Subgroups — C₅×Dic₃×AGL(1,ℤ/8) #14416661

Order 1920.

1096 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	C₂×C₃×C₅×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic
2	C₅×Dic₃×#41	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×D₄×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5232	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#5215	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×#5121	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×Dic₃×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×C₅×AGL(1,ℤ/8)	—	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	C₂³×C₅×Dic₃	—	2	1	no	—
16	C₃×C₅×AGL(1,ℤ/8)	C₄	1	8	yes	complemented
17	C₂×C₃×C₅×SD₁₆	C₂²	1	2	yes	—
18	C₂×C₃×C₅×D₈	C₂²	1	2	yes	—
19	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
20	C₂×C₅×#217	—	2	1	no	—
21	C₅×Q₈×Dic₃	C₂²	1	1	yes	characteristic, complemented
22	C₅×Q₈×Dic₃	C₂²	1	1	yes	characteristic, complemented
23	C₅×D₄×Dic₃	—	2	1	no	—
24	C₅×D₄×Dic₃	—	2	1	no	—
25	C₅×D₄×Dic₃	—	2	1	no	—
26	C₅×D₄×Dic₃	—	2	1	no	—
27	C₅×D₄×Dic₃	C₂²	1	2	yes	—
28	C₅×D₄×Dic₃	C₂²	1	2	yes	—
29	C₅×D₄×Dic₃	C₂²	1	1	yes	characteristic, complemented
30	C₅×D₄×Dic₃	C₂²	1	1	yes	characteristic, complemented
31	C₅×#926	—	2	1	no	—
32	C₅×#926	C₂²	1	1	yes	characteristic
33	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
34	C₂×C₄×C₅×Dic₃	—	2	1	no	—
35	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
36	C₂×C₅×#208	C₂²	1	1	yes	characteristic
37	C₅×#835	C₂²	1	2	yes	complemented
38	C₅×#832	C₂²	1	2	yes	—
39	C₅×#832	C₂²	1	2	yes	—
40	C₅×#832	C₂²	1	2	yes	complemented
41	C₅×#818	C₂²	1	2	yes	complemented
42	C₅×#817	C₂²	1	2	yes	complemented
43	C₅×#815	C₂²	1	2	yes	complemented
44	C₅×C₈×Dic₃	C₂²	1	2	yes	complemented
45	Dic₃×AGL(1,ℤ/8)	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
46	C₂×C₅×AGL(1,ℤ/8)	D₃	1	1	yes	characteristic
47	C₄×C₅×#41	—	3	1	no	—
48	C₂×C₄×C₅×D₄	—	3	1	no	—
49	C₅×#442	—	3	2	no	—
50	C₅×#440	—	3	2	no	—
51	C₄×C₅×SD₁₆	—	3	2	no	—
52	C₄×C₅×D₈	—	3	2	no	—
53	C₅×#428	—	3	1	no	—
54	C₅×#418	—	3	1	no	—
55	C₅×#417	—	3	1	no	—
56	C₄×C₅×M₁₆	—	3	1	no	—
57	C₂⁴×C₃×C₅	—	2	1	no	—
58	C₃×C₅×#41	—	2	2	no	—
59	C₃×C₅×#41	C₂×C₄	1	4	yes	complemented
60	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
61	C₂×C₃×C₅×D₄	—	2	1	no	—
62	C₂×C₃×C₅×D₄	—	2	1	no	—
63	C₂×C₃×C₅×D₄	—	2	2	no	—
64	C₂×C₃×C₅×D₄	C₂×C₄	1	4	yes	complemented
65	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
66	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
67	C₂²×C₃×C₄×C₅	—	2	1	no	—
68	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
69	C₂²×C₅×Dic₃	—	2	1	no	—
70	C₂²×C₅×Dic₃	—	2	1	no	—
71	C₂²×C₅×Dic₃	—	2	1	no	—
72	C₂²×C₅×Dic₃	—	2	2	no	—
73	C₂²×C₅×Dic₃	—	2	2	no	—
74	C₂²×C₅×Dic₃	—	4	4	no	—
75	C₂²×C₅×Dic₃	D₄	1	1	yes	characteristic
