Subgroups — C₅×#83930 #14417006

Order 1920.

1012 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic
2	C₅×#5827	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#5798	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5233	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₅×#832	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#5164	C₂	1	2	yes	maximal, complemented
7	C₅×Dic₃×SD₁₆	C₂	1	2	yes	maximal, complemented
8	C₅×#5152	C₂	1	2	yes	maximal, complemented
9	C₅×Dic₃×D₈	C₂	1	2	yes	maximal, complemented
10	C₅×#5122	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#5121	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#2946	—	3	1	no	maximal, Hall
13	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
14	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
15	C₃×C₅×AGL(1,ℤ/8)	C₄	1	8	yes	complemented
16	C₂×C₃×C₅×SD₁₆	C₂²	1	2	yes	—
17	C₂×C₃×C₅×D₈	C₂²	1	2	yes	—
18	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
19	C₂×C₅×#217	—	2	2	no	—
20	C₅×Q₈×Dic₃	C₂²	1	2	yes	complemented
21	C₅×D₄×Dic₃	—	2	2	no	—
22	C₅×D₄×Dic₃	—	2	1	no	—
23	C₅×D₄×Dic₃	—	2	1	no	—
24	C₅×D₄×Dic₃	C₂²	1	2	yes	—
25	C₅×D₄×Dic₃	C₂²	1	2	yes	—
26	C₅×D₄×Dic₃	C₂²	1	2	yes	complemented
27	C₅×#926	—	2	1	no	—
28	C₅×#926	C₂²	1	1	yes	characteristic
29	C₅×#926	C₂²	1	1	yes	characteristic
30	C₂×C₅×C₄⋊Dic₃	—	2	1	no	—
31	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
32	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
33	C₅×#835	C₂²	1	1	yes	characteristic, complemented
34	C₅×#835	C₂²	1	1	yes	characteristic, complemented
35	C₅×#832	C₂²	1	2	yes	—
36	C₅×#832	C₂²	1	2	yes	—
37	C₅×#832	C₂²	1	1	yes	characteristic, complemented
38	C₅×#832	C₂²	1	1	yes	characteristic, complemented
39	C₅×#818	C₂²	1	2	yes	complemented
40	C₅×#817	C₂²	1	2	yes	complemented
41	C₅×#815	C₂²	1	2	yes	complemented
42	C₅×C₈×Dic₃	C₂²	1	2	yes	complemented
43	#83930	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
44	C₂×C₅×AGL(1,ℤ/8)	D₃	1	1	yes	characteristic
45	C₅×#520	—	3	1	no	—
46	C₅×#518	—	3	1	no	—
47	C₅×#442	—	3	2	no	—
48	C₅×#440	—	3	2	no	—
49	C₄×C₅×SD₁₆	—	3	2	no	—
50	C₄×C₅×D₈	—	3	2	no	—
51	C₅×#428	—	3	1	no	—
52	C₅×#416	—	3	1	no	—
53	C₂×C₅×#102	—	3	1	no	—
54	C₅×#405	—	3	1	no	—
55	C₂⁴×C₃×C₅	—	2	1	no	—
56	C₃×C₅×#41	—	2	2	no	—
57	C₃×C₅×#41	C₂×C₄	1	4	yes	complemented
58	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
59	C₂×C₃×C₅×D₄	—	2	1	no	—
60	C₂×C₃×C₅×D₄	—	2	1	no	—
61	C₂×C₃×C₅×D₄	—	2	2	no	—
62	C₂×C₃×C₅×D₄	C₂×C₄	1	4	yes	complemented
63	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
