	1	1	yes	characteristic, complemented
151	#1588	C₂×C₅	1	1	yes	characteristic, complemented
152	#1586	C₂×C₅	1	1	yes	characteristic, complemented
153	#1583	C₂×C₅	1	1	yes	characteristic, complemented
154	#1581	C₂×C₅	1	1	yes	characteristic, complemented
155	SD₁₆⋊C₈	C₂×C₅	1	1	yes	characteristic, complemented
156	C₈×SD₁₆	C₂×C₅	1	1	yes	characteristic, complemented
157	#1573	C₂×C₅	1	1	yes	characteristic, complemented
158	#1496	C₂×C₅	1	1	yes	characteristic, complemented
159	#1477	C₂×C₅	1	1	yes	characteristic, complemented
160	#1453	C₂×C₅	1	1	yes	characteristic, complemented
161	C₅×#41	—	2	2	no	—
162	C₅×#41	—	4	1	no	—
163	C₅×#41	—	4	2	no	—
164	C₅×#41	—	4	2	no	—
165	C₂×C₅×Q₈	—	2	1	no	—
166	C₂×C₅×Q₈	C₂²×C₄	1	1	yes	characteristic
167	C₂×C₅×D₄	—	2	1	no	—
168	C₂×C₅×D₄	—	2	1	no	—
169	C₂×C₅×D₄	—	2	1	no	—
170	C₂×C₅×D₄	—	2	1	no	—
171	C₂×C₅×D₄	—	2	1	no	—
172	C₂×C₅×D₄	C₂²×C₄	1	1	yes	characteristic
173	C₂×C₅×D₄	C₂²×C₄	1	1	yes	characteristic
174	C₂×C₅×D₄	C₂²×C₄	1	1	yes	characteristic
175	C₂²×C₄×C₅	—	2	1	no	—
176	C₂²×C₄×C₅	—	2	1	no	—
177	C₂²×C₄×C₅	—	2	1	no	—
178	C₂²×C₄×C₅	—	2	1	no	—
179	C₂²×C₄×C₅	—	2	1	no	—
180	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
181	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
182	C₂²×C₄×C₅	#41	1	1	yes	characteristic
183	C₅×SD₁₆	—	2	2	no	—
184	C₅×SD₁₆	—	2	2	no	—
185	C₅×D₈	—	4	1	no	—
186	C₅×D₈	—	4	1	no	—
187	C₅×M₁₆	—	2	2	no	—
188	C₅×M₁₆	—	4	1	no	—
189	C₅×M₁₆	—	4	2	no	—
190	C₅×M₁₆	—	4	2	no	—
191	C₅×M₁₆	—	4	2	no	—
192	C₅×M₁₆	—	4	2	no	—
193	C₂×C₅×C₈	—	2	1	no	—
194	C₂×C₅×C₈	—	2	1	no	—
195	C₂×C₅×C₈	—	2	1	no	—
196	C₂×C₅×C₈	—	2	1	no	—
197	C₂×C₅×C₈	—	2	1	no	—
198	C₂×C₅×C₈	—	2	1	no	—
199	C₂×C₅×C₈	—	4	2	no	—
200	C₂×C₅×C₈	—	4	2	no	—
201	C₂×C₅×C₈	—	4	2	no	—
202	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
203	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
204	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
205	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
206	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
207	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
208	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
209	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
210	C₅×C₄⋊C₄	—	2	1	no	—
211	C₅×C₄⋊C₄	—	2	1	no	—
212	C₅×C₄⋊C₄	—	2	1	no	—
213	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
214	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
215	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
216	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
217	C₅×C₂²⋊C₄	—	2	1	no	—
218	C₅×C₂²⋊C₄	—	2	1	no	—
219	C₅×C₂²⋊C₄	—	2	1	no	—
220	C₅×C₂²⋊C₄	—	2	1	no	—
221	C₅×C₂²⋊C₄	—	2	1	no	—
222	C₅×C₂²⋊C₄	—	2	1	no	—
223	C₅×C₂²⋊C₄	—	2	1	no	—
224	C₄²×C₅	—	2	1	no	—
