Subgroups — C₅×D₃×#472 #14429367

Order 1920.

976 conjugacy classes of subgroups.

The subgroup lattice has 688 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×D₃×AGL(1,ℤ/8)	C₂	1	2	yes	maximal, complemented
2	C₂×C₅×D₃×D₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×D₃×#131	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#472	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#5199	C₂	1	2	yes	maximal, complemented
6	C₅×#5160	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#5142	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#4897	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×D₃×#108	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#4749	C₂	1	2	yes	maximal, complemented
11	C₅×D₃×#100	C₂	1	2	yes	maximal, complemented
12	C₂×C₅×#472	—	3	1	no	maximal, Hall
13	C₅×D₃×#41	C₂²	1	1	yes	characteristic
14	C₂×C₅×D₃×D₄	C₂²	1	2	yes	—
15	C₃×C₅×AGL(1,ℤ/8)	C₂²	1	2	yes	complemented
16	C₂×C₃×C₅×D₈	C₂²	1	1	yes	characteristic, complemented
17	C₃×C₅×#131	C₂²	1	1	yes	characteristic, complemented
18	C₅×#949	C₂²	1	2	yes	complemented
19	C₅×#948	C₂²	1	1	yes	characteristic, complemented
20	C₅×#932	C₂²	1	2	yes	complemented
21	C₂×C₅×#213	C₂²	1	2	yes	complemented
22	C₅×#914	—	2	2	no	—
23	C₅×D₃×SD₁₆	—	2	2	no	—
24	C₅×#911	—	2	2	no	—
25	C₅×D₃×D₈	—	2	2	no	—
26	C₅×D₃×D₈	—	2	1	no	—
27	C₅×D₃×D₈	—	2	1	no	—
28	C₅×D₃×D₈	—	2	1	no	—
29	C₅×D₃×D₈	—	2	1	no	—
30	C₅×#908	C₂²	1	2	yes	complemented
31	C₅×#907	—	2	1	no	—
32	C₅×#907	C₂²	1	1	yes	characteristic, complemented
33	C₅×D₃×M₁₆	—	2	1	no	—
34	C₅×D₃×M₁₆	C₂²	1	1	yes	characteristic
35	C₅×D₃×M₁₆	C₂²	1	2	yes	—
36	C₂×C₅×D₂₄	C₂²	1	1	yes	characteristic, complemented
37	C₅×#901	—	2	1	no	—
38	C₅×#901	C₂²	1	1	yes	characteristic, complemented
39	C₂×C₅×D₃×C₈	—	2	1	no	—
40	C₂×C₅×D₃×C₈	C₂²	1	1	yes	characteristic
41	C₃×C₅×#108	C₂²	1	1	yes	characteristic, complemented
42	C₃×C₅×#100	C₂²	1	2	yes	complemented
43	C₅×#833	C₂²	1	2	yes	complemented
44	C₅×#823	C₂²	1	2	yes	complemented
45	C₅×#823	C₂²	1	2	yes	complemented
46	C₅×#822	C₂²	1	2	yes	complemented
47	C₅×#819	C₂²	1	1	yes	characteristic, complemented
48	D₃×#472	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
49	C₂×C₅×AGL(1,ℤ/8)	—	3	2	no	—
50	C₂²×C₅×D₈	—	3	1	no	—
51	C₂×C₅×#131	—	3	1	no	—
52	C₅×#472	—	3	1	no	—
53	C₅×#472	—	3	2	no	—
54	C₅×#472	—	3	2	no	—
55	C₅×#472	—	3	1	no	—
56	C₅×#472	—	3	1	no	—
57	C₅×#472	D₃	1	1	yes	characteristic, direct product factor
58	C₂×C₅×#108	—	3	1	no	—
59	C₂×C₅×#100	—	3	2	no	—
60	C₂³×C₅×D₃	—	2	2	no	—
61	C₃×C₅×#41	C₂³	1	1	yes	characteristic
62	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
63	C₂×C₅×#67	—	2	2	no	—
64	C₅×#239	D₄	1	1	yes	characteristic
65	C₅×D₃×Q₈	D₄	1	1	yes	characteristic
66	C₅×#237	—	2	1	no	—
67	C₅×#237	D₄	1	1	yes	characteristic
68	C₅×D₃×D₄	—	2	1	no	—
