Subgroups — C₅×#18008 #11940728

Order 1280.

670 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3105	C₂	1	1	yes	maximal, characteristic
2	C₅×#2969	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×D₄×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#1592	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#1589	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#1586	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#1585	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×#1580	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×C₈×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#1574	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#1495	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#1478	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#1453	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₅×M₁₆	—	2	1	no	—
17	C₅×#529	C₂²	1	1	yes	characteristic
18	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
19	C₅×#484	C₄	1	1	yes	characteristic
20	C₅×#481	C₄	1	1	yes	characteristic
21	C₅×#478	C₄	1	1	yes	characteristic
22	C₅×#478	C₄	1	1	yes	characteristic
23	C₅×#463	C₄	1	1	yes	characteristic
24	C₅×#463	C₄	1	1	yes	characteristic
25	C₅×#450	C₄	1	1	yes	characteristic
26	C₅×#447	C₄	1	1	yes	characteristic
27	C₅×#446	C₂²	1	1	yes	characteristic, complemented
28	C₅×C₈×Q₈	C₂²	1	1	yes	characteristic, complemented
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	C₂²	1	1	yes	characteristic
35	C₅×#436	C₂²	1	1	yes	characteristic
36	C₅×#436	C₂²	1	1	yes	characteristic, complemented
37	C₅×#435	—	2	1	no	—
38	C₅×#435	—	2	1	no	—
39	C₅×#435	—	2	1	no	—
40	C₅×C₈×D₄	C₂²	1	1	yes	characteristic
41	C₅×C₈×D₄	C₂²	1	1	yes	characteristic
42	C₅×C₈×D₄	C₂²	1	1	yes	characteristic, complemented
43	C₅×#433	—	2	1	no	—
44	C₅×#431	C₂²	1	1	yes	characteristic
45	C₅×#431	C₂²	1	1	yes	characteristic
46	C₅×#431	C₂²	1	1	yes	characteristic
47	C₅×#423	C₂²	1	1	yes	characteristic
48	C₅×#407	—	2	1	no	—
49	C₅×#405	—	2	1	no	—
50	C₄×C₅×M₁₆	C₂²	1	1	yes	characteristic
51	C₅×#335	C₂²	1	1	yes	characteristic, complemented
52	C₅×#335	C₂²	1	1	yes	characteristic, complemented
53	C₅×#334	C₂²	1	1	yes	characteristic, complemented
54	C₅×#334	C₂²	1	1	yes	characteristic, complemented
55	C₅×Q₈⋊C₈	C₂²	1	1	yes	characteristic, complemented
56	C₅×Q₈⋊C₈	C₂²	1	1	yes	characteristic, complemented
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, complemented
62	C₅×D₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
63	C₅×#322	C₂²	1	1	yes	characteristic, complemented
64	C₅×#322	C₂²	1	1	yes	characteristic, complemented
65	C₅×#322	C₂²	1	1	yes	characteristic, complemented
66	C₅×C₈²	C₂²	1	1	yes	characteristic, complemented
67	#18008	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
68	C₂²×C₅×D₄	C₂×C₄	1	1	yes	characteristic
69	C₂³×C₄×C₅	—	2	1	no	—
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	C₂×C₅×M₁₆	—	2	1	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	—	4	4	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×#126	—	2	1	no	—
85	C₅×#125	C₂×C₄	1	1	yes	characteristic
86	C₅×#124	C₂×C₄	1	1	yes	characteristic