64	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
65	C₂²×C₃×C₄×C₅	—	2	1	no	—
66	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
67	C₂²×C₅×Dic₃	—	2	1	no	—
68	C₂²×C₅×Dic₃	—	2	2	no	—
69	C₂²×C₅×Dic₃	—	2	2	no	—
70	C₂²×C₅×Dic₃	—	2	2	no	—
71	C₃×C₅×SD₁₆	C₂×C₄	1	8	yes	complemented
72	C₃×C₅×D₈	C₂×C₄	1	8	yes	complemented
73	C₃×C₅×M₁₆	C₂×C₄	1	4	yes	complemented
74	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
75	C₅×#217	—	2	1	no	—
76	C₅×#217	—	2	2	no	—
77	C₅×#217	—	2	2	no	—
78	C₅×#217	—	2	2	no	—
79	C₅×#217	D₄	1	2	yes	—
80	C₅×C₄⋊Dic₃	—	2	1	no	—
81	C₅×C₄⋊Dic₃	—	2	2	no	—
82	C₅×C₄⋊Dic₃	D₄	1	1	yes	characteristic
83	C₅×C₄⋊Dic₃	D₄	1	1	yes	characteristic
84	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
85	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
86	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
87	C₄×C₅×Dic₃	—	2	1	no	—
88	C₄×C₅×Dic₃	—	2	2	no	—
89	C₄×C₅×Dic₃	C₂³	1	2	yes	—
90	C₂×C₅×C₃⋊C₈	—	2	2	no	—
91	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
92	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
93	C₂×C₃×AGL(1,ℤ/8)	C₂×C₅	1	1	yes	characteristic
94	#5827	C₂×C₅	1	1	yes	characteristic, complemented
95	#5798	C₂×C₅	1	1	yes	characteristic, complemented
96	#5233	C₂×C₅	1	1	yes	characteristic, complemented
97	C₂×#832	C₂×C₅	1	1	yes	characteristic, complemented
98	#5164	C₂×C₅	1	2	yes	complemented
99	Dic₃×SD₁₆	C₂×C₅	1	2	yes	complemented
100	#5152	C₂×C₅	1	2	yes	complemented
101	Dic₃×D₈	C₂×C₅	1	2	yes	complemented
102	#5122	C₂×C₅	1	1	yes	characteristic, complemented
103	#5121	C₂×C₅	1	1	yes	characteristic, complemented
104	C₂×C₅×#41	C₂×D₃	1	1	yes	characteristic
105	C₂²×C₅×D₄	C₂×D₃	1	1	yes	characteristic
106	C₅×AGL(1,ℤ/8)	Dic₃	1	8	yes	complemented
107	C₂×C₅×SD₁₆	C₂×D₃	1	2	yes	—
108	C₂×C₅×D₈	C₂×D₃	1	2	yes	—
109	C₂×C₅×M₁₆	C₂×D₃	1	1	yes	characteristic
110	C₂²×C₅×C₈	—	3	1	no	—
111	C₄×C₅×Q₈	—	3	2	no	—
112	C₄×C₅×D₄	—	3	2	no	—
113	C₄×C₅×D₄	—	3	2	no	—
114	C₄×C₅×D₄	—	3	2	no	—
115	C₄×C₅×D₄	—	6	2	no	—
116	C₄×C₅×D₄	—	6	1	no	—
117	C₄×C₅×D₄	—	6	1	no	—
118	C₅×#117	—	3	1	no	—
119	C₅×#117	—	3	1	no	—
120	C₅×#117	—	6	1	no	—
121	C₂×C₅×C₄⋊C₄	—	3	1	no	—
122	C₂×C₅×C₄⋊C₄	—	6	1	no	—
123	C₂×C₅×C₂²⋊C₄	—	6	2	no	—
124	C₅×#107	—	3	2	no	—
125	C₅×#106	—	3	2	no	—
126	C₅×#103	—	3	1	no	—
127	C₅×#103	—	3	1	no	—
128	C₅×#102	—	3	2	no	—
129	C₅×#102	—	3	2	no	—
130	C₅×#102	—	3	1	no	—
131	C₅×#102	—	3	1	no	—
132	C₅×#97	—	3	2	no	—
133	C₄×C₅×C₈	—	3	2	no	—
134	#2946	—	3	1	no	Sylow
135	C₂³×C₃×C₅	—	2	1	no	—
136	C₂³×C₃×C₅	—	2	2	no	—
137	C₂³×C₃×C₅	—	2	4	no	—