69	C₅×D₃×D₄	—	2	2	no	—
70	C₅×D₃×D₄	—	2	2	no	—
71	C₅×D₃×D₄	—	2	2	no	—
72	C₅×D₃×D₄	—	2	2	no	—
73	C₅×D₃×D₄	D₄	1	1	yes	characteristic
74	C₅×#235	—	2	1	no	—
75	C₅×#235	C₂³	1	1	yes	characteristic
76	C₂×C₅×D₁₂	C₂³	1	2	yes	—
77	C₂×C₄×C₅×D₃	—	2	1	no	—
78	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
79	C₃×C₅×SD₁₆	—	2	2	no	—
80	C₃×C₅×D₈	—	2	2	no	—
81	C₃×C₅×D₈	—	2	1	no	—
82	C₃×C₅×D₈	—	2	1	no	—
83	C₃×C₅×M₁₆	—	2	1	no	—
84	C₃×C₅×M₁₆	C₂³	1	1	yes	characteristic
85	C₃×C₅×M₁₆	C₂³	1	2	yes	—
86	C₂×C₃×C₅×C₈	—	2	1	no	—
87	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
88	C₅×#215	—	2	2	no	—
89	C₅×#214	—	2	2	no	—
90	C₅×#213	—	2	2	no	—
91	C₅×#213	—	2	2	no	—
92	C₅×#213	—	2	2	no	—
93	C₅×#213	—	2	2	no	—
94	C₅×#208	—	2	1	no	—
95	C₅×#208	C₂³	1	1	yes	characteristic
96	C₅×#208	C₂³	1	2	yes	—
97	C₂×C₅×C₃⋊C₈	—	2	1	no	—
98	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
99	C₅×D₂₄	—	2	2	no	—
100	C₅×D₂₄	—	2	1	no	—
101	C₅×D₂₄	—	2	1	no	—
102	C₅×#204	—	2	2	no	—
103	C₅×ΓL(1,𝔽₂₅)	—	2	1	no	—
104	C₅×ΓL(1,𝔽₂₅)	—	2	2	no	—
105	C₅×ΓL(1,𝔽₂₅)	—	2	1	no	—
106	C₅×ΓL(1,𝔽₂₅)	—	2	1	no	—
107	C₅×D₃×C₈	—	2	1	no	—
108	C₅×D₃×C₈	—	2	2	no	—
109	C₅×D₃×C₈	—	2	1	no	—
110	C₅×D₃×C₈	—	2	1	no	—
111	C₅×D₃×C₈	D₄	1	1	yes	characteristic
112	C₅×D₃×C₈	D₄	1	1	yes	characteristic
113	C₅×D₃×C₈	D₄	1	1	yes	characteristic
114	C₅×D₃×C₈	D₄	1	1	yes	characteristic
115	D₃×AGL(1,ℤ/8)	C₂×C₅	1	2	yes	complemented
116	C₂×D₃×D₈	C₂×C₅	1	1	yes	characteristic, complemented
117	D₃×#131	C₂×C₅	1	1	yes	characteristic, complemented
118	C₃×#472	C₂×C₅	1	1	yes	characteristic, complemented
119	#5199	C₂×C₅	1	2	yes	complemented
120	#5160	C₂×C₅	1	1	yes	characteristic, complemented
121	#5142	C₂×C₅	1	1	yes	characteristic, complemented
122	#4897	C₂×C₅	1	1	yes	characteristic, complemented
123	D₃×#108	C₂×C₅	1	1	yes	characteristic, complemented
124	#4749	C₂×C₅	1	2	yes	complemented
125	D₃×#100	C₂×C₅	1	2	yes	complemented
126	C₂×C₅×#41	—	3	1	no	—
127	C₂²×C₅×D₄	—	3	2	no	—
128	C₅×AGL(1,ℤ/8)	—	3	2	no	—
129	C₅×AGL(1,ℤ/8)	—	3	2	no	—
130	C₅×AGL(1,ℤ/8)	—	3	2	no	—
131	C₅×AGL(1,ℤ/8)	—	6	2	no	—
132	C₅×AGL(1,ℤ/8)	—	6	2	no	—
133	C₅×AGL(1,ℤ/8)	C₂×D₃	1	2	yes	complemented
134	C₂×C₅×SD₁₆	—	6	2	no	—
135	C₂×C₅×D₈	—	3	2	no	—
136	C₂×C₅×D₈	—	3	1	no	—
137	C₂×C₅×D₈	—	6	1	no	—
138	C₂×C₅×D₈	—	6	1	no	—
139	C₂×C₅×D₈	—	6	1	no	—
140	C₂×C₅×D₈	—	6	1	no	—
141	C₂×C₅×D₈	—	6	2	no	—
142	C₂×C₅×D₈	C₂×D₃	1	1	yes	characteristic, complemented
143	C₅×#131	—	3	1	no	—
144	C₅×#131	—	3	1	no	—
145	C₅×#131	—	3	1	no	—
146	C₅×#131	—	6	1	no	—
147	C₅×#131	—	6	1	no	—
148	C₅×#131	C₂×D₃	1	1	yes	characteristic, complemented
149	C₂×C₅×M₁₆	—	3	1	no	—
150	C₂×C₅×M₁₆	—	3	2	no	—
151	C₂×C₅×M₁₆	—	6	1	no	—
152	C₂²×C₅×C₈	—	3	1	no	—
153	C₂²×C₅×C₈	—	6	1	no	—
154	C₅×#108	—	3	2	no	—
155	C₅×#108	—	3	1	no	—
156	C₅×#108	C₂×D₃	1	1	yes	characteristic, complemented