225	C₄²×C₅	—	2	1	no	—
226	C₄²×C₅	—	2	1	no	—
227	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
228	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
229	C₄²×C₅	#41	1	1	yes	characteristic
230	C₄²×C₅	C₂⁴	1	1	yes	characteristic
231	C₂×#131	—	2	1	no	—
232	#532	C₂²×C₅	1	1	yes	characteristic
233	C₄×#41	C₂²×C₅	1	1	yes	characteristic
234	#482	C₄×C₅	1	1	yes	characteristic
235	#482	C₄×C₅	1	1	yes	characteristic
236	#477	C₄×C₅	1	1	yes	characteristic
237	#476	C₄×C₅	1	1	yes	characteristic
238	#460	C₄×C₅	1	1	yes	characteristic
239	#459	C₄×C₅	1	1	yes	characteristic
240	#449	C₄×C₅	1	1	yes	characteristic
241	#449	C₄×C₅	1	1	yes	characteristic
242	C₈×Q₈	C₂²×C₅	1	1	yes	characteristic
243	C₈×Q₈	C₂²×C₅	1	1	yes	characteristic
244	C₄×SD₁₆	C₂²×C₅	1	1	yes	characteristic
245	C₄×SD₁₆	C₂²×C₅	1	1	yes	characteristic
246	C₄×D₈	C₂²×C₅	1	1	yes	characteristic
247	C₄×D₈	C₂²×C₅	1	1	yes	characteristic
248	#436	—	2	1	no	—
249	#436	—	2	1	no	—
250	#436	C₂²×C₅	1	1	yes	characteristic
251	#436	C₂²×C₅	1	1	yes	characteristic
252	#436	C₂²×C₅	1	1	yes	characteristic
253	#436	C₂²×C₅	1	1	yes	characteristic
254	#435	—	2	1	no	—
255	#435	—	2	1	no	—
256	C₈×D₄	C₂²×C₅	1	1	yes	characteristic
257	C₈×D₄	C₂²×C₅	1	1	yes	characteristic
258	#432	—	2	1	no	—
259	#432	C₂²×C₅	1	1	yes	characteristic
260	#431	C₂²×C₅	1	1	yes	characteristic
261	#431	C₂²×C₅	1	1	yes	characteristic
262	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
263	#408	—	2	1	no	—
264	C₄×M₁₆	—	2	1	no	—
265	C₄×M₁₆	C₂²×C₅	1	1	yes	characteristic
266	#335	C₂²×C₅	1	1	yes	characteristic
267	#335	C₂²×C₅	1	1	yes	characteristic
268	#334	C₂²×C₅	1	1	yes	characteristic
269	#334	C₂²×C₅	1	1	yes	characteristic
270	Q₈⋊C₈	C₂²×C₅	1	1	yes	characteristic
271	Q₈⋊C₈	C₂²×C₅	1	1	yes	characteristic
272	D₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
273	D₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
274	D₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
275	D₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
276	D₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
277	D₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
278	#322	C₂²×C₅	1	1	yes	characteristic
279	#322	C₂²×C₅	1	1	yes	characteristic
280	#322	C₂²×C₅	1	1	yes	characteristic
281	C₈²	C₂²×C₅	1	1	yes	characteristic
282	C₂³×C₅	—	2	1	no	—
283	C₂³×C₅	—	2	1	no	—
284	C₂³×C₅	—	2	1	no	—
285	C₂³×C₅	C₄×D₄	1	1	yes	characteristic
286	C₅×Q₈	—	2	1	no	—
287	C₅×Q₈	—	4	2	no	—
288	C₅×Q₈	#131	1	2	yes	complemented
289	C₅×D₄	—	2	1	no	—
290	C₅×D₄	—	2	1	no	—
291	C₅×D₄	—	2	1	no	—
292	C₅×D₄	—	2	1	no	—
293	C₅×D₄	—	2	1	no	—
294	C₅×D₄	—	2	1	no	—
295	C₅×D₄	—	4	2	no	—
296	C₅×D₄	—	4	2	no	—
297	C₅×D₄	—	4	2	no	—
298	C₅×D₄	—	4	2	no	—
299	C₅×D₄	—	8	1	no	—