138	C₂³×C₃×C₅	—	8	1	no	—
139	C₂³×C₃×C₅	—	8	1	no	—
140	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
141	C₃×C₅×Q₈	—	2	1	no	—
142	C₃×C₅×Q₈	C₂²×C₄	1	2	yes	—
143	C₃×C₅×D₄	—	2	4	no	—
144	C₃×C₅×D₄	—	2	4	no	—
145	C₃×C₅×D₄	—	2	2	no	—
146	C₃×C₅×D₄	—	2	1	no	—
147	C₃×C₅×D₄	C₂²×C₄	1	2	yes	—
148	C₃×C₅×D₄	C₂²×C₄	1	4	yes	—
149	C₂×C₃×C₄×C₅	—	2	1	no	—
150	C₂×C₃×C₄×C₅	—	2	4	no	—
151	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
152	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
153	C₂×C₃×C₄×C₅	#41	1	2	yes	—
154	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
155	C₂×C₅×Dic₃	—	2	2	no	—
156	C₂×C₅×Dic₃	—	2	1	no	—
157	C₂×C₅×Dic₃	—	2	1	no	—
158	C₂×C₅×Dic₃	—	8	2	no	—
159	C₂×C₅×Dic₃	—	8	2	no	—
160	C₂×C₅×Dic₃	—	8	2	no	—
161	C₂×C₅×Dic₃	—	8	1	no	—
162	C₂×C₅×Dic₃	C₂×D₄	1	2	yes	—
163	C₂×C₅×Dic₃	C₂×D₄	1	2	yes	—
164	C₃×C₅×C₈	C₂²×C₄	1	4	yes	—
165	C₅×C₃⋊C₈	—	2	1	no	—
166	C₅×C₃⋊C₈	—	2	1	no	—
167	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
168	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
169	C₃×AGL(1,ℤ/8)	C₄×C₅	1	8	yes	complemented
170	C₂×C₃×SD₁₆	C₂²×C₅	1	2	yes	—
171	C₂×C₃×D₈	C₂²×C₅	1	2	yes	—
172	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
173	C₂×#217	—	2	2	no	—
174	Q₈×Dic₃	C₂²×C₅	1	2	yes	complemented
175	D₄×Dic₃	—	2	2	no	—
176	D₄×Dic₃	—	2	1	no	—
177	D₄×Dic₃	—	2	1	no	—
178	D₄×Dic₃	C₂²×C₅	1	2	yes	—
179	D₄×Dic₃	C₂²×C₅	1	2	yes	—
180	D₄×Dic₃	C₂²×C₅	1	2	yes	complemented
181	#926	—	2	1	no	—
182	#926	C₂²×C₅	1	1	yes	characteristic
183	#926	C₂²×C₅	1	1	yes	characteristic
184	C₂×C₄⋊Dic₃	—	2	1	no	—
185	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
186	C₂²×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
187	#835	C₂²×C₅	1	1	yes	characteristic, complemented
188	#835	C₂²×C₅	1	1	yes	characteristic, complemented
189	#832	C₂²×C₅	1	2	yes	—
190	#832	C₂²×C₅	1	2	yes	—
191	#832	C₂²×C₅	1	1	yes	characteristic, complemented
192	#832	C₂²×C₅	1	1	yes	characteristic, complemented
193	#818	C₂²×C₅	1	2	yes	complemented
194	#817	C₂²×C₅	1	2	yes	complemented
195	#815	C₂²×C₅	1	2	yes	complemented
196	C₈×Dic₃	C₂²×C₅	1	2	yes	complemented
197	C₂⁴×C₅	—	2	1	no	—
198	C₅×#41	—	2	2	no	—
199	C₅×#41	C₂×Dic₃	1	4	yes	complemented
200	C₂×C₅×Q₈	C₂²×D₃	1	1	yes	characteristic
201	C₂×C₅×D₄	—	2	1	no	—
202	C₂×C₅×D₄	—	2	1	no	—
203	C₂×C₅×D₄	—	2	2	no	—
204	C₂×C₅×D₄	C₂×Dic₃	1	4	yes	complemented
205	C₂×C₅×D₄	C₂²×D₃	1	1	yes	characteristic
206	C₂×C₅×D₄	C₂²×D₃	1	2	yes	—
207	C₂²×C₄×C₅	—	2	1	no	—
208	C₂²×C₄×C₅	—	6	2	no	—
209	C₂²×C₄×C₅	—	6	2	no	—
210	C₂²×C₄×C₅	—	6	2	no	—
211	C₂²×C₄×C₅	—	6	1	no	—