87	C₅×#123	—	2	1	no	—
88	C₅×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
89	C₅×#121	C₂×C₄	1	1	yes	characteristic
90	C₄×C₅×Q₈	C₂³	1	1	yes	characteristic
91	C₄×C₅×D₄	—	2	1	no	—
92	C₄×C₅×D₄	—	2	1	no	—
93	C₄×C₅×D₄	—	2	1	no	—
94	C₄×C₅×D₄	C₂×C₄	1	1	yes	characteristic
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	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
101	C₂×C₅×C₂²⋊C₄	—	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	#3105	C₂×C₅	1	1	yes	characteristic
147	#2969	C₂×C₅	1	1	yes	characteristic, complemented
148	D₄×M₁₆	C₂×C₅	1	1	yes	characteristic, complemented
149	#1592	C₂×C₅	1	1	yes	characteristic, complemented
150	#1589	C₂×C₅	1	1	yes	characteristic, complemented
151	#1586	C₂×C₅	1	1	yes	characteristic, complemented
152	#1585	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	#1580	C₂×C₅	1	1	yes	characteristic, complemented
156	C₈×SD₁₆	C₂×C₅	1	1	yes	characteristic, complemented
157	#1574	C₂×C₅	1	1	yes	characteristic, complemented
158	#1495	C₂×C₅	1	1	yes	characteristic, complemented
159	#1478	C₂×C₅	1	1	yes	characteristic, complemented
160	#1453	C₂×C₅	1	1	yes	characteristic, complemented
161	C₂⁴×C₅	—	2	1	no	—
162	C₂×C₅×Q₈	C₂²×C₄	1	1	yes	characteristic
163	C₂×C₅×D₄	—	2	2	no	—
164	C₂×C₅×D₄	—	2	1	no	—
165	C₂×C₅×D₄	—	2	1	no	—
166	C₂×C₅×D₄	—	4	1	no	—
167	C₂×C₅×D₄	C₂²×C₄	1	1	yes	characteristic
168	C₂×C₅×D₄	C₂²×C₄	1	1	yes	characteristic
169	C₂×C₅×D₄	C₂²×C₄	1	1	yes	characteristic
170	C₂²×C₄×C₅	—	2	1	no	—
171	C₂²×C₄×C₅	—	2	1	no	—
172	C₂²×C₄×C₅	—	2	1	no	—
173	C₂²×C₄×C₅	—	2	1	no	—
174	C₂²×C₄×C₅	—	2	1	no	—
175	C₂²×C₄×C₅	—	2	1	no	—
176	C₂²×C₄×C₅	—	4	2	no	—
177	C₂²×C₄×C₅	—	4	2	no	—
178	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
179	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
180	C₂²×C₄×C₅	#41	1	1	yes	characteristic
181	C₅×SD₁₆	—	2	2	no	—
182	C₅×SD₁₆	—	4	1	no	—
183	C₅×D₈	—	2	2	no	—
184	C₅×D₈	—	4	1	no	—
185	C₅×M₁₆	—	2	2	no	—
186	C₅×M₁₆	—	4	1	no	—
187	C₅×M₁₆	—	4	2	no	—
188	C₅×M₁₆	—	4	2	no	—
189	C₅×M₁₆	—	4	2	no	—
190	C₅×M₁₆	—	4	2	no	—
191	C₂×C₅×C₈	—	2	1	no	—
192	C₂×C₅×C₈	—	2	1	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	—	4	2	no	—
198	C₂×C₅×C₈	—	4	2	no	—
199	C₂×C₅×C₈	—	4	2	no	—
200	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
201	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
202	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
203	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
204	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
205	C₂×C₅×C₈	C₂×D₄	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	C₅×C₄⋊C₄	—	2	1	no	—
209	C₅×C₄⋊C₄	—	2	1	no	—
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	C₅×C₂²⋊C₄	—	2	1	no	—
225	C₅×C₂²⋊C₄	—	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	C₂²×M₁₆	—	2	1	no	—
232	#529	C₂²×C₅	1	1	yes	characteristic
233	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
234	#484	C₄×C₅	1	1	yes	characteristic
235	#481	C₄×C₅	1	1	yes	characteristic
236	#478	C₄×C₅	1	1	yes	characteristic
237	#478	C₄×C₅	1	1	yes	characteristic
238	#463	C₄×C₅	1	1	yes	characteristic
239	#463	C₄×C₅	1	1	yes	characteristic