76	C₂²×C₅×Dic₃	D₄	1	1	yes	characteristic
77	C₃×C₅×SD₁₆	C₂×C₄	1	8	yes	complemented
78	C₃×C₅×D₈	C₂×C₄	1	8	yes	complemented
79	C₃×C₅×M₁₆	C₂×C₄	1	4	yes	complemented
80	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
81	C₅×#217	—	2	1	no	—
82	C₅×#217	—	2	1	no	—
83	C₅×#217	—	2	1	no	—
84	C₅×#217	—	2	2	no	—
85	C₅×#217	—	2	2	no	—
86	C₅×C₄⋊Dic₃	—	2	1	no	—
87	C₅×C₄⋊Dic₃	—	2	1	no	—
88	C₅×C₄⋊Dic₃	—	2	1	no	—
89	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
90	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
91	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
92	C₄×C₅×Dic₃	—	2	1	no	—
93	C₄×C₅×Dic₃	—	2	1	no	—
94	C₄×C₅×Dic₃	—	2	1	no	—
95	C₄×C₅×Dic₃	D₄	1	1	yes	characteristic
96	C₄×C₅×Dic₃	D₄	1	1	yes	characteristic
97	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
98	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
99	C₅×#208	—	2	2	no	—
100	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
101	C₂×C₃×AGL(1,ℤ/8)	C₂×C₅	1	1	yes	characteristic
102	Dic₃×#41	C₂×C₅	1	1	yes	characteristic, complemented
103	C₂×D₄×Dic₃	C₂×C₅	1	1	yes	characteristic, complemented
104	#5232	C₂×C₅	1	1	yes	characteristic, complemented
105	#5215	C₂×C₅	1	1	yes	characteristic, complemented
106	#5164	C₂×C₅	1	2	yes	complemented
107	Dic₃×SD₁₆	C₂×C₅	1	2	yes	complemented
108	#5152	C₂×C₅	1	2	yes	complemented
109	Dic₃×D₈	C₂×C₅	1	2	yes	complemented
110	#5121	C₂×C₅	1	1	yes	characteristic, complemented
111	Dic₃×M₁₆	C₂×C₅	1	1	yes	characteristic, complemented
112	C₂×C₅×#41	C₂×D₃	1	1	yes	characteristic
113	C₂²×C₅×D₄	C₂×D₃	1	1	yes	characteristic
114	C₂³×C₄×C₅	—	6	1	no	—
115	C₅×AGL(1,ℤ/8)	Dic₃	1	8	yes	direct product factor
116	C₂×C₅×SD₁₆	C₂×D₃	1	2	yes	—
117	C₂×C₅×D₈	C₂×D₃	1	2	yes	—
118	C₂×C₅×M₁₆	—	3	1	no	—
119	C₂×C₅×M₁₆	C₂×D₃	1	1	yes	characteristic
120	C₄×C₅×Q₈	—	3	1	no	—
121	C₄×C₅×Q₈	—	3	1	no	—
122	C₄×C₅×D₄	—	3	1	no	—
123	C₄×C₅×D₄	—	3	2	no	—
124	C₄×C₅×D₄	—	3	2	no	—
125	C₄×C₅×D₄	—	3	1	no	—
126	C₄×C₅×D₄	—	6	1	no	—
127	C₄×C₅×D₄	—	6	1	no	—
128	C₄×C₅×D₄	—	6	1	no	—
129	C₄×C₅×D₄	—	6	1	no	—
130	C₅×#117	—	3	1	no	—
131	C₅×#117	—	6	1	no	—
132	C₂×C₅×C₄⋊C₄	—	3	1	no	—
133	C₂×C₅×C₂²⋊C₄	—	6	1	no	—
134	C₂×C₄²×C₅	—	3	1	no	—
135	C₂×C₄²×C₅	—	6	1	no	—
136	C₅×#107	—	3	2	no	—
137	C₅×#106	—	3	2	no	—
138	C₅×#103	—	3	2	no	—
139	C₅×#102	—	3	2	no	—
140	C₅×#102	—	3	2	no	—
141	C₅×#102	—	3	2	no	—
142	C₅×#97	—	3	2	no	—
143	C₄×C₅×C₈	—	3	2	no	—
144	C₄×AGL(1,ℤ/8)	—	3	1	no	Sylow
145	C₂³×C₃×C₅	—	2	4	no	—
146	C₂³×C₃×C₅	—	2	1	no	—
147	C₂³×C₃×C₅	—	2	2	no	—
148	C₂³×C₃×C₅	—	4	2	no	—
149	C₂³×C₃×C₅	—	4	2	no	—
150	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
151	C₃×C₅×Q₈	—	2	1	no	—
152	C₃×C₅×Q₈	C₂²×C₄	1	2	yes	complemented
153	C₃×C₅×D₄	—	2	4	no	—
154	C₃×C₅×D₄	—	2	4	no	—
155	C₃×C₅×D₄	—	2	2	no	—
156	C₃×C₅×D₄	—	2	1	no	—
157	C₃×C₅×D₄	C₂²×C₄	1	4	yes	—
158	C₃×C₅×D₄	C₂²×C₄	1	2	yes	complemented