212	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
213	C₅×SD₁₆	C₂×Dic₃	1	8	yes	complemented
214	C₅×D₈	C₂×Dic₃	1	8	yes	complemented
215	C₅×M₁₆	C₂×Dic₃	1	4	yes	complemented
216	C₂×C₅×C₈	—	3	1	no	—
217	C₂×C₅×C₈	—	3	1	no	—
218	C₂×C₅×C₈	—	6	2	no	—
219	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
220	C₅×C₄⋊C₄	—	3	1	no	—
221	C₅×C₄⋊C₄	—	3	1	no	—
222	C₅×C₄⋊C₄	—	3	2	no	—
223	C₅×C₄⋊C₄	—	3	1	no	—
224	C₅×C₄⋊C₄	—	3	1	no	—
225	C₅×C₄⋊C₄	—	6	2	no	—
226	C₅×C₄⋊C₄	—	6	1	no	—
227	C₅×C₂²⋊C₄	—	3	2	no	—
228	C₅×C₂²⋊C₄	—	6	2	no	—
229	C₅×C₂²⋊C₄	—	6	2	no	—
230	C₅×C₂²⋊C₄	—	6	2	no	—
231	C₅×C₂²⋊C₄	—	6	1	no	—
232	C₄²×C₅	—	3	2	no	—
233	C₄²×C₅	—	6	2	no	—
234	C₄²×C₅	—	6	1	no	—
235	C₂×AGL(1,ℤ/8)	C₅×D₃	1	1	yes	characteristic
236	#520	—	3	1	no	—
237	#518	—	3	1	no	—
238	#442	—	3	2	no	—
239	#440	—	3	2	no	—
240	C₄×SD₁₆	—	3	2	no	—
241	C₄×D₈	—	3	2	no	—
242	#428	—	3	1	no	—
243	#416	—	3	1	no	—
244	C₂×#102	—	3	1	no	—
245	#405	—	3	1	no	—
246	C₂²×C₃×C₅	—	2	1	no	—
247	C₂²×C₃×C₅	—	2	1	no	—
248	C₂²×C₃×C₅	—	2	2	no	—
249	C₂²×C₃×C₅	—	2	4	no	—
250	C₂²×C₃×C₅	—	4	1	no	—
251	C₂²×C₃×C₅	—	4	2	no	—
252	C₂²×C₃×C₅	—	4	2	no	—
253	C₂²×C₃×C₅	—	4	1	no	—
254	C₂²×C₃×C₅	—	8	4	no	—
255	C₂²×C₃×C₅	C₄×D₄	1	2	yes	—
256	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
257	C₃×C₄×C₅	—	2	2	no	—
258	C₃×C₄×C₅	C₄×D₄	1	2	yes	—
259	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
260	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
261	C₅×Dic₃	—	2	2	no	—
262	C₅×Dic₃	—	2	2	no	—
263	C₅×Dic₃	—	4	2	no	—
264	C₅×Dic₃	—	4	1	no	—
265	C₅×Dic₃	—	4	1	no	—
266	C₂⁴×C₃	—	2	1	no	—
267	C₃×#41	—	2	2	no	—
268	C₃×#41	C₂×C₄×C₅	1	4	yes	complemented
269	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
270	C₂×C₃×D₄	—	2	1	no	—
271	C₂×C₃×D₄	—	2	1	no	—
272	C₂×C₃×D₄	—	2	2	no	—
273	C₂×C₃×D₄	C₂×C₄×C₅	1	4	yes	complemented
274	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
275	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
276	C₂²×C₃×C₄	—	2	1	no	—
277	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
278	C₂²×Dic₃	—	2	1	no	—
279	C₂²×Dic₃	—	2	2	no	—
280	C₂²×Dic₃	—	2	2	no	—
281	C₂²×Dic₃	—	2	2	no	—
282	C₃×SD₁₆	C₂×C₄×C₅	1	8	yes	complemented
283	C₃×D₈	C₂×C₄×C₅	1	8	yes	complemented
284	C₃×M₁₆	C₂×C₄×C₅	1	4	yes	complemented
285	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
286	#217	—	2	1	no	—
287	#217	—	2	2	no	—
288	#217	—	2	2	no	—
289	#217	—	2	2	no	—
290	#217	C₅×D₄	1	2	yes	—
291	C₄⋊Dic₃	—	2	1	no	—
292	C₄⋊Dic₃	—	2	2	no	—
293	C₄⋊Dic₃	C₅×D₄	1	1	yes	characteristic
294	C₄⋊Dic₃	C₅×D₄	1	1	yes	characteristic