300	C₂×C₄×C₅	—	2	1	no	—
301	C₂×C₄×C₅	—	2	1	no	—
302	C₂×C₄×C₅	—	2	1	no	—
303	C₂×C₄×C₅	—	2	1	no	—
304	C₂×C₄×C₅	—	2	1	no	—
305	C₂×C₄×C₅	—	2	1	no	—
306	C₂×C₄×C₅	—	2	1	no	—
307	C₂×C₄×C₅	—	2	1	no	—
308	C₂×C₄×C₅	—	2	1	no	—
309	C₂×C₄×C₅	—	4	1	no	—
310	C₂×C₄×C₅	—	4	2	no	—
311	C₂×C₄×C₅	—	4	1	no	—
312	C₂×C₄×C₅	—	4	1	no	—
313	C₂×C₄×C₅	—	4	1	no	—
314	C₂×C₄×C₅	—	4	1	no	—
315	C₂×C₄×C₅	—	4	1	no	—
316	C₂×C₄×C₅	—	4	1	no	—
317	C₂×C₄×C₅	—	8	1	no	—
318	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
319	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
320	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
321	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
322	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
323	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
324	C₅×C₈	—	2	1	no	—
325	C₅×C₈	—	2	1	no	—
326	C₅×C₈	—	2	1	no	—
327	C₅×C₈	—	2	1	no	—
328	C₅×C₈	—	2	1	no	—
329	C₅×C₈	—	2	1	no	—
330	C₅×C₈	—	2	1	no	—
331	C₅×C₈	—	4	1	no	—
332	C₅×C₈	—	4	1	no	—
333	C₅×C₈	—	4	1	no	—
334	C₅×C₈	—	4	1	no	—
335	C₅×C₈	—	4	1	no	—
336	C₅×C₈	—	4	1	no	—
337	C₅×C₈	AGL(1,ℤ/8)	1	2	yes	—
338	C₂×#41	—	2	1	no	—
339	C₂×#41	C₂×C₄×C₅	1	1	yes	characteristic
340	C₂×SD₁₆	C₂×C₄×C₅	1	1	yes	characteristic
341	C₂×SD₁₆	C₂×C₄×C₅	1	1	yes	characteristic
342	C₂×D₈	C₂×C₄×C₅	1	1	yes	characteristic
343	C₂×D₈	C₂×C₄×C₅	1	1	yes	characteristic
344	#131	—	4	4	no	—
345	C₂×M₁₆	—	2	1	no	—
346	C₂×M₁₆	—	2	1	no	—
347	C₂×M₁₆	—	2	1	no	—
348	C₂×M₁₆	—	2	1	no	—
349	C₂×M₁₆	C₅×D₄	1	1	yes	characteristic
350	C₂×M₁₆	C₅×D₄	1	1	yes	characteristic
351	C₂²×C₈	—	2	1	no	—
352	C₂²×C₈	—	2	1	no	—
353	C₂²×C₈	—	2	1	no	—
354	C₄⋊Q₈	C₂×C₄×C₅	1	1	yes	characteristic
355	#127	C₂×C₄×C₅	1	1	yes	characteristic
356	#124	—	2	1	no	—
357	#121	—	2	1	no	—
358	#121	C₂×C₄×C₅	1	1	yes	characteristic
359	#121	C₂×C₄×C₅	1	1	yes	characteristic
360	C₄×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
361	C₄×Q₈	C₂³×C₅	1	1	yes	characteristic
362	C₄×D₄	—	2	1	no	—
363	C₄×D₄	—	2	1	no	—
364	C₄×D₄	—	2	1	no	—
365	C₄×D₄	C₂×C₄×C₅	1	1	yes	characteristic
366	C₄×D₄	C₂³×C₅	1	1	yes	characteristic
367	C₄×D₄	C₂³×C₅	1	1	yes	characteristic
368	C₄×D₄	C₂³×C₅	1	1	yes	characteristic
369	#117	—	2	1	no	—
370	#117	C₂×C₄×C₅	1	1	yes	characteristic
371	C₂×C₄²	—	2	1	no	—
372	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
373	#107	C₂×C₄×C₅	1	1	yes	characteristic
374	#107	C₂×C₄×C₅	1	1	yes	characteristic
375	#106	C₂×C₄×C₅	1	1	yes	characteristic
376	#106	C₂×C₄×C₅	1	1	yes	characteristic
377	C₄⋊C₈	—	2	1	no	—
378	C₄⋊C₈	—	2	1	no	—
379	C₄⋊C₈	—	2	1	no	—
380	C₄⋊C₈	—	2	1	no	—
381	C₄⋊C₈	C₂×C₄×C₅	1	1	yes	characteristic
382	C₄⋊C₈	C₂×C₄×C₅	1	1	yes	characteristic
383	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