157	C₅×#100	—	3	2	no	—
158	C₅×#100	—	3	2	no	—
159	C₅×#100	—	3	2	no	—
160	C₅×#100	C₂×D₃	1	2	yes	complemented
161	C₂×#472	—	3	1	no	Sylow
162	C₂³×C₃×C₅	—	2	2	no	—
163	C₂²×C₅×D₃	—	2	1	no	—
164	C₂²×C₅×D₃	—	2	2	no	—
165	C₂²×C₅×D₃	—	4	2	no	—
166	C₂²×C₅×D₃	—	4	2	no	—
167	C₂²×C₅×D₃	—	8	4	no	—
168	C₂²×C₅×D₃	#41	1	1	yes	characteristic
169	C₃×C₅×Q₈	C₂×D₄	1	1	yes	characteristic
170	C₃×C₅×D₄	—	2	1	no	—
171	C₃×C₅×D₄	—	2	2	no	—
172	C₃×C₅×D₄	—	2	2	no	—
173	C₃×C₅×D₄	C₂×D₄	1	1	yes	characteristic
174	C₂×C₃×C₄×C₅	—	2	1	no	—
175	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
176	C₅×#67	—	2	1	no	—
177	C₅×#67	—	2	1	no	—
178	C₅×#67	—	2	1	no	—
179	C₅×#67	—	4	2	no	—
180	C₅×#67	—	4	2	no	—
181	C₂×C₅×Dic₃	—	2	1	no	—
182	C₂×C₅×Dic₃	#41	1	1	yes	characteristic
183	C₅×D₁₂	—	2	1	no	—
184	C₅×D₁₂	—	2	2	no	—
185	C₅×D₁₂	—	2	2	no	—
186	C₅×D₁₂	C₂×D₄	1	1	yes	characteristic
187	C₄×C₅×D₃	—	2	1	no	—
188	C₄×C₅×D₃	—	2	1	no	—
189	C₄×C₅×D₃	—	2	1	no	—
190	C₄×C₅×D₃	C₂×D₄	1	1	yes	characteristic
191	C₄×C₅×D₃	C₂×D₄	1	1	yes	characteristic
192	C₄×C₅×D₃	C₂×D₄	1	1	yes	characteristic
193	C₄×C₅×D₃	C₂×D₄	1	1	yes	characteristic
194	C₅×Dic₆	—	2	1	no	—
195	C₅×Dic₆	C₂×D₄	1	1	yes	characteristic
196	C₃×C₅×C₈	—	2	1	no	—
197	C₃×C₅×C₈	—	2	2	no	—
198	C₃×C₅×C₈	C₂×D₄	1	1	yes	characteristic
199	C₃×C₅×C₈	C₂×D₄	1	1	yes	characteristic
200	C₅×C₃⋊C₈	—	2	1	no	—
201	C₅×C₃⋊C₈	—	2	2	no	—
202	C₅×C₃⋊C₈	C₂×D₄	1	1	yes	characteristic
203	C₅×C₃⋊C₈	C₂×D₄	1	1	yes	characteristic
204	D₃×#41	C₂²×C₅	1	1	yes	characteristic
205	C₂×D₃×D₄	C₂²×C₅	1	2	yes	—
206	C₃×AGL(1,ℤ/8)	C₂²×C₅	1	2	yes	complemented
207	C₂×C₃×D₈	C₂²×C₅	1	1	yes	characteristic, complemented
208	C₃×#131	C₂²×C₅	1	1	yes	characteristic, complemented
209	#949	C₂²×C₅	1	2	yes	complemented
210	#948	C₂²×C₅	1	1	yes	characteristic, complemented
211	#932	C₂²×C₅	1	2	yes	complemented
212	C₂×#213	C₂²×C₅	1	2	yes	complemented
213	#914	—	2	2	no	—
214	D₃×SD₁₆	—	2	2	no	—
215	#911	—	2	2	no	—
216	D₃×D₈	—	2	2	no	—
217	D₃×D₈	—	2	1	no	—
218	D₃×D₈	—	2	1	no	—
219	D₃×D₈	—	2	1	no	—
220	D₃×D₈	—	2	1	no	—
221	#908	C₂²×C₅	1	2	yes	complemented
222	#907	—	2	1	no	—
223	#907	C₂²×C₅	1	1	yes	characteristic, complemented
224	D₃×M₁₆	—	2	1	no	—
225	D₃×M₁₆	C₂²×C₅	1	2	yes	—
226	D₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
227	C₂×D₂₄	C₂²×C₅	1	1	yes	characteristic, complemented
228	#901	—	2	1	no	—
229	#901	C₂²×C₅	1	1	yes	characteristic, complemented
230	C₂×D₃×C₈	—	2	1	no	—
231	C₂×D₃×C₈	C₂²×C₅	1	1	yes	characteristic
232	C₃×#108	C₂²×C₅	1	1	yes	characteristic, complemented
233	C₃×#100	C₂²×C₅	1	2	yes	complemented
234	#833	C₂²×C₅	1	2	yes	complemented
235	#823	C₂²×C₅	1	2	yes	complemented
236	#823	C₂²×C₅	1	2	yes	complemented
237	#822	C₂²×C₅	1	2	yes	complemented
238	#819	C₂²×C₅	1	1	yes	characteristic, complemented
239	C₂⁴×C₅	—	6	2	no	—