240	#450	C₄×C₅	1	1	yes	characteristic
241	#447	C₄×C₅	1	1	yes	characteristic
242	#446	C₂²×C₅	1	1	yes	characteristic, complemented
243	C₈×Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
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	C₂²×C₅	1	1	yes	characteristic
250	#436	C₂²×C₅	1	1	yes	characteristic
251	#436	C₂²×C₅	1	1	yes	characteristic, complemented
252	#435	—	2	1	no	—
253	#435	—	2	1	no	—
254	#435	—	2	1	no	—
255	C₈×D₄	C₂²×C₅	1	1	yes	characteristic
256	C₈×D₄	C₂²×C₅	1	1	yes	characteristic
257	C₈×D₄	C₂²×C₅	1	1	yes	characteristic, complemented
258	#433	—	2	1	no	—
259	#431	C₂²×C₅	1	1	yes	characteristic
260	#431	C₂²×C₅	1	1	yes	characteristic
261	#431	C₂²×C₅	1	1	yes	characteristic
262	#423	C₂²×C₅	1	1	yes	characteristic
263	#407	—	2	1	no	—
264	#405	—	2	1	no	—
265	C₄×M₁₆	C₂²×C₅	1	1	yes	characteristic
266	#335	C₂²×C₅	1	1	yes	characteristic, complemented
267	#335	C₂²×C₅	1	1	yes	characteristic, complemented
268	#334	C₂²×C₅	1	1	yes	characteristic, complemented
269	#334	C₂²×C₅	1	1	yes	characteristic, complemented
270	Q₈⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
271	Q₈⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
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, complemented
277	D₄⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
278	#322	C₂²×C₅	1	1	yes	characteristic, complemented
279	#322	C₂²×C₅	1	1	yes	characteristic, complemented
280	#322	C₂²×C₅	1	1	yes	characteristic, complemented
281	C₈²	C₂²×C₅	1	1	yes	characteristic, complemented
282	C₂³×C₅	—	2	1	no	—
283	C₂³×C₅	—	2	1	no	—
284	C₂³×C₅	—	2	1	no	—
285	C₂³×C₅	—	4	2	no	—
286	C₂³×C₅	—	4	2	no	—
287	C₂³×C₅	—	8	1	no	—
288	C₂³×C₅	C₄×D₄	1	1	yes	characteristic
289	C₅×Q₈	—	2	1	no	—
290	C₅×Q₈	—	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	—	2	1	no	—
296	C₅×D₄	—	4	2	no	—
297	C₅×D₄	—	8	1	no	—
298	C₅×D₄	#131	1	2	yes	—
299	C₂×C₄×C₅	—	2	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	—	4	1	no	—
309	C₂×C₄×C₅	—	4	2	no	—
310	C₂×C₄×C₅	—	4	2	no	—
311	C₂×C₄×C₅	—	4	2	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	—	4	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	C₂²×D₄	C₂×C₄×C₅	1	1	yes	characteristic
339	C₂³×C₄	—	2	1	no	—
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	C₂×M₁₆	—	2	1	no	—
345	C₂×M₁₆	—	2	1	no	—
346	C₂×M₁₆	—	2	1	no	—
347	C₂×M₁₆	—	2	1	no	—
348	C₂×M₁₆	—	4	4	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	#126	—	2	1	no	—
355	#125	C₂×C₄×C₅	1	1	yes	characteristic
356	#124	C₂×C₄×C₅	1	1	yes	characteristic
357	#123	—	2	1	no	—
358	C₂²⋊Q₈	C₂×C₄×C₅	1	1	yes	characteristic
359	#121	C₂×C₄×C₅	1	1	yes	characteristic
360	C₄×Q₈	C₂³×C₅	1	1	yes	characteristic
361	C₄×D₄	—	2	1	no	—
362	C₄×D₄	—	2	1	no	—
363	C₄×D₄	—	2	1	no	—
364	C₄×D₄	C₂×C₄×C₅	1	1	yes	characteristic
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	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
371	C₂×C₂²⋊C₄	—	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	2	no	—
418	C₂²×C₅	—	2	1	no	—
419	C₂²×C₅	—	2	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	—	8	4	no	—
429	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