159	C₂×C₃×C₄×C₅	—	2	1	no	—
160	C₂×C₃×C₄×C₅	—	2	4	no	—
161	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
162	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
163	C₂×C₃×C₄×C₅	#41	1	2	yes	—
164	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
165	C₂×C₅×Dic₃	—	2	2	no	—
166	C₂×C₅×Dic₃	—	2	1	no	—
167	C₂×C₅×Dic₃	—	2	1	no	—
168	C₂×C₅×Dic₃	—	2	2	no	—
169	C₂×C₅×Dic₃	—	4	1	no	—
170	C₂×C₅×Dic₃	—	4	2	no	—
171	C₂×C₅×Dic₃	—	4	4	no	—
172	C₂×C₅×Dic₃	—	4	2	no	—
173	C₂×C₅×Dic₃	—	4	2	no	—
174	C₂×C₅×Dic₃	—	4	4	no	—
175	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
176	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
177	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
178	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
179	C₃×C₅×C₈	C₂²×C₄	1	4	yes	complemented
180	C₅×C₃⋊C₈	—	2	2	no	—
181	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
182	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
183	C₂³×Dic₃	—	2	1	no	—
184	C₃×AGL(1,ℤ/8)	C₄×C₅	1	8	yes	complemented
185	C₂×C₃×SD₁₆	C₂²×C₅	1	2	yes	—
186	C₂×C₃×D₈	C₂²×C₅	1	2	yes	—
187	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
188	C₂×#217	—	2	1	no	—
189	Q₈×Dic₃	C₂²×C₅	1	1	yes	characteristic, complemented
190	Q₈×Dic₃	C₂²×C₅	1	1	yes	characteristic, complemented
191	D₄×Dic₃	—	2	1	no	—
192	D₄×Dic₃	—	2	1	no	—
193	D₄×Dic₃	—	2	1	no	—
194	D₄×Dic₃	—	2	1	no	—
195	D₄×Dic₃	C₂²×C₅	1	2	yes	—
196	D₄×Dic₃	C₂²×C₅	1	2	yes	—
197	D₄×Dic₃	C₂²×C₅	1	1	yes	characteristic, complemented
198	D₄×Dic₃	C₂²×C₅	1	1	yes	characteristic, complemented
199	#926	—	2	1	no	—
200	#926	C₂²×C₅	1	1	yes	characteristic
201	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
202	C₂×C₄×Dic₃	—	2	1	no	—
203	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
204	C₂×#208	C₂²×C₅	1	1	yes	characteristic
205	#835	C₂²×C₅	1	2	yes	complemented
206	#832	C₂²×C₅	1	2	yes	—
207	#832	C₂²×C₅	1	2	yes	—
208	#832	C₂²×C₅	1	2	yes	complemented
209	#818	C₂²×C₅	1	2	yes	complemented
210	#817	C₂²×C₅	1	2	yes	complemented
211	#815	C₂²×C₅	1	2	yes	complemented
212	C₈×Dic₃	C₂²×C₅	1	2	yes	complemented
213	C₂⁴×C₅	—	2	1	no	—
214	C₅×#41	—	2	2	no	—
215	C₅×#41	C₂×Dic₃	1	4	yes	complemented
216	C₂×C₅×Q₈	C₂²×D₃	1	1	yes	characteristic
217	C₂×C₅×D₄	—	2	1	no	—
218	C₂×C₅×D₄	—	2	1	no	—
219	C₂×C₅×D₄	—	2	2	no	—
220	C₂×C₅×D₄	C₂×Dic₃	1	4	yes	complemented
221	C₂×C₅×D₄	C₂²×D₃	1	2	yes	—
222	C₂×C₅×D₄	C₂²×D₃	1	1	yes	characteristic
223	C₂²×C₄×C₅	—	2	1	no	—
224	C₂²×C₄×C₅	—	3	1	no	—
225	C₂²×C₄×C₅	—	3	1	no	—
226	C₂²×C₄×C₅	—	6	1	no	—
227	C₂²×C₄×C₅	—	6	1	no	—
228	C₂²×C₄×C₅	—	6	2	no	—
229	C₂²×C₄×C₅	—	6	2	no	—
230	C₂²×C₄×C₅	—	6	1	no	—
231	C₂²×C₄×C₅	—	12	4	no	—
232	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
233	C₅×SD₁₆	C₂×Dic₃	1	8	yes	complemented
234	C₅×D₈	C₂×Dic₃	1	8	yes	complemented