240	C₅×#41	—	3	1	no	—
241	C₅×#41	—	3	1	no	—
242	C₅×#41	—	3	1	no	—
243	C₅×#41	—	6	1	no	—
244	C₅×#41	—	6	1	no	—
245	C₅×#41	C₂²×D₃	1	1	yes	characteristic
246	C₂×C₅×Q₈	—	3	1	no	—
247	C₂×C₅×D₄	—	3	1	no	—
248	C₂×C₅×D₄	—	3	2	no	—
249	C₂×C₅×D₄	—	6	2	no	—
250	C₂×C₅×D₄	—	6	2	no	—
251	C₂×C₅×D₄	—	6	2	no	—
252	C₂×C₅×D₄	—	6	2	no	—
253	C₂×C₅×D₄	—	6	2	no	—
254	C₂×C₅×D₄	—	6	1	no	—
255	C₂×C₅×D₄	C₂²×D₃	1	2	yes	—
256	C₂²×C₄×C₅	—	3	1	no	—
257	C₂²×C₄×C₅	—	6	1	no	—
258	C₅×SD₁₆	—	2	2	no	—
259	C₅×SD₁₆	—	6	2	no	—
260	C₅×SD₁₆	—	6	2	no	—
261	C₅×SD₁₆	—	6	2	no	—
262	C₅×D₈	—	2	2	no	—
263	C₅×D₈	—	2	1	no	—
264	C₅×D₈	—	2	1	no	—
265	C₅×D₈	—	6	2	no	—
266	C₅×D₈	—	6	2	no	—
267	C₅×D₈	—	6	2	no	—
268	C₅×D₈	—	6	2	no	—
269	C₅×D₈	—	6	2	no	—
270	C₅×D₈	—	6	1	no	—
271	C₅×D₈	—	6	1	no	—
272	C₅×M₁₆	—	2	1	no	—
273	C₅×M₁₆	—	3	1	no	—
274	C₅×M₁₆	—	3	2	no	—
275	C₅×M₁₆	—	6	1	no	—
276	C₅×M₁₆	—	6	1	no	—
277	C₅×M₁₆	—	6	2	no	—
278	C₅×M₁₆	—	6	1	no	—
279	C₅×M₁₆	—	6	1	no	—
280	C₅×M₁₆	C₂²×D₃	1	1	yes	characteristic
281	C₅×M₁₆	C₂²×D₃	1	2	yes	—
282	C₂×C₅×C₈	—	2	1	no	—
283	C₂×C₅×C₈	—	3	1	no	—
284	C₂×C₅×C₈	—	3	1	no	—
285	C₂×C₅×C₈	—	3	1	no	—
286	C₂×C₅×C₈	—	3	1	no	—
287	C₂×C₅×C₈	—	3	1	no	—
288	C₂×C₅×C₈	—	6	1	no	—
289	C₂×C₅×C₈	—	6	1	no	—
290	C₂×C₅×C₈	—	6	2	no	—
291	C₂×C₅×C₈	—	6	1	no	—
292	C₂×C₅×C₈	—	6	1	no	—
293	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
294	C₂×AGL(1,ℤ/8)	—	3	2	no	—
295	C₂²×D₈	—	3	1	no	—
296	C₂×#131	—	3	1	no	—
297	#472	—	3	2	no	—
298	#472	—	3	1	no	—
299	#472	—	3	1	no	—
300	#472	—	3	1	no	—
301	#472	—	3	2	no	—
302	#472	C₅×D₃	1	1	yes	characteristic, direct product factor
303	C₂×#108	—	3	1	no	—
304	C₂×#100	—	3	2	no	—
305	C₂²×C₃×C₅	—	2	1	no	—
306	C₂²×C₃×C₅	—	4	2	no	—
307	C₂²×C₃×C₅	—	8	2	no	—
308	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
309	C₂×C₅×D₃	—	2	2	no	—
310	C₂×C₅×D₃	—	2	1	no	—
311	C₂×C₅×D₃	—	4	2	no	—
312	C₂×C₅×D₃	—	4	2	no	—
313	C₂×C₅×D₃	—	8	4	no	—
314	C₂×C₅×D₃	—	8	4	no	—
315	C₂×C₅×D₃	—	8	2	no	—
316	C₂×C₅×D₃	#121	1	1	yes	characteristic
317	C₂×C₅×D₃	#121	1	1	yes	characteristic
318	C₃×C₄×C₅	—	2	1	no	—
319	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
320	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
321	C₅×Dic₃	—	2	1	no	—
322	C₅×Dic₃	#121	1	1	yes	characteristic
323	C₅×Dic₃	#121	1	1	yes	characteristic
324	C₂³×D₃	—	2	2	no	—
325	C₃×#41	C₂³×C₅	1	1	yes	characteristic
326	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
327	C₂×#67	—	2	2	no	—
328	#239	C₅×D₄	1	1	yes	characteristic
329	D₃×Q₈	C₅×D₄	1	1	yes	characteristic
330	#237	—	2	1	no	—
331	#237	C₅×D₄	1	1	yes	characteristic
332	D₃×D₄	—	2	1	no	—
333	D₃×D₄	—	2	2	no	—
334	D₃×D₄	—	2	2	no	—
335	D₃×D₄	—	2	2	no	—
336	D₃×D₄	—	2	2	no	—
337	D₃×D₄	C₅×D₄	1	1	yes	characteristic
338	#235	—	2	1	no	—
339	#235	C₂³×C₅	1	1	yes	characteristic
340	C₂×D₁₂	C₂³×C₅	1	2	yes	—