295	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
296	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
297	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
298	C₄×Dic₃	—	2	1	no	—
299	C₄×Dic₃	—	2	2	no	—
300	C₄×Dic₃	C₂³×C₅	1	2	yes	—
301	C₂×C₃⋊C₈	—	2	2	no	—
302	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
303	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
304	C₂³×C₅	—	2	1	no	—
305	C₂³×C₅	—	2	2	no	—
306	C₂³×C₅	—	2	4	no	—
307	C₂³×C₅	—	8	1	no	—
308	C₂³×C₅	—	8	1	no	—
309	C₂³×C₅	D₃×D₄	1	1	yes	characteristic
310	C₅×Q₈	—	2	1	no	—
311	C₅×Q₈	C₂²×Dic₃	1	2	yes	—
312	C₅×D₄	—	2	4	no	—
313	C₅×D₄	—	2	4	no	—
314	C₅×D₄	—	2	2	no	—
315	C₅×D₄	—	2	1	no	—
316	C₅×D₄	C₂²×Dic₃	1	2	yes	—
317	C₅×D₄	C₂²×Dic₃	1	4	yes	—
318	C₂×C₄×C₅	—	2	1	no	—
319	C₂×C₄×C₅	—	2	4	no	—
320	C₂×C₄×C₅	—	3	2	no	—
321	C₂×C₄×C₅	—	3	2	no	—
322	C₂×C₄×C₅	—	6	1	no	—
323	C₂×C₄×C₅	—	6	1	no	—
324	C₂×C₄×C₅	—	6	2	no	—
325	C₂×C₄×C₅	—	24	2	no	—
326	C₂×C₄×C₅	—	24	2	no	—
327	C₂×C₄×C₅	—	24	2	no	—
328	C₂×C₄×C₅	—	24	1	no	—
329	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
330	C₂×C₄×C₅	#237	1	2	yes	—
331	C₂×C₄×C₅	C₂²×Dic₃	1	2	yes	—
332	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
333	C₅×C₈	—	6	1	no	—
334	C₅×C₈	—	6	1	no	—
335	C₅×C₈	C₂²×Dic₃	1	4	yes	—
336	C₂×#41	C₂×C₅×D₃	1	1	yes	characteristic
337	C₂²×D₄	C₂×C₅×D₃	1	1	yes	characteristic
338	AGL(1,ℤ/8)	C₅×Dic₃	1	8	yes	complemented
339	C₂×SD₁₆	C₂×C₅×D₃	1	2	yes	—
340	C₂×D₈	C₂×C₅×D₃	1	2	yes	—
341	C₂×M₁₆	C₂×C₅×D₃	1	1	yes	characteristic
342	C₂²×C₈	—	3	1	no	—
343	C₄×Q₈	—	3	2	no	—
344	C₄×D₄	—	3	2	no	—
345	C₄×D₄	—	3	2	no	—
346	C₄×D₄	—	3	2	no	—
347	C₄×D₄	—	6	2	no	—
348	C₄×D₄	—	6	1	no	—
349	C₄×D₄	—	6	1	no	—
350	#117	—	3	1	no	—
351	#117	—	3	1	no	—
352	#117	—	6	1	no	—
353	C₂×C₄⋊C₄	—	3	1	no	—
354	C₂×C₄⋊C₄	—	6	1	no	—
355	C₂×C₂²⋊C₄	—	6	2	no	—
356	#107	—	3	2	no	—
357	#106	—	3	2	no	—
358	#103	—	3	1	no	—
359	#103	—	3	1	no	—
360	#102	—	3	2	no	—
361	#102	—	3	2	no	—
362	#102	—	3	1	no	—
363	#102	—	3	1	no	—
364	#97	—	3	2	no	—
365	C₄×C₈	—	3	2	no	—
366	C₂×C₃×C₅	—	2	2	no	—
367	C₂×C₃×C₅	—	4	2	no	—
368	C₂×C₃×C₅	—	4	4	no	—
369	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
370	C₂×C₃×C₅	#576	1	1	yes	characteristic
371	C₂×C₃×C₅	#577	1	1	yes	characteristic
372	C₂³×C₃	—	2	1	no	—
373	C₂³×C₃	—	2	2	no	—
374	C₂³×C₃	—	2	4	no	—
375	C₂³×C₃	—	8	1	no	—
376	C₂³×C₃	—	8	1	no	—
377	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
378	C₃×Q₈	—	2	1	no	—
379	C₃×Q₈	C₂²×C₄×C₅	1	2	yes	—
380	C₃×D₄	—	2	4	no	—
381	C₃×D₄	—	2	4	no	—
382	C₃×D₄	—	2	2	no	—