235	C₅×M₁₆	—	6	2	no	—
236	C₅×M₁₆	C₂×Dic₃	1	4	yes	complemented
237	C₂×C₅×C₈	—	3	2	no	—
238	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
239	C₅×C₄⋊C₄	—	3	2	no	—
240	C₅×C₄⋊C₄	—	3	1	no	—
241	C₅×C₄⋊C₄	—	3	1	no	—
242	C₅×C₄⋊C₄	—	6	1	no	—
243	C₅×C₄⋊C₄	—	6	1	no	—
244	C₅×C₄⋊C₄	—	6	1	no	—
245	C₅×C₂²⋊C₄	—	6	2	no	—
246	C₅×C₂²⋊C₄	—	6	2	no	—
247	C₅×C₂²⋊C₄	—	6	1	no	—
248	C₅×C₂²⋊C₄	—	6	1	no	—
249	C₅×C₂²⋊C₄	—	6	1	no	—
250	C₄²×C₅	—	3	1	no	—
251	C₄²×C₅	—	3	1	no	—
252	C₄²×C₅	—	3	1	no	—
253	C₄²×C₅	—	3	1	no	—
254	C₄²×C₅	—	6	1	no	—
255	C₄²×C₅	—	6	1	no	—
256	C₄²×C₅	—	6	1	no	—
257	C₂×AGL(1,ℤ/8)	C₅×D₃	1	1	yes	characteristic
258	C₄×#41	—	3	1	no	—
259	C₂×C₄×D₄	—	3	1	no	—
260	#442	—	3	2	no	—
261	#440	—	3	2	no	—
262	C₄×SD₁₆	—	3	2	no	—
263	C₄×D₈	—	3	2	no	—
264	#428	—	3	1	no	—
265	#418	—	3	1	no	—
266	#417	—	3	1	no	—
267	C₄×M₁₆	—	3	1	no	—
268	C₂²×C₃×C₅	—	2	1	no	—
269	C₂²×C₃×C₅	—	2	1	no	—
270	C₂²×C₃×C₅	—	2	2	no	—
271	C₂²×C₃×C₅	—	2	4	no	—
272	C₂²×C₃×C₅	—	4	8	no	—
273	C₂²×C₃×C₅	—	4	2	no	—
274	C₂²×C₃×C₅	—	4	1	no	—
275	C₂²×C₃×C₅	—	4	1	no	—
276	C₂²×C₃×C₅	—	4	2	no	—
277	C₂²×C₃×C₅	C₄×D₄	1	2	yes	—
278	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
279	C₃×C₄×C₅	—	2	2	no	—
280	C₃×C₄×C₅	C₄×D₄	1	2	yes	—
281	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
282	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
283	C₅×Dic₃	—	2	1	no	—
284	C₅×Dic₃	—	2	1	no	—
285	C₅×Dic₃	—	2	1	no	—
286	C₅×Dic₃	—	4	1	no	—
287	C₅×Dic₃	—	4	2	no	—
288	C₅×Dic₃	—	4	1	no	—
289	C₅×Dic₃	AGL(1,ℤ/8)	1	2	yes	direct product factor
290	C₂⁴×C₃	—	2	1	no	—
291	C₃×#41	—	2	2	no	—
292	C₃×#41	C₂×C₄×C₅	1	4	yes	complemented
293	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
294	C₂×C₃×D₄	—	2	1	no	—
295	C₂×C₃×D₄	—	2	1	no	—
296	C₂×C₃×D₄	—	2	2	no	—
297	C₂×C₃×D₄	C₂×C₄×C₅	1	4	yes	complemented
298	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
299	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
300	C₂²×C₃×C₄	—	2	1	no	—
301	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
302	C₂²×Dic₃	—	2	1	no	—
303	C₂²×Dic₃	—	2	1	no	—
304	C₂²×Dic₃	—	2	1	no	—
305	C₂²×Dic₃	—	2	2	no	—
306	C₂²×Dic₃	—	2	2	no	—
307	C₂²×Dic₃	—	4	4	no	—
308	C₂²×Dic₃	C₅×D₄	1	1	yes	characteristic
309	C₂²×Dic₃	C₅×D₄	1	1	yes	characteristic
310	C₃×SD₁₆	C₂×C₄×C₅	1	8	yes	complemented
311	C₃×D₈	C₂×C₄×C₅	1	8	yes	complemented
312	C₃×M₁₆	C₂×C₄×C₅	1	4	yes	complemented
313	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
314	#217	—	2	1	no	—
315	#217	—	2	1	no	—
316	#217	—	2	1	no	—
317	#217	—	2	2	no	—
318	#217	—	2	2	no	—
319	C₄⋊Dic₃	—	2	1	no	—
320	C₄⋊Dic₃	—	2	1	no	—
321	C₄⋊Dic₃	—	2	1	no	—
322	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
323	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
324	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
325	C₄×Dic₃	—	2	1	no	—