430	C₄×C₅	—	2	1	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	—	4	1	no	—
439	C₄×C₅	C₂×#131	1	1	yes	characteristic
440	C₄×C₅	#568	1	1	yes	characteristic
441	C₄×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
442	C₄×C₅	#575	1	1	yes	characteristic
443	C₂⁴	—	2	1	no	—
444	C₂×Q₈	C₂²×C₄×C₅	1	1	yes	characteristic
445	C₂×D₄	—	2	2	no	—
446	C₂×D₄	—	2	1	no	—
447	C₂×D₄	—	2	1	no	—
448	C₂×D₄	—	4	1	no	—
449	C₂×D₄	C₂²×C₄×C₅	1	1	yes	characteristic
450	C₂×D₄	C₂²×C₄×C₅	1	1	yes	characteristic
451	C₂×D₄	C₂²×C₄×C₅	1	1	yes	characteristic
452	C₂²×C₄	—	2	1	no	—
453	C₂²×C₄	—	2	1	no	—
454	C₂²×C₄	—	2	1	no	—
455	C₂²×C₄	—	2	1	no	—
456	C₂²×C₄	—	2	1	no	—
457	C₂²×C₄	—	2	1	no	—
458	C₂²×C₄	—	4	2	no	—
459	C₂²×C₄	—	4	2	no	—
460	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
461	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
462	C₂²×C₄	C₅×#41	1	1	yes	characteristic
463	SD₁₆	—	2	2	no	—
464	SD₁₆	—	4	1	no	—
465	D₈	—	2	2	no	—
466	D₈	—	4	1	no	—
467	M₁₆	—	2	2	no	—
468	M₁₆	—	4	1	no	—
469	M₁₆	—	4	2	no	—
470	M₁₆	—	4	2	no	—
471	M₁₆	—	4	2	no	—
472	M₁₆	—	4	2	no	—
473	C₂×C₈	—	2	1	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	—	4	2	no	—
480	C₂×C₈	—	4	2	no	—
481	C₂×C₈	—	4	2	no	—
482	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
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	C₂×C₅×D₄	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	C₄⋊C₄	—	2	1	no	—
491	C₄⋊C₄	—	2	1	no	—
492	C₄⋊C₄	—	2	1	no	—
493	C₄⋊C₄	—	2	1	no	—
494	C₄⋊C₄	—	2	1	no	—
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	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
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	C₂²⋊C₄	—	2	1	no	—
506	C₂²⋊C₄	—	2	1	no	—
507	C₂²⋊C₄	—	2	1	no	—
508	C₄²	—	2	1	no	—
509	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
510	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
511	C₄²	C₅×#41	1	1	yes	characteristic
512	C₄²	C₂⁴×C₅	1	1	yes	characteristic
513	C₂×C₅	—	4	1	no	—
514	C₂×C₅	—	4	2	no	—
515	C₂×C₅	—	8	1	no	—
516	C₂×C₅	—	8	1	no	—
517	C₂×C₅	#2933	1	1	yes	characteristic
518	C₂×C₅	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic
519	C₂×C₅	#2957	1	1	yes	characteristic
520	C₂³	—	2	1	no	—
521	C₂³	—	2	1	no	—
522	C₂³	—	2	1	no	—
523	C₂³	—	4	2	no	—
524	C₂³	—	4	2	no	—
525	C₂³	—	8	1	no	—
526	C₂³	C₄×C₅×D₄	1	1	yes	characteristic
527	Q₈	—	2	1	no	—
528	Q₈	—	2	1	no	—
529	D₄	—	2	1	no	—
530	D₄	—	2	1	no	—
531	D₄	—	2	1	no	—
532	D₄	—	2	1	no	—
533	D₄	—	2	1	no	—
534	D₄	—	4	2	no	—
535	D₄	—	8	1	no	—
536	D₄	C₅×#131	1	2	yes	—
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	2	no	—
549	C₂×C₄	—	4	2	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	—	4	1	no	—
555	C₂×C₄	—	4	1	no	—
556	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
557	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
558	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
559	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
560	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
561	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