341	C₂×C₄×D₃	—	2	1	no	—
342	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
343	C₃×SD₁₆	—	2	2	no	—
344	C₃×D₈	—	2	2	no	—
345	C₃×D₈	—	2	1	no	—
346	C₃×D₈	—	2	1	no	—
347	C₃×M₁₆	—	2	1	no	—
348	C₃×M₁₆	C₂³×C₅	1	2	yes	—
349	C₃×M₁₆	C₂³×C₅	1	1	yes	characteristic
350	C₂×C₃×C₈	—	2	1	no	—
351	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
352	#215	—	2	2	no	—
353	#214	—	2	2	no	—
354	#213	—	2	2	no	—
355	#213	—	2	2	no	—
356	#213	—	2	2	no	—
357	#213	—	2	2	no	—
358	#208	—	2	1	no	—
359	#208	C₂³×C₅	1	2	yes	—
360	#208	C₂³×C₅	1	1	yes	characteristic
361	C₂×C₃⋊C₈	—	2	1	no	—
362	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
363	D₂₄	—	2	2	no	—
364	D₂₄	—	2	1	no	—
365	D₂₄	—	2	1	no	—
366	#204	—	2	2	no	—
367	ΓL(1,𝔽₂₅)	—	2	1	no	—
368	ΓL(1,𝔽₂₅)	—	2	2	no	—
369	ΓL(1,𝔽₂₅)	—	2	1	no	—
370	ΓL(1,𝔽₂₅)	—	2	1	no	—
371	D₃×C₈	—	2	1	no	—
372	D₃×C₈	—	2	2	no	—
373	D₃×C₈	—	2	1	no	—
374	D₃×C₈	—	2	1	no	—
375	D₃×C₈	C₅×D₄	1	1	yes	characteristic
376	D₃×C₈	C₅×D₄	1	1	yes	characteristic
377	D₃×C₈	C₅×D₄	1	1	yes	characteristic
378	D₃×C₈	C₅×D₄	1	1	yes	characteristic
379	C₂³×C₅	—	2	2	no	—
380	C₂³×C₅	—	3	1	no	—
381	C₂³×C₅	—	6	1	no	—
382	C₂³×C₅	—	6	2	no	—
383	C₂³×C₅	—	12	2	no	—
384	C₂³×C₅	—	12	2	no	—
385	C₂³×C₅	—	24	4	no	—
386	C₅×Q₈	—	3	1	no	—
387	C₅×Q₈	—	6	1	no	—
388	C₅×Q₈	D₃×D₄	1	1	yes	characteristic
389	C₅×D₄	—	2	1	no	—
390	C₅×D₄	—	2	2	no	—
391	C₅×D₄	—	2	2	no	—
392	C₅×D₄	—	3	1	no	—
393	C₅×D₄	—	6	1	no	—
394	C₅×D₄	—	6	1	no	—
395	C₅×D₄	—	6	1	no	—
396	C₅×D₄	—	6	1	no	—
397	C₅×D₄	—	6	2	no	—
398	C₅×D₄	—	6	2	no	—
399	C₅×D₄	—	12	2	no	—
400	C₅×D₄	—	12	2	no	—
401	C₅×D₄	D₃×D₄	1	1	yes	characteristic
402	C₂×C₄×C₅	—	2	1	no	—
403	C₂×C₄×C₅	—	3	1	no	—
404	C₂×C₄×C₅	—	3	1	no	—
405	C₂×C₄×C₅	—	3	1	no	—
406	C₂×C₄×C₅	—	3	1	no	—
407	C₂×C₄×C₅	—	3	1	no	—
408	C₂×C₄×C₅	—	6	1	no	—
409	C₂×C₄×C₅	—	6	1	no	—
410	C₂×C₄×C₅	—	6	1	no	—
411	C₂×C₄×C₅	—	6	1	no	—
412	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
413	C₅×C₈	—	2	1	no	—
414	C₅×C₈	—	2	2	no	—
415	C₅×C₈	—	3	1	no	—
416	C₅×C₈	—	3	1	no	—
417	C₅×C₈	—	6	1	no	—
418	C₅×C₈	—	6	2	no	—
419	C₅×C₈	D₃×D₄	1	1	yes	characteristic
420	C₅×C₈	D₃×D₄	1	1	yes	characteristic
421	C₂×#41	—	3	1	no	—
422	C₂²×D₄	—	3	2	no	—
423	AGL(1,ℤ/8)	—	3	2	no	—
424	AGL(1,ℤ/8)	—	3	2	no	—
425	AGL(1,ℤ/8)	—	3	2	no	—
426	AGL(1,ℤ/8)	—	6	2	no	—
427	AGL(1,ℤ/8)	—	6	2	no	—
428	AGL(1,ℤ/8)	C₂×C₅×D₃	1	2	yes	complemented
429	C₂×SD₁₆	—	6	2	no	—
430	C₂×D₈	—	3	2	no	—
431	C₂×D₈	—	3	1	no	—
432	C₂×D₈	—	6	1	no	—
433	C₂×D₈	—	6	1	no	—
434	C₂×D₈	—	6	1	no	—
435	C₂×D₈	—	6	1	no	—
436	C₂×D₈	—	6	2	no	—
437	C₂×D₈	C₂×C₅×D₃	1	1	yes	characteristic, complemented
438	#131	—	3	1	no	—
439	#131	—	3	1	no	—
440	#131	—	3	1	no	—
441	#131	—	6	1	no	—
442	#131	—	6	1	no	—
443	#131	C₂×C₅×D₃	1	1	yes	characteristic, complemented
444	C₂×M₁₆	—	3	1	no	—
445	C₂×M₁₆	—	3	2	no	—