383	C₃×D₄	—	2	1	no	—
384	C₃×D₄	C₂²×C₄×C₅	1	2	yes	—
385	C₃×D₄	C₂²×C₄×C₅	1	4	yes	—
386	C₂×C₃×C₄	—	2	1	no	—
387	C₂×C₃×C₄	—	2	4	no	—
388	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
389	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
390	C₂×C₃×C₄	C₅×#41	1	2	yes	—
391	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
392	C₂×Dic₃	—	2	2	no	—
393	C₂×Dic₃	—	2	1	no	—
394	C₂×Dic₃	—	2	1	no	—
395	C₂×Dic₃	—	8	2	no	—
396	C₂×Dic₃	—	8	2	no	—
397	C₂×Dic₃	—	8	2	no	—
398	C₂×Dic₃	—	8	1	no	—
399	C₂×Dic₃	C₂×C₅×D₄	1	2	yes	—
400	C₂×Dic₃	C₂×C₅×D₄	1	2	yes	—
401	C₃×C₈	C₂²×C₄×C₅	1	4	yes	—
402	C₃⋊C₈	—	2	1	no	—
403	C₃⋊C₈	—	2	1	no	—
404	C₂²×C₅	—	2	1	no	—
405	C₂²×C₅	—	2	1	no	—
406	C₂²×C₅	—	2	2	no	—
407	C₂²×C₅	—	2	4	no	—
408	C₂²×C₅	—	4	1	no	—
409	C₂²×C₅	—	4	2	no	—
410	C₂²×C₅	—	4	2	no	—
411	C₂²×C₅	—	4	1	no	—
412	C₂²×C₅	—	8	4	no	—
413	C₂²×C₅	D₄×Dic₃	1	2	yes	—
414	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
415	C₄×C₅	—	2	2	no	—
416	C₄×C₅	—	6	2	no	—
417	C₄×C₅	—	6	2	no	—
418	C₄×C₅	—	12	1	no	—
419	C₄×C₅	—	12	2	no	—
420	C₄×C₅	—	12	1	no	—
421	C₄×C₅	D₄×Dic₃	1	2	yes	—
422	C₄×C₅	C₂×#237	1	1	yes	characteristic
423	C₄×C₅	C₂³×Dic₃	1	1	yes	characteristic
424	C₂⁴	—	2	1	no	—
425	#41	—	2	2	no	—
426	#41	C₂×C₅×Dic₃	1	4	yes	complemented
427	C₂×Q₈	C₂²×C₅×D₃	1	1	yes	characteristic
428	C₂×D₄	—	2	1	no	—
429	C₂×D₄	—	2	1	no	—
430	C₂×D₄	—	2	2	no	—
431	C₂×D₄	C₂×C₅×Dic₃	1	4	yes	complemented
432	C₂×D₄	C₂²×C₅×D₃	1	1	yes	characteristic
433	C₂×D₄	C₂²×C₅×D₃	1	2	yes	—
434	C₂²×C₄	—	2	1	no	—
435	C₂²×C₄	—	6	2	no	—
436	C₂²×C₄	—	6	2	no	—
437	C₂²×C₄	—	6	2	no	—
438	C₂²×C₄	—	6	1	no	—
439	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
440	SD₁₆	C₂×C₅×Dic₃	1	8	yes	complemented
441	D₈	C₂×C₅×Dic₃	1	8	yes	complemented
442	M₁₆	C₂×C₅×Dic₃	1	4	yes	complemented
443	C₂×C₈	—	3	1	no	—
444	C₂×C₈	—	3	1	no	—
445	C₂×C₈	—	6	2	no	—
446	C₂×C₈	C₂²×C₅×D₃	1	2	yes	—
447	C₄⋊C₄	—	3	1	no	—
448	C₄⋊C₄	—	3	1	no	—
449	C₄⋊C₄	—	3	2	no	—
450	C₄⋊C₄	—	3	1	no	—
451	C₄⋊C₄	—	3	1	no	—
452	C₄⋊C₄	—	6	2	no	—
453	C₄⋊C₄	—	6	1	no	—
454	C₂²⋊C₄	—	3	2	no	—
455	C₂²⋊C₄	—	6	2	no	—
456	C₂²⋊C₄	—	6	2	no	—
457	C₂²⋊C₄	—	6	2	no	—
458	C₂²⋊C₄	—	6	1	no	—
459	C₄²	—	3	2	no	—
460	C₄²	—	6	2	no	—
461	C₄²	—	6	1	no	—
462	C₃×C₅	#2946	1	1	yes	characteristic, complemented, Hall
463	C₂²×C₃	—	2	1	no	—
464	C₂²×C₃	—	2	1	no	—
465	C₂²×C₃	—	2	2	no	—
466	C₂²×C₃	—	2	4	no	—
467	C₂²×C₃	—	4	1	no	—
468	C₂²×C₃	—	4	2	no	—
469	C₂²×C₃	—	4	2	no	—
470	C₂²×C₃	—	4	1	no	—
471	C₂²×C₃	—	8	4	no	—
472	C₂²×C₃	C₄×C₅×D₄	1	2	yes	—
473	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