326	C₄×Dic₃	—	2	1	no	—
327	C₄×Dic₃	—	2	1	no	—
328	C₄×Dic₃	C₅×D₄	1	1	yes	characteristic
329	C₄×Dic₃	C₅×D₄	1	1	yes	characteristic
330	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
331	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
332	#208	—	2	2	no	—
333	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
334	C₂³×C₅	—	2	4	no	—
335	C₂³×C₅	—	2	1	no	—
336	C₂³×C₅	—	2	2	no	—
337	C₂³×C₅	—	4	2	no	—
338	C₂³×C₅	—	4	2	no	—
339	C₂³×C₅	D₃×D₄	1	1	yes	characteristic
340	C₅×Q₈	—	2	1	no	—
341	C₅×Q₈	C₂²×Dic₃	1	2	yes	complemented
342	C₅×D₄	—	2	4	no	—
343	C₅×D₄	—	2	4	no	—
344	C₅×D₄	—	2	2	no	—
345	C₅×D₄	—	2	1	no	—
346	C₅×D₄	C₂²×Dic₃	1	4	yes	—
347	C₅×D₄	C₂²×Dic₃	1	2	yes	complemented
348	C₂×C₄×C₅	—	2	1	no	—
349	C₂×C₄×C₅	—	2	4	no	—
350	C₂×C₄×C₅	—	3	1	no	—
351	C₂×C₄×C₅	—	3	1	no	—
352	C₂×C₄×C₅	—	3	1	no	—
353	C₂×C₄×C₅	—	3	1	no	—
354	C₂×C₄×C₅	—	6	2	no	—
355	C₂×C₄×C₅	—	6	1	no	—
356	C₂×C₄×C₅	—	6	1	no	—
357	C₂×C₄×C₅	—	6	2	no	—
358	C₂×C₄×C₅	—	12	2	no	—
359	C₂×C₄×C₅	—	12	4	no	—
360	C₂×C₄×C₅	—	12	1	no	—
361	C₂×C₄×C₅	—	12	2	no	—
362	C₂×C₄×C₅	—	12	4	no	—
363	C₂×C₄×C₅	—	12	2	no	—
364	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
365	C₂×C₄×C₅	#237	1	2	yes	—
366	C₂×C₄×C₅	C₂²×Dic₃	1	2	yes	—
367	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
368	C₅×C₈	—	6	2	no	—
369	C₅×C₈	C₂²×Dic₃	1	4	yes	complemented
370	C₂×#41	C₂×C₅×D₃	1	1	yes	characteristic
371	C₂²×D₄	C₂×C₅×D₃	1	1	yes	characteristic
372	C₂³×C₄	—	6	1	no	—
373	AGL(1,ℤ/8)	C₅×Dic₃	1	8	yes	direct product factor
374	C₂×SD₁₆	C₂×C₅×D₃	1	2	yes	—
375	C₂×D₈	C₂×C₅×D₃	1	2	yes	—
376	C₂×M₁₆	—	3	1	no	—
377	C₂×M₁₆	C₂×C₅×D₃	1	1	yes	characteristic
378	C₄×Q₈	—	3	1	no	—
379	C₄×Q₈	—	3	1	no	—
380	C₄×D₄	—	3	2	no	—
381	C₄×D₄	—	3	2	no	—
382	C₄×D₄	—	3	1	no	—
383	C₄×D₄	—	3	1	no	—
384	C₄×D₄	—	6	1	no	—
385	C₄×D₄	—	6	1	no	—
386	C₄×D₄	—	6	1	no	—
387	C₄×D₄	—	6	1	no	—
388	#117	—	3	1	no	—
389	#117	—	6	1	no	—
390	C₂×C₄⋊C₄	—	3	1	no	—
391	C₂×C₂²⋊C₄	—	6	1	no	—
392	C₂×C₄²	—	3	1	no	—
393	C₂×C₄²	—	6	1	no	—
394	#107	—	3	2	no	—
395	#106	—	3	2	no	—
396	#103	—	3	2	no	—
397	#102	—	3	2	no	—
398	#102	—	3	2	no	—
399	#102	—	3	2	no	—
400	#97	—	3	2	no	—
401	C₄×C₈	—	3	2	no	—
402	C₂×C₃×C₅	—	2	2	no	—
403	C₂×C₃×C₅	—	4	2	no	—
404	C₂×C₃×C₅	—	4	4	no	—
405	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
406	C₂×C₃×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
407	C₂×C₃×C₅	#575	1	1	yes	characteristic
408	C₂³×C₃	—	2	4	no	—
409	C₂³×C₃	—	2	1	no	—
410	C₂³×C₃	—	2	2	no	—
411	C₂³×C₃	—	4	2	no	—
412	C₂³×C₃	—	4	2	no	—
413	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
414	C₃×Q₈	—	2	1	no	—
415	C₃×Q₈	C₂²×C₄×C₅	1	2	yes	complemented
416	C₃×D₄	—	2	4	no	—
417	C₃×D₄	—	2	4	no	—
418	C₃×D₄	—	2	2	no	—
419	C₃×D₄	—	2	1	no	—
420	C₃×D₄	C₂²×C₄×C₅	1	4	yes	—
421	C₃×D₄	C₂²×C₄×C₅	1	2	yes	complemented
422	C₂×C₃×C₄	—	2	1	no	—