384	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
385	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
386	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
387	#103	C₂×C₄×C₅	1	1	yes	characteristic
388	#103	C₂×C₄×C₅	1	1	yes	characteristic
389	#102	C₂×C₄×C₅	1	1	yes	characteristic
390	#102	C₂×C₄×C₅	1	1	yes	characteristic
391	#102	C₂×C₄×C₅	1	1	yes	characteristic
392	#102	C₂×C₄×C₅	1	1	yes	characteristic
393	#102	C₂×C₄×C₅	1	1	yes	characteristic
394	#102	C₂×C₄×C₅	1	1	yes	characteristic
395	C₂²⋊C₈	—	2	1	no	—
396	C₂²⋊C₈	—	2	1	no	—
397	C₂²⋊C₈	—	2	1	no	—
398	C₂²⋊C₈	—	2	1	no	—
399	C₂²⋊C₈	—	2	1	no	—
400	C₂²⋊C₈	—	2	1	no	—
401	C₂²⋊C₈	—	2	1	no	—
402	C₂²⋊C₈	—	2	1	no	—
403	C₂²⋊C₈	C₂×C₄×C₅	1	1	yes	characteristic
404	C₂²⋊C₈	C₂×C₄×C₅	1	1	yes	characteristic
405	#97	—	2	1	no	—
406	#97	C₅×D₄	1	1	yes	characteristic
407	#97	C₅×D₄	1	1	yes	characteristic
408	C₄×C₈	—	2	1	no	—
409	C₄×C₈	—	2	1	no	—
410	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
411	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
412	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
413	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
414	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
415	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
416	C₂²×C₅	—	2	1	no	—
417	C₂²×C₅	—	2	1	no	—
418	C₂²×C₅	—	2	1	no	—
419	C₂²×C₅	—	4	1	no	—
420	C₂²×C₅	—	4	1	no	—
421	C₂²×C₅	—	4	1	no	—
422	C₂²×C₅	—	4	1	no	—
423	C₂²×C₅	—	4	1	no	—
424	C₂²×C₅	—	4	1	no	—
425	C₂²×C₅	—	4	1	no	—
426	C₂²×C₅	—	4	1	no	—
427	C₂²×C₅	—	4	1	no	—
428	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
429	C₄×C₅	—	2	1	no	—
430	C₄×C₅	—	2	2	no	—
431	C₄×C₅	—	2	1	no	—
432	C₄×C₅	—	2	1	no	—
433	C₄×C₅	—	2	1	no	—
434	C₄×C₅	—	4	1	no	—
435	C₄×C₅	—	4	1	no	—
436	C₄×C₅	—	4	1	no	—
437	C₄×C₅	—	4	1	no	—
438	C₄×C₅	C₂×#131	1	1	yes	characteristic
439	C₄×C₅	#568	1	1	yes	characteristic
440	C₄×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
441	C₄×C₅	#575	1	1	yes	characteristic
442	#41	—	2	2	no	—
443	#41	—	4	1	no	—
444	#41	—	4	2	no	—
445	#41	—	4	2	no	—
446	C₂×Q₈	—	2	1	no	—
447	C₂×Q₈	C₂²×C₄×C₅	1	1	yes	characteristic
448	C₂×D₄	—	2	1	no	—
449	C₂×D₄	—	2	1	no	—
450	C₂×D₄	—	2	1	no	—
451	C₂×D₄	—	2	1	no	—
452	C₂×D₄	—	2	1	no	—
453	C₂×D₄	C₂²×C₄×C₅	1	1	yes	characteristic
454	C₂×D₄	C₂²×C₄×C₅	1	1	yes	characteristic
455	C₂×D₄	C₂²×C₄×C₅	1	1	yes	characteristic
456	C₂²×C₄	—	2	1	no	—
457	C₂²×C₄	—	2	1	no	—
458	C₂²×C₄	—	2	1	no	—
459	C₂²×C₄	—	2	1	no	—
460	C₂²×C₄	—	2	1	no	—
461	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
462	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
463	C₂²×C₄	C₅×#41	1	1	yes	characteristic
464	SD₁₆	—	2	2	no	—
465	SD₁₆	—	2	2	no	—
466	D₈	—	4	1	no	—
467	D₈	—	4	1	no	—