446	C₂×M₁₆	—	6	1	no	—
447	C₂²×C₈	—	3	1	no	—
448	C₂²×C₈	—	6	1	no	—
449	#108	—	3	2	no	—
450	#108	—	3	1	no	—
451	#108	C₂×C₅×D₃	1	1	yes	characteristic, complemented
452	#100	—	3	2	no	—
453	#100	—	3	2	no	—
454	#100	—	3	2	no	—
455	#100	C₂×C₅×D₃	1	2	yes	complemented
456	C₂×C₃×C₅	—	2	1	no	—
457	C₂×C₃×C₅	—	4	1	no	—
458	C₂×C₃×C₅	—	8	2	no	—
459	C₂×C₃×C₅	C₂×#121	1	1	yes	characteristic
460	C₅×D₃	—	2	1	no	—
461	C₅×D₃	—	4	1	no	—
462	C₅×D₃	—	8	2	no	—
463	C₅×D₃	#472	1	2	yes	direct product factor
464	C₂³×C₃	—	2	2	no	—
465	C₂²×D₃	—	2	1	no	—
466	C₂²×D₃	—	2	2	no	—
467	C₂²×D₃	—	4	2	no	—
468	C₂²×D₃	—	4	2	no	—
469	C₂²×D₃	—	8	4	no	—
470	C₂²×D₃	C₅×#41	1	1	yes	characteristic
471	C₃×Q₈	C₂×C₅×D₄	1	1	yes	characteristic
472	C₃×D₄	—	2	1	no	—
473	C₃×D₄	—	2	2	no	—
474	C₃×D₄	—	2	2	no	—
475	C₃×D₄	C₂×C₅×D₄	1	1	yes	characteristic
476	C₂×C₃×C₄	—	2	1	no	—
477	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
478	#67	—	2	1	no	—
479	#67	—	2	1	no	—
480	#67	—	2	1	no	—
481	#67	—	4	2	no	—
482	#67	—	4	2	no	—
483	C₂×Dic₃	—	2	1	no	—
484	C₂×Dic₃	C₅×#41	1	1	yes	characteristic
485	D₁₂	—	2	1	no	—
486	D₁₂	—	2	2	no	—
487	D₁₂	—	2	2	no	—
488	D₁₂	C₂×C₅×D₄	1	1	yes	characteristic
489	C₄×D₃	—	2	1	no	—
490	C₄×D₃	—	2	1	no	—
491	C₄×D₃	—	2	1	no	—
492	C₄×D₃	C₂×C₅×D₄	1	1	yes	characteristic
493	C₄×D₃	C₂×C₅×D₄	1	1	yes	characteristic
494	C₄×D₃	C₂×C₅×D₄	1	1	yes	characteristic
495	C₄×D₃	C₂×C₅×D₄	1	1	yes	characteristic
496	Dic₆	—	2	1	no	—
497	Dic₆	C₂×C₅×D₄	1	1	yes	characteristic
498	C₃×C₈	—	2	1	no	—
499	C₃×C₈	—	2	2	no	—
500	C₃×C₈	C₂×C₅×D₄	1	1	yes	characteristic
501	C₃×C₈	C₂×C₅×D₄	1	1	yes	characteristic
502	C₃⋊C₈	—	2	1	no	—
503	C₃⋊C₈	—	2	2	no	—
504	C₃⋊C₈	C₂×C₅×D₄	1	1	yes	characteristic
505	C₃⋊C₈	C₂×C₅×D₄	1	1	yes	characteristic
506	C₂²×C₅	—	2	1	no	—
507	C₂²×C₅	—	3	1	no	—
508	C₂²×C₅	—	3	1	no	—
509	C₂²×C₅	—	4	2	no	—
510	C₂²×C₅	—	6	2	no	—
511	C₂²×C₅	—	6	1	no	—
512	C₂²×C₅	—	8	2	no	—
513	C₂²×C₅	—	12	2	no	—
514	C₂²×C₅	—	12	2	no	—
515	C₂²×C₅	—	24	2	no	—
516	C₂²×C₅	—	24	4	no	—
517	C₂²×C₅	—	24	4	no	—
518	C₂²×C₅	D₃×#41	1	1	yes	characteristic
519	C₄×C₅	—	2	1	no	—
520	C₄×C₅	—	3	1	no	—
521	C₄×C₅	—	3	1	no	—
522	C₄×C₅	—	6	1	no	—
523	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
524	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
525	C₂⁴	—	6	2	no	—
526	#41	—	3	1	no	—
527	#41	—	3	1	no	—
528	#41	—	3	1	no	—
529	#41	—	6	1	no	—
530	#41	—	6	1	no	—
531	#41	C₂²×C₅×D₃	1	1	yes	characteristic
532	C₂×Q₈	—	3	1	no	—
533	C₂×D₄	—	3	1	no	—
534	C₂×D₄	—	3	2	no	—
535	C₂×D₄	—	6	2	no	—
536	C₂×D₄	—	6	2	no	—
537	C₂×D₄	—	6	2	no	—
538	C₂×D₄	—	6	2	no	—
539	C₂×D₄	—	6	2	no	—
540	C₂×D₄	—	6	1	no	—
541	C₂×D₄	C₂²×C₅×D₃	1	2	yes	—
542	C₂²×C₄	—	3	1	no	—
543	C₂²×C₄	—	6	1	no	—
544	SD₁₆	—	2	2	no	—
545	SD₁₆	—	6	2	no	—
546	SD₁₆	—	6	2	no	—
547	SD₁₆	—	6	2	no	—
548	D₈	—	2	2	no	—
549	D₈	—	2	1	no	—