474	C₃×C₄	—	2	2	no	—
475	C₃×C₄	C₄×C₅×D₄	1	2	yes	—
476	C₃×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
477	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
478	Dic₃	—	2	2	no	—
479	Dic₃	—	2	2	no	—
480	Dic₃	—	4	2	no	—
481	Dic₃	—	4	1	no	—
482	Dic₃	—	4	1	no	—
483	C₂×C₅	—	2	2	no	—
484	C₂×C₅	—	4	4	no	—
485	C₂×C₅	—	4	2	no	—
486	C₂×C₅	#5774	1	1	yes	characteristic
487	C₂×C₅	#5775	1	1	yes	characteristic
488	C₂×C₅	C₂×D₄×Dic₃	1	1	yes	characteristic
489	C₂³	—	2	1	no	—
490	C₂³	—	2	2	no	—
491	C₂³	—	2	4	no	—
492	C₂³	—	8	1	no	—
493	C₂³	—	8	1	no	—
494	C₂³	C₅×D₃×D₄	1	1	yes	characteristic
495	Q₈	—	2	1	no	—
496	Q₈	C₂²×C₅×Dic₃	1	2	yes	—
497	D₄	—	2	4	no	—
498	D₄	—	2	4	no	—
499	D₄	—	2	2	no	—
500	D₄	—	2	1	no	—
501	D₄	C₂²×C₅×Dic₃	1	2	yes	—
502	D₄	C₂²×C₅×Dic₃	1	4	yes	—
503	C₂×C₄	—	2	1	no	—
504	C₂×C₄	—	2	4	no	—
505	C₂×C₄	—	3	2	no	—
506	C₂×C₄	—	3	2	no	—
507	C₂×C₄	—	6	1	no	—
508	C₂×C₄	—	6	1	no	—
509	C₂×C₄	—	6	2	no	—
510	C₂×C₄	—	24	2	no	—
511	C₂×C₄	—	24	2	no	—
512	C₂×C₄	—	24	2	no	—
513	C₂×C₄	—	24	1	no	—
514	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
515	C₂×C₄	C₅×#237	1	2	yes	—
516	C₂×C₄	C₂²×C₅×Dic₃	1	2	yes	—
517	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
518	C₈	—	6	1	no	—
519	C₈	—	6	1	no	—
520	C₈	C₂²×C₅×Dic₃	1	4	yes	—
521	C₂×C₃	—	2	2	no	—
522	C₂×C₃	—	4	4	no	—
523	C₂×C₃	—	4	2	no	—
524	C₂×C₃	C₂×C₄×C₅×D₄	1	1	yes	characteristic
525	C₂×C₃	C₅×#576	1	1	yes	characteristic
526	C₂×C₃	C₅×#577	1	1	yes	characteristic
527	C₅	#83930	1	1	yes	characteristic, direct product factor, Sylow
528	C₂²	—	2	1	no	—
529	C₂²	—	2	1	no	—
530	C₂²	—	2	2	no	—
531	C₂²	—	2	4	no	—
532	C₂²	—	4	1	no	—
533	C₂²	—	4	2	no	—
534	C₂²	—	4	2	no	—
535	C₂²	—	4	1	no	—
536	C₂²	—	8	4	no	—
537	C₂²	C₅×D₄×Dic₃	1	2	yes	—
538	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
539	C₄	—	2	2	no	—
540	C₄	—	6	2	no	—
541	C₄	—	6	2	no	—
542	C₄	—	12	1	no	—
543	C₄	—	12	2	no	—
544	C₄	—	12	1	no	—
545	C₄	C₅×D₄×Dic₃	1	2	yes	—
546	C₄	C₂×C₅×#237	1	1	yes	characteristic
547	C₄	C₂³×C₅×Dic₃	1	1	yes	characteristic
548	C₃	C₅×#2946	1	1	yes	characteristic, complemented, Sylow
549	C₂	—	2	2	no	—
550	C₂	—	4	4	no	—
551	C₂	—	4	2	no	—
552	C₂	C₅×#5774	1	1	yes	characteristic
553	C₂	C₅×#5775	1	1	yes	characteristic
554	C₂	C₂×C₅×D₄×Dic₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₅	C₂×D₃×D₄
commutator	C₃×C₄	C₂³×C₄×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting, prime radical	C₂×C₃×C₅×AGL(1,ℤ/8)	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
cosocle	C₂×C₃×C₄	C₂⁴×C₅
hypercenter	C₂×C₅×AGL(1,ℤ/8)	D₃