468	M₁₆	—	2	2	no	—
469	M₁₆	—	4	1	no	—
470	M₁₆	—	4	2	no	—
471	M₁₆	—	4	2	no	—
472	M₁₆	—	4	2	no	—
473	M₁₆	—	4	2	no	—
474	C₂×C₈	—	2	1	no	—
475	C₂×C₈	—	2	1	no	—
476	C₂×C₈	—	2	1	no	—
477	C₂×C₈	—	2	1	no	—
478	C₂×C₈	—	2	1	no	—
479	C₂×C₈	—	2	1	no	—
480	C₂×C₈	—	4	2	no	—
481	C₂×C₈	—	4	2	no	—
482	C₂×C₈	—	4	2	no	—
483	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
484	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
485	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
486	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
487	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
488	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
489	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
490	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
491	C₄⋊C₄	—	2	1	no	—
492	C₄⋊C₄	—	2	1	no	—
493	C₄⋊C₄	—	2	1	no	—
494	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
495	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
496	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
497	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
498	C₂²⋊C₄	—	2	1	no	—
499	C₂²⋊C₄	—	2	1	no	—
500	C₂²⋊C₄	—	2	1	no	—
501	C₂²⋊C₄	—	2	1	no	—
502	C₂²⋊C₄	—	2	1	no	—
503	C₂²⋊C₄	—	2	1	no	—
504	C₂²⋊C₄	—	2	1	no	—
505	C₄²	—	2	1	no	—
506	C₄²	—	2	1	no	—
507	C₄²	—	2	1	no	—
508	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
509	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
510	C₄²	C₅×#41	1	1	yes	characteristic
511	C₄²	C₂⁴×C₅	1	1	yes	characteristic
512	C₂×C₅	—	4	1	no	—
513	C₂×C₅	—	8	1	no	—
514	C₂×C₅	—	8	1	no	—
515	C₂×C₅	—	8	1	no	—
516	C₂×C₅	#2933	1	1	yes	characteristic
517	C₂×C₅	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic
518	C₂×C₅	#2957	1	1	yes	characteristic
519	C₂³	—	2	1	no	—
520	C₂³	—	2	1	no	—
521	C₂³	—	2	1	no	—
522	C₂³	C₄×C₅×D₄	1	1	yes	characteristic
523	Q₈	—	2	1	no	—
524	Q₈	—	4	2	no	—
525	Q₈	C₅×#131	1	2	yes	complemented
526	D₄	—	2	1	no	—
527	D₄	—	2	1	no	—
528	D₄	—	2	1	no	—
529	D₄	—	2	1	no	—
530	D₄	—	2	1	no	—
531	D₄	—	2	1	no	—
532	D₄	—	4	2	no	—
533	D₄	—	4	2	no	—
534	D₄	—	4	2	no	—
535	D₄	—	4	2	no	—
536	D₄	—	8	1	no	—
537	C₂×C₄	—	2	1	no	—
538	C₂×C₄	—	2	1	no	—
539	C₂×C₄	—	2	1	no	—
540	C₂×C₄	—	2	1	no	—
541	C₂×C₄	—	2	1	no	—
542	C₂×C₄	—	2	1	no	—
543	C₂×C₄	—	2	1	no	—
544	C₂×C₄	—	2	1	no	—
545	C₂×C₄	—	2	1	no	—
546	C₂×C₄	—	4	1	no	—
547	C₂×C₄	—	4	2	no	—
548	C₂×C₄	—	4	1	no	—
549	C₂×C₄	—	4	1	no	—
550	C₂×C₄	—	4	1	no	—
551	C₂×C₄	—	4	1	no	—
552	C₂×C₄	—	4	1	no	—
553	C₂×C₄	—	4	1	no	—
554	C₂×C₄	—	8	1	no	—
555	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
556	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
557	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
558	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