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	—	2	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	—	4	1	no	—
575	C₈	C₅×AGL(1,ℤ/8)	1	2	yes	—
576	C₅	#18008	1	1	yes	characteristic, direct product factor, Sylow
577	C₂²	—	2	1	no	—
578	C₂²	—	2	2	no	—
579	C₂²	—	2	1	no	—
580	C₂²	—	2	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	—	4	1	no	—
589	C₂²	—	8	4	no	—
590	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
591	C₄	—	2	1	no	—
592	C₄	—	2	1	no	—
593	C₄	—	2	1	no	—
594	C₄	—	2	1	no	—
595	C₄	—	4	1	no	—
596	C₄	—	4	1	no	—
597	C₄	—	4	1	no	—
598	C₄	—	4	1	no	—
599	C₄	—	4	1	no	—
600	C₄	C₂×C₅×#131	1	1	yes	characteristic
601	C₄	C₅×#568	1	1	yes	characteristic
602	C₄	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
603	C₄	C₅×#575	1	1	yes	characteristic
604	C₂	—	4	1	no	—
605	C₂	—	4	2	no	—
606	C₂	—	8	1	no	—
607	C₂	—	8	1	no	—
608	C₂	C₅×#2933	1	1	yes	characteristic
609	C₂	C₄×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
610	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×#447	C₄
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×#2969	C₂	semidirect
3. C₅×D₄×M₁₆	C₂	semidirect
4. C₅×#1592	C₂	semidirect
5. C₅×#1589	C₂	semidirect
6. C₅×#1586	C₂	semidirect
7. C₅×#1585	C₂	semidirect
8. C₅×#1583	C₂	semidirect
9. C₅×#1581	C₂	semidirect
10. C₅×#1580	C₂	semidirect
11. C₅×C₈×SD₁₆	C₂	semidirect
12. C₅×#1574	C₂	semidirect
13. C₅×#1495	C₂	semidirect
14. C₅×#1478	C₂	semidirect
15. C₅×#1453	C₂	semidirect
27. C₅×#446	C₂²	semidirect
28. C₅×C₈×Q₈	C₂²	semidirect
36. C₅×#436	C₂²	semidirect
42. C₅×C₈×D₄	C₂²	semidirect
51. C₅×#335	C₂²	semidirect
52. C₅×#335	C₂²	semidirect
53. C₅×#334	C₂²	semidirect
54. C₅×#334	C₂²	semidirect
55. C₅×Q₈⋊C₈	C₂²	semidirect
56. C₅×Q₈⋊C₈	C₂²	semidirect
61. C₅×D₄⋊C₈	C₂²	semidirect
62. C₅×D₄⋊C₈	C₂²	semidirect
63. C₅×#322	C₂²	semidirect
64. C₅×#322	C₂²	semidirect
65. C₅×#322	C₂²	semidirect
66. C₅×C₈²	C₂²	semidirect
67. #18008	C₅	direct (N × H)
147. #2969	C₂×C₅	semidirect
148. D₄×M₁₆	C₂×C₅	semidirect
149. #1592	C₂×C₅	semidirect
150. #1589	C₂×C₅	semidirect
151. #1586	C₂×C₅	semidirect
152. #1585	C₂×C₅	semidirect
153. #1583	C₂×C₅	semidirect
154. #1581	C₂×C₅	semidirect
155. #1580	C₂×C₅	semidirect
156. C₈×SD₁₆	C₂×C₅	semidirect
157. #1574	C₂×C₅	semidirect
158. #1495	C₂×C₅	semidirect
159. #1478	C₂×C₅	semidirect
160. #1453	C₂×C₅	semidirect
242. #446	C₂²×C₅	semidirect
243. C₈×Q₈	C₂²×C₅	semidirect
251. #436	C₂²×C₅	semidirect
257. C₈×D₄	C₂²×C₅	semidirect
266. #335	C₂²×C₅	semidirect
267. #335	C₂²×C₅	semidirect
268. #334	C₂²×C₅	semidirect
269. #334	C₂²×C₅	semidirect
270. Q₈⋊C₈	C₂²×C₅	semidirect
271. Q₈⋊C₈	C₂²×C₅	semidirect
276. D₄⋊C₈	C₂²×C₅	semidirect
277. D₄⋊C₈	C₂²×C₅	semidirect
278. #322	C₂²×C₅	semidirect
279. #322	C₂²×C₅	semidirect
280. #322	C₂²×C₅	semidirect
281. C₈²	C₂²×C₅	semidirect
576. C₅	#18008	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×#3105	2
C₅×#2969	2
C₅×D₄×M₁₆	2
C₅×#1592	2
C₅×#1589	2
C₅×#1586	2
C₅×#1585	2
C₅×#1583	2
C₅×#1581	2
C₅×#1580	2
C₅×C₈×SD₁₆	2
C₅×#1574	2
C₅×#1495	2
C₅×#1478	2
C₅×#1453	2
#18008	5

Subgroups — C5×#18008 #11940728

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#18008 #11940728