423	C₂×C₃×C₄	—	2	4	no	—
424	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
425	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
426	C₂×C₃×C₄	C₅×#41	1	2	yes	—
427	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
428	C₂×Dic₃	—	2	2	no	—
429	C₂×Dic₃	—	2	1	no	—
430	C₂×Dic₃	—	2	1	no	—
431	C₂×Dic₃	—	2	2	no	—
432	C₂×Dic₃	—	4	1	no	—
433	C₂×Dic₃	—	4	2	no	—
434	C₂×Dic₃	—	4	4	no	—
435	C₂×Dic₃	—	4	2	no	—
436	C₂×Dic₃	—	4	2	no	—
437	C₂×Dic₃	—	4	4	no	—
438	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
439	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
440	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
441	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
442	C₃×C₈	C₂²×C₄×C₅	1	4	yes	complemented
443	C₃⋊C₈	—	2	2	no	—
444	C₂²×C₅	—	2	1	no	—
445	C₂²×C₅	—	2	1	no	—
446	C₂²×C₅	—	2	2	no	—
447	C₂²×C₅	—	2	4	no	—
448	C₂²×C₅	—	4	8	no	—
449	C₂²×C₅	—	4	2	no	—
450	C₂²×C₅	—	4	1	no	—
451	C₂²×C₅	—	4	1	no	—
452	C₂²×C₅	—	4	2	no	—
453	C₂²×C₅	D₄×Dic₃	1	2	yes	—
454	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
455	C₄×C₅	—	2	2	no	—
456	C₄×C₅	—	3	2	no	—
457	C₄×C₅	—	6	1	no	—
458	C₄×C₅	—	6	1	no	—
459	C₄×C₅	—	6	1	no	—
460	C₄×C₅	—	12	1	no	—
461	C₄×C₅	—	12	2	no	—
462	C₄×C₅	—	12	1	no	—
463	C₄×C₅	D₄×Dic₃	1	2	yes	—
464	C₄×C₅	C₂×#237	1	1	yes	characteristic
465	C₄×C₅	C₂³×Dic₃	1	1	yes	characteristic
466	C₂⁴	—	2	1	no	—
467	#41	—	2	2	no	—
468	#41	C₂×C₅×Dic₃	1	4	yes	complemented
469	C₂×Q₈	C₂²×C₅×D₃	1	1	yes	characteristic
470	C₂×D₄	—	2	1	no	—
471	C₂×D₄	—	2	1	no	—
472	C₂×D₄	—	2	2	no	—
473	C₂×D₄	C₂×C₅×Dic₃	1	4	yes	complemented
474	C₂×D₄	C₂²×C₅×D₃	1	2	yes	—
475	C₂×D₄	C₂²×C₅×D₃	1	1	yes	characteristic
476	C₂²×C₄	—	2	1	no	—
477	C₂²×C₄	—	3	1	no	—
478	C₂²×C₄	—	3	1	no	—
479	C₂²×C₄	—	6	1	no	—
480	C₂²×C₄	—	6	1	no	—
481	C₂²×C₄	—	6	2	no	—
482	C₂²×C₄	—	6	2	no	—
483	C₂²×C₄	—	6	1	no	—
484	C₂²×C₄	—	12	4	no	—
485	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
486	SD₁₆	C₂×C₅×Dic₃	1	8	yes	complemented
487	D₈	C₂×C₅×Dic₃	1	8	yes	complemented
488	M₁₆	—	6	2	no	—
489	M₁₆	C₂×C₅×Dic₃	1	4	yes	complemented
490	C₂×C₈	—	3	2	no	—
491	C₂×C₈	C₂²×C₅×D₃	1	2	yes	—
492	C₄⋊C₄	—	3	1	no	—
493	C₄⋊C₄	—	3	1	no	—
494	C₄⋊C₄	—	3	2	no	—
495	C₄⋊C₄	—	6	1	no	—
496	C₄⋊C₄	—	6	1	no	—
497	C₄⋊C₄	—	6	1	no	—
498	C₂²⋊C₄	—	6	2	no	—
499	C₂²⋊C₄	—	6	2	no	—
500	C₂²⋊C₄	—	6	1	no	—
501	C₂²⋊C₄	—	6	1	no	—
502	C₂²⋊C₄	—	6	1	no	—
503	C₄²	—	3	1	no	—
504	C₄²	—	3	1	no	—
505	C₄²	—	3	1	no	—
506	C₄²	—	3	1	no	—
507	C₄²	—	6	1	no	—
508	C₄²	—	6	1	no	—
509	C₄²	—	6	1	no	—
510	C₃×C₅	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic, complemented, Hall
511	C₂²×C₃	—	2	1	no	—
512	C₂²×C₃	—	2	1	no	—
513	C₂²×C₃	—	2	2	no	—
514	C₂²×C₃	—	2	4	no	—
515	C₂²×C₃	—	4	8	no	—
516	C₂²×C₃	—	4	2	no	—
517	C₂²×C₃	—	4	1	no	—
518	C₂²×C₃	—	4	1	no	—
519	C₂²×C₃	—	4	2	no	—