559	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
560	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
561	C₈	—	2	1	no	—
562	C₈	—	2	1	no	—
563	C₈	—	2	1	no	—
564	C₈	—	2	1	no	—
565	C₈	—	2	1	no	—
566	C₈	—	2	1	no	—
567	C₈	—	2	1	no	—
568	C₈	—	4	1	no	—
569	C₈	—	4	1	no	—
570	C₈	—	4	1	no	—
571	C₈	—	4	1	no	—
572	C₈	—	4	1	no	—
573	C₈	—	4	1	no	—
574	C₈	C₅×AGL(1,ℤ/8)	1	2	yes	—
575	C₅	#18011	1	1	yes	characteristic, direct product factor, Sylow
576	C₂²	—	2	1	no	—
577	C₂²	—	2	1	no	—
578	C₂²	—	2	1	no	—
579	C₂²	—	4	1	no	—
580	C₂²	—	4	1	no	—
581	C₂²	—	4	1	no	—
582	C₂²	—	4	1	no	—
583	C₂²	—	4	1	no	—
584	C₂²	—	4	1	no	—
585	C₂²	—	4	1	no	—
586	C₂²	—	4	1	no	—
587	C₂²	—	4	1	no	—
588	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
589	C₄	—	2	1	no	—
590	C₄	—	2	2	no	—
591	C₄	—	2	1	no	—
592	C₄	—	2	1	no	—
593	C₄	—	2	1	no	—
594	C₄	—	4	1	no	—
595	C₄	—	4	1	no	—
596	C₄	—	4	1	no	—
597	C₄	—	4	1	no	—
598	C₄	C₂×C₅×#131	1	1	yes	characteristic
599	C₄	C₅×#568	1	1	yes	characteristic
600	C₄	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
601	C₄	C₅×#575	1	1	yes	characteristic
602	C₂	—	4	1	no	—
603	C₂	—	8	1	no	—
604	C₂	—	8	1	no	—
605	C₂	—	8	1	no	—
606	C₂	C₅×#2933	1	1	yes	characteristic
607	C₂	C₄×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
608	C₂	C₅×#2957	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	C₅×#3106	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₄×C₅×M₁₆ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₅×#2971	C₂	semidirect
3. C₅×#2935	C₂	semidirect
4. C₅×#1594	C₂	semidirect
5. C₅×#1589	C₂	semidirect
6. C₅×#1588	C₂	semidirect
7. C₅×#1586	C₂	semidirect
8. C₅×#1583	C₂	semidirect
9. C₅×#1581	C₂	semidirect
10. C₅×SD₁₆⋊C₈	C₂	semidirect
11. C₅×C₈×SD₁₆	C₂	semidirect
12. C₅×#1573	C₂	semidirect
13. C₅×#1496	C₂	semidirect
14. C₅×#1477	C₂	semidirect
15. C₅×#1453	C₂	semidirect
67. #18011	C₅	direct (N × H)
147. #2971	C₂×C₅	semidirect
148. #2935	C₂×C₅	semidirect
149. #1594	C₂×C₅	semidirect
150. #1589	C₂×C₅	semidirect
151. #1588	C₂×C₅	semidirect
152. #1586	C₂×C₅	semidirect
153. #1583	C₂×C₅	semidirect
154. #1581	C₂×C₅	semidirect
155. SD₁₆⋊C₈	C₂×C₅	semidirect
156. C₈×SD₁₆	C₂×C₅	semidirect
157. #1573	C₂×C₅	semidirect
158. #1496	C₂×C₅	semidirect
159. #1477	C₂×C₅	semidirect
160. #1453	C₂×C₅	semidirect
288. C₅×Q₈	#131	semidirect
525. Q₈	C₅×#131	semidirect
575. C₅	#18011	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×#3106	2
C₅×#2971	2
C₅×#2935	2
C₅×#1594	2
C₅×#1589	2
C₅×#1588	2
C₅×#1586	2
C₅×#1583	2
C₅×#1581	2
C₅×SD₁₆⋊C₈	2
C₅×C₈×SD₁₆	2
C₅×#1573	2
C₅×#1496	2
C₅×#1477	2
C₅×#1453	2
#18011	5

Subgroups — C5×#18011 #11940731

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#18011 #11940731