550	D₈	—	2	1	no	—
551	D₈	—	6	2	no	—
552	D₈	—	6	2	no	—
553	D₈	—	6	2	no	—
554	D₈	—	6	2	no	—
555	D₈	—	6	2	no	—
556	D₈	—	6	1	no	—
557	D₈	—	6	1	no	—
558	M₁₆	—	2	1	no	—
559	M₁₆	—	3	1	no	—
560	M₁₆	—	3	2	no	—
561	M₁₆	—	6	1	no	—
562	M₁₆	—	6	1	no	—
563	M₁₆	—	6	2	no	—
564	M₁₆	—	6	1	no	—
565	M₁₆	—	6	1	no	—
566	M₁₆	C₂²×C₅×D₃	1	1	yes	characteristic
567	M₁₆	C₂²×C₅×D₃	1	2	yes	—
568	C₂×C₈	—	2	1	no	—
569	C₂×C₈	—	3	1	no	—
570	C₂×C₈	—	3	1	no	—
571	C₂×C₈	—	3	1	no	—
572	C₂×C₈	—	3	1	no	—
573	C₂×C₈	—	3	1	no	—
574	C₂×C₈	—	6	1	no	—
575	C₂×C₈	—	6	1	no	—
576	C₂×C₈	—	6	2	no	—
577	C₂×C₈	—	6	1	no	—
578	C₂×C₈	—	6	1	no	—
579	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
580	C₃×C₅	C₂×#472	1	1	yes	characteristic, complemented, Hall
581	C₂²×C₃	—	2	1	no	—
582	C₂²×C₃	—	4	2	no	—
583	C₂²×C₃	—	8	2	no	—
584	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
585	C₂×D₃	—	2	2	no	—
586	C₂×D₃	—	2	1	no	—
587	C₂×D₃	—	4	2	no	—
588	C₂×D₃	—	4	2	no	—
589	C₂×D₃	—	8	4	no	—
590	C₂×D₃	—	8	4	no	—
591	C₂×D₃	—	8	2	no	—
592	C₂×D₃	C₅×#121	1	1	yes	characteristic
593	C₂×D₃	C₅×#121	1	1	yes	characteristic
594	C₃×C₄	—	2	1	no	—
595	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
596	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
597	Dic₃	—	2	1	no	—
598	Dic₃	C₅×#121	1	1	yes	characteristic
599	Dic₃	C₅×#121	1	1	yes	characteristic
600	C₂×C₅	—	2	1	no	—
601	C₂×C₅	—	3	2	no	—
602	C₂×C₅	—	4	1	no	—
603	C₂×C₅	—	6	1	no	—
604	C₂×C₅	—	8	2	no	—
605	C₂×C₅	—	12	1	no	—
606	C₂×C₅	—	24	2	no	—
607	C₂×C₅	D₃×#121	1	1	yes	characteristic
608	C₂³	—	2	2	no	—
609	C₂³	—	3	1	no	—
610	C₂³	—	6	1	no	—
611	C₂³	—	6	2	no	—
612	C₂³	—	12	2	no	—
613	C₂³	—	12	2	no	—
614	C₂³	—	24	4	no	—
615	Q₈	—	3	1	no	—
616	Q₈	—	6	1	no	—
617	Q₈	C₅×D₃×D₄	1	1	yes	characteristic
618	D₄	—	2	1	no	—
619	D₄	—	2	2	no	—
620	D₄	—	2	2	no	—
621	D₄	—	3	1	no	—
622	D₄	—	6	1	no	—
623	D₄	—	6	1	no	—
624	D₄	—	6	1	no	—
625	D₄	—	6	1	no	—
626	D₄	—	6	2	no	—
627	D₄	—	6	2	no	—
628	D₄	—	12	2	no	—
629	D₄	—	12	2	no	—
630	D₄	C₅×D₃×D₄	1	1	yes	characteristic
631	C₂×C₄	—	2	1	no	—
632	C₂×C₄	—	3	1	no	—
633	C₂×C₄	—	3	1	no	—
634	C₂×C₄	—	3	1	no	—
635	C₂×C₄	—	3	1	no	—
636	C₂×C₄	—	3	1	no	—
637	C₂×C₄	—	6	1	no	—
638	C₂×C₄	—	6	1	no	—
639	C₂×C₄	—	6	1	no	—
640	C₂×C₄	—	6	1	no	—
641	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
642	C₈	—	2	1	no	—
643	C₈	—	2	2	no	—
644	C₈	—	3	1	no	—
645	C₈	—	3	1	no	—
646	C₈	—	6	1	no	—
647	C₈	—	6	2	no	—
648	C₈	C₅×D₃×D₄	1	1	yes	characteristic
649	C₈	C₅×D₃×D₄	1	1	yes	characteristic
650	C₂×C₃	—	2	1	no	—
651	C₂×C₃	—	4	1	no	—
652	C₂×C₃	—	8	2	no	—
653	C₂×C₃	C₂×C₅×#121	1	1	yes	characteristic
654	D₃	—	2	1	no	—
655	D₃	—	4	1	no	—
656	D₃	—	8	2	no	—
657	D₃	C₅×#472	1	2	yes	direct product factor
658	C₅	D₃×#472	1	1	yes	characteristic, direct product factor, Sylow
659	C₂²	—	2	1	no	—
660	C₂²	—	3	1	no	—