520	C₂²×C₃	C₄×C₅×D₄	1	2	yes	—
521	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
522	C₃×C₄	—	2	2	no	—
523	C₃×C₄	C₄×C₅×D₄	1	2	yes	—
524	C₃×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
525	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
526	Dic₃	—	2	1	no	—
527	Dic₃	—	2	1	no	—
528	Dic₃	—	2	1	no	—
529	Dic₃	—	4	1	no	—
530	Dic₃	—	4	2	no	—
531	Dic₃	—	4	1	no	—
532	Dic₃	C₅×AGL(1,ℤ/8)	1	2	yes	direct product factor
533	C₂×C₅	—	2	2	no	—
534	C₂×C₅	—	4	4	no	—
535	C₂×C₅	—	4	2	no	—
536	C₂×C₅	D₃×AGL(1,ℤ/8)	1	1	yes	characteristic
537	C₂×C₅	#5773	1	1	yes	characteristic
538	C₂×C₅	C₂×D₄×Dic₃	1	1	yes	characteristic
539	C₂³	—	2	4	no	—
540	C₂³	—	2	1	no	—
541	C₂³	—	2	2	no	—
542	C₂³	—	4	2	no	—
543	C₂³	—	4	2	no	—
544	C₂³	C₅×D₃×D₄	1	1	yes	characteristic
545	Q₈	—	2	1	no	—
546	Q₈	C₂²×C₅×Dic₃	1	2	yes	complemented
547	D₄	—	2	4	no	—
548	D₄	—	2	4	no	—
549	D₄	—	2	2	no	—
550	D₄	—	2	1	no	—
551	D₄	C₂²×C₅×Dic₃	1	4	yes	—
552	D₄	C₂²×C₅×Dic₃	1	2	yes	complemented
553	C₂×C₄	—	2	1	no	—
554	C₂×C₄	—	2	4	no	—
555	C₂×C₄	—	3	1	no	—
556	C₂×C₄	—	3	1	no	—
557	C₂×C₄	—	3	1	no	—
558	C₂×C₄	—	3	1	no	—
559	C₂×C₄	—	6	2	no	—
560	C₂×C₄	—	6	1	no	—
561	C₂×C₄	—	6	1	no	—
562	C₂×C₄	—	6	2	no	—
563	C₂×C₄	—	12	4	no	—
564	C₂×C₄	—	12	2	no	—
565	C₂×C₄	—	12	1	no	—
566	C₂×C₄	—	12	4	no	—
567	C₂×C₄	—	12	2	no	—
568	C₂×C₄	—	12	2	no	—
569	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
570	C₂×C₄	C₅×#237	1	2	yes	—
571	C₂×C₄	C₂²×C₅×Dic₃	1	2	yes	—
572	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
573	C₈	—	6	2	no	—
574	C₈	C₂²×C₅×Dic₃	1	4	yes	complemented
575	C₂×C₃	—	2	2	no	—
576	C₂×C₃	—	4	4	no	—
577	C₂×C₃	—	4	2	no	—
578	C₂×C₃	C₂×C₄×C₅×D₄	1	1	yes	characteristic
579	C₂×C₃	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
580	C₂×C₃	C₅×#575	1	1	yes	characteristic
581	C₅	Dic₃×AGL(1,ℤ/8)	1	1	yes	characteristic, direct product factor, Sylow
582	C₂²	—	2	1	no	—
583	C₂²	—	2	1	no	—
584	C₂²	—	2	2	no	—
585	C₂²	—	2	4	no	—
586	C₂²	—	4	8	no	—
587	C₂²	—	4	2	no	—
588	C₂²	—	4	1	no	—
589	C₂²	—	4	1	no	—
590	C₂²	—	4	2	no	—
591	C₂²	C₅×D₄×Dic₃	1	2	yes	—
592	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
593	C₄	—	2	2	no	—
594	C₄	—	3	2	no	—
595	C₄	—	6	1	no	—
596	C₄	—	6	1	no	—
597	C₄	—	6	1	no	—
598	C₄	—	12	2	no	—
599	C₄	—	12	1	no	—
600	C₄	—	12	1	no	—
601	C₄	C₅×D₄×Dic₃	1	2	yes	—
602	C₄	C₂×C₅×#237	1	1	yes	characteristic
603	C₄	C₂³×C₅×Dic₃	1	1	yes	characteristic
604	C₃	C₄×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic, complemented, Sylow
605	C₂	—	2	2	no	—
606	C₂	—	4	4	no	—
607	C₂	—	4	2	no	—
608	C₂	C₅×D₃×AGL(1,ℤ/8)	1	1	yes	characteristic
609	C₂	C₅×#5773	1	1	yes	characteristic
610	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	C₄×C₅×AGL(1,ℤ/8)
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×Dic₃×#41	C₂	semidirect
3. C₂×C₅×D₄×Dic₃	C₂	semidirect