hypocenter	C₃	C₅×#2946
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₂²×C₄×C₅ ◁ C₂×C₅×AGL(1,ℤ/8)

Complements

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

N	H ≅ G/N	type
2. C₅×#5827	C₂	semidirect
3. C₅×#5798	C₂	semidirect
4. C₅×#5233	C₂	semidirect
5. C₂×C₅×#832	C₂	semidirect
6. C₅×#5164	C₂	semidirect
7. C₅×Dic₃×SD₁₆	C₂	semidirect
8. C₅×#5152	C₂	semidirect
9. C₅×Dic₃×D₈	C₂	semidirect
10. C₅×#5122	C₂	semidirect
11. C₅×#5121	C₂	semidirect
15. C₃×C₅×AGL(1,ℤ/8)	C₄	semidirect
20. C₅×Q₈×Dic₃	C₂²	semidirect
26. C₅×D₄×Dic₃	C₂²	semidirect
33. C₅×#835	C₂²	semidirect
34. C₅×#835	C₂²	semidirect
37. C₅×#832	C₂²	semidirect
38. C₅×#832	C₂²	semidirect
39. C₅×#818	C₂²	semidirect
40. C₅×#817	C₂²	semidirect
41. C₅×#815	C₂²	semidirect
42. C₅×C₈×Dic₃	C₂²	semidirect
43. #83930	C₅	direct (N × H)
57. C₃×C₅×#41	C₂×C₄	semidirect
62. C₂×C₃×C₅×D₄	C₂×C₄	semidirect
71. C₃×C₅×SD₁₆	C₂×C₄	semidirect
72. C₃×C₅×D₈	C₂×C₄	semidirect
73. C₃×C₅×M₁₆	C₂×C₄	semidirect
94. #5827	C₂×C₅	semidirect
95. #5798	C₂×C₅	semidirect
96. #5233	C₂×C₅	semidirect
97. C₂×#832	C₂×C₅	semidirect
98. #5164	C₂×C₅	semidirect
99. Dic₃×SD₁₆	C₂×C₅	semidirect
100. #5152	C₂×C₅	semidirect
101. Dic₃×D₈	C₂×C₅	semidirect
102. #5122	C₂×C₅	semidirect
103. #5121	C₂×C₅	semidirect
106. C₅×AGL(1,ℤ/8)	Dic₃	semidirect
169. C₃×AGL(1,ℤ/8)	C₄×C₅	semidirect
174. Q₈×Dic₃	C₂²×C₅	semidirect
180. D₄×Dic₃	C₂²×C₅	semidirect
187. #835	C₂²×C₅	semidirect
188. #835	C₂²×C₅	semidirect
191. #832	C₂²×C₅	semidirect
192. #832	C₂²×C₅	semidirect
193. #818	C₂²×C₅	semidirect
194. #817	C₂²×C₅	semidirect
195. #815	C₂²×C₅	semidirect
196. C₈×Dic₃	C₂²×C₅	semidirect
199. C₅×#41	C₂×Dic₃	semidirect
204. C₂×C₅×D₄	C₂×Dic₃	semidirect
213. C₅×SD₁₆	C₂×Dic₃	semidirect
214. C₅×D₈	C₂×Dic₃	semidirect
215. C₅×M₁₆	C₂×Dic₃	semidirect
268. C₃×#41	C₂×C₄×C₅	semidirect
273. C₂×C₃×D₄	C₂×C₄×C₅	semidirect
282. C₃×SD₁₆	C₂×C₄×C₅	semidirect
283. C₃×D₈	C₂×C₄×C₅	semidirect
284. C₃×M₁₆	C₂×C₄×C₅	semidirect
338. AGL(1,ℤ/8)	C₅×Dic₃	semidirect
426. #41	C₂×C₅×Dic₃	semidirect
431. C₂×D₄	C₂×C₅×Dic₃	semidirect
440. SD₁₆	C₂×C₅×Dic₃	semidirect
441. D₈	C₂×C₅×Dic₃	semidirect
442. M₁₆	C₂×C₅×Dic₃	semidirect
462. C₃×C₅	#2946	semidirect
527. C₅	#83930	direct (N × H)
548. C₃	C₅×#2946	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×C₅×AGL(1,ℤ/8)	2
C₅×#5827	2
C₅×#5798	2
C₅×#5233	2
C₂×C₅×#832	2
C₅×#5164	2
C₅×Dic₃×SD₁₆	2
C₅×#5152	2
C₅×Dic₃×D₈	2
C₅×#5122	2
C₅×#5121	2
C₅×#2946	3
#83930	5

Subgroups — C5×#83930 #14417006

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#83930 #14417006