4. C₅×#5232	C₂	semidirect
5. C₅×#5215	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×#5121	C₂	semidirect
11. C₅×Dic₃×M₁₆	C₂	semidirect
16. C₃×C₅×AGL(1,ℤ/8)	C₄	semidirect
21. C₅×Q₈×Dic₃	C₂²	semidirect
22. C₅×Q₈×Dic₃	C₂²	semidirect
29. C₅×D₄×Dic₃	C₂²	semidirect
30. C₅×D₄×Dic₃	C₂²	semidirect
37. C₅×#835	C₂²	semidirect
40. C₅×#832	C₂²	semidirect
41. C₅×#818	C₂²	semidirect
42. C₅×#817	C₂²	semidirect
43. C₅×#815	C₂²	semidirect
44. C₅×C₈×Dic₃	C₂²	semidirect
45. Dic₃×AGL(1,ℤ/8)	C₅	direct (N × H)
59. C₃×C₅×#41	C₂×C₄	semidirect
64. C₂×C₃×C₅×D₄	C₂×C₄	semidirect
77. C₃×C₅×SD₁₆	C₂×C₄	semidirect
78. C₃×C₅×D₈	C₂×C₄	semidirect
79. C₃×C₅×M₁₆	C₂×C₄	semidirect
102. Dic₃×#41	C₂×C₅	semidirect
103. C₂×D₄×Dic₃	C₂×C₅	semidirect
104. #5232	C₂×C₅	semidirect
105. #5215	C₂×C₅	semidirect
106. #5164	C₂×C₅	semidirect
107. Dic₃×SD₁₆	C₂×C₅	semidirect
108. #5152	C₂×C₅	semidirect
109. Dic₃×D₈	C₂×C₅	semidirect
110. #5121	C₂×C₅	semidirect
111. Dic₃×M₁₆	C₂×C₅	semidirect
115. C₅×AGL(1,ℤ/8)	Dic₃	direct (N × H)
152. C₃×C₅×Q₈	C₂²×C₄	semidirect
158. C₃×C₅×D₄	C₂²×C₄	semidirect
179. C₃×C₅×C₈	C₂²×C₄	semidirect
184. C₃×AGL(1,ℤ/8)	C₄×C₅	semidirect
189. Q₈×Dic₃	C₂²×C₅	semidirect
190. Q₈×Dic₃	C₂²×C₅	semidirect
197. D₄×Dic₃	C₂²×C₅	semidirect
198. D₄×Dic₃	C₂²×C₅	semidirect
205. #835	C₂²×C₅	semidirect
208. #832	C₂²×C₅	semidirect
209. #818	C₂²×C₅	semidirect
210. #817	C₂²×C₅	semidirect
211. #815	C₂²×C₅	semidirect
212. C₈×Dic₃	C₂²×C₅	semidirect
215. C₅×#41	C₂×Dic₃	semidirect
220. C₂×C₅×D₄	C₂×Dic₃	semidirect
233. C₅×SD₁₆	C₂×Dic₃	semidirect
234. C₅×D₈	C₂×Dic₃	semidirect
236. C₅×M₁₆	C₂×Dic₃	semidirect
289. C₅×Dic₃	AGL(1,ℤ/8)	direct (N × H)
292. C₃×#41	C₂×C₄×C₅	semidirect
297. C₂×C₃×D₄	C₂×C₄×C₅	semidirect
310. C₃×SD₁₆	C₂×C₄×C₅	semidirect
311. C₃×D₈	C₂×C₄×C₅	semidirect
312. C₃×M₁₆	C₂×C₄×C₅	semidirect
341. C₅×Q₈	C₂²×Dic₃	semidirect
347. C₅×D₄	C₂²×Dic₃	semidirect
369. C₅×C₈	C₂²×Dic₃	semidirect
373. AGL(1,ℤ/8)	C₅×Dic₃	direct (N × H)
415. C₃×Q₈	C₂²×C₄×C₅	semidirect
421. C₃×D₄	C₂²×C₄×C₅	semidirect
442. C₃×C₈	C₂²×C₄×C₅	semidirect
468. #41	C₂×C₅×Dic₃	semidirect
473. C₂×D₄	C₂×C₅×Dic₃	semidirect
486. SD₁₆	C₂×C₅×Dic₃	semidirect
487. D₈	C₂×C₅×Dic₃	semidirect
489. M₁₆	C₂×C₅×Dic₃	semidirect
510. C₃×C₅	C₄×AGL(1,ℤ/8)	semidirect
532. Dic₃	C₅×AGL(1,ℤ/8)	direct (N × H)
546. Q₈	C₂²×C₅×Dic₃	semidirect
552. D₄	C₂²×C₅×Dic₃	semidirect
574. C₈	C₂²×C₅×Dic₃	semidirect
581. C₅	Dic₃×AGL(1,ℤ/8)	direct (N × H)
604. C₃	C₄×C₅×AGL(1,ℤ/8)	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×Dic₃×#41	2
C₂×C₅×D₄×Dic₃	2
C₅×#5232	2
C₅×#5215	2
C₅×#5164	2
C₅×Dic₃×SD₁₆	2
C₅×#5152	2
C₅×Dic₃×D₈	2
C₅×#5121	2
C₅×Dic₃×M₁₆	2
C₄×C₅×AGL(1,ℤ/8)	3
Dic₃×AGL(1,ℤ/8)	5

Subgroups — C5×Dic3×AGL(1,ℤ/8) #14416661

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×Dic₃×AGL(1,ℤ/8) #14416661