661	C₂²	—	3	1	no	—
662	C₂²	—	4	2	no	—
663	C₂²	—	6	2	no	—
664	C₂²	—	6	1	no	—
665	C₂²	—	8	2	no	—
666	C₂²	—	12	2	no	—
667	C₂²	—	12	2	no	—
668	C₂²	—	24	2	no	—
669	C₂²	—	24	4	no	—
670	C₂²	—	24	4	no	—
671	C₂²	C₅×D₃×#41	1	1	yes	characteristic
672	C₄	—	2	1	no	—
673	C₄	—	3	1	no	—
674	C₄	—	3	1	no	—
675	C₄	—	6	1	no	—
676	C₄	C₂×C₅×D₃×D₄	1	1	yes	characteristic
677	C₄	C₂×C₅×D₃×D₄	1	1	yes	characteristic
678	C₃	C₂×C₅×#472	1	1	yes	characteristic, complemented, Sylow
679	C₂	—	2	1	no	—
680	C₂	—	3	2	no	—
681	C₂	—	4	1	no	—
682	C₂	—	6	1	no	—
683	C₂	—	8	2	no	—
684	C₂	—	12	1	no	—
685	C₂	—	24	2	no	—
686	C₂	C₅×D₃×#121	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₅	D₃×#121
commutator, cosocle	C₂×C₃×C₄	C₂⁴×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₃×C₅×#472	C₂
socle	C₂×C₃×C₅	C₂×#121
hypercenter	C₅×#472	D₃
hypocenter	C₃	C₂×C₅×#472
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₅ ◁ C₂×C₄×C₅ ◁ C₅×#472

Complements

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

N	H ≅ G/N	type
1. C₅×D₃×AGL(1,ℤ/8)	C₂	semidirect
2. C₂×C₅×D₃×D₈	C₂	semidirect
3. C₅×D₃×#131	C₂	semidirect
4. C₃×C₅×#472	C₂	semidirect
5. C₅×#5199	C₂	semidirect
6. C₅×#5160	C₂	semidirect
7. C₅×#5142	C₂	semidirect
8. C₅×#4897	C₂	semidirect
9. C₅×D₃×#108	C₂	semidirect
10. C₅×#4749	C₂	semidirect
11. C₅×D₃×#100	C₂	semidirect
15. C₃×C₅×AGL(1,ℤ/8)	C₂²	semidirect
16. C₂×C₃×C₅×D₈	C₂²	semidirect
17. C₃×C₅×#131	C₂²	semidirect
18. C₅×#949	C₂²	semidirect
19. C₅×#948	C₂²	semidirect
20. C₅×#932	C₂²	semidirect
21. C₂×C₅×#213	C₂²	semidirect
30. C₅×#908	C₂²	semidirect
32. C₅×#907	C₂²	semidirect
36. C₂×C₅×D₂₄	C₂²	semidirect
38. C₅×#901	C₂²	semidirect
41. C₃×C₅×#108	C₂²	semidirect
42. C₃×C₅×#100	C₂²	semidirect
43. C₅×#833	C₂²	semidirect
44. C₅×#823	C₂²	semidirect
45. C₅×#823	C₂²	semidirect
46. C₅×#822	C₂²	semidirect
47. C₅×#819	C₂²	semidirect
48. D₃×#472	C₅	direct (N × H)
57. C₅×#472	D₃	direct (N × H)
115. D₃×AGL(1,ℤ/8)	C₂×C₅	semidirect
116. C₂×D₃×D₈	C₂×C₅	semidirect
117. D₃×#131	C₂×C₅	semidirect
118. C₃×#472	C₂×C₅	semidirect
119. #5199	C₂×C₅	semidirect
120. #5160	C₂×C₅	semidirect
121. #5142	C₂×C₅	semidirect
122. #4897	C₂×C₅	semidirect
123. D₃×#108	C₂×C₅	semidirect
124. #4749	C₂×C₅	semidirect
125. D₃×#100	C₂×C₅	semidirect
133. C₅×AGL(1,ℤ/8)	C₂×D₃	semidirect
142. C₂×C₅×D₈	C₂×D₃	semidirect
148. C₅×#131	C₂×D₃	semidirect
156. C₅×#108	C₂×D₃	semidirect
160. C₅×#100	C₂×D₃	semidirect
206. C₃×AGL(1,ℤ/8)	C₂²×C₅	semidirect
207. C₂×C₃×D₈	C₂²×C₅	semidirect
208. C₃×#131	C₂²×C₅	semidirect
209. #949	C₂²×C₅	semidirect
210. #948	C₂²×C₅	semidirect
211. #932	C₂²×C₅	semidirect
212. C₂×#213	C₂²×C₅	semidirect
221. #908	C₂²×C₅	semidirect
223. #907	C₂²×C₅	semidirect
227. C₂×D₂₄	C₂²×C₅	semidirect
229. #901	C₂²×C₅	semidirect
232. C₃×#108	C₂²×C₅	semidirect
233. C₃×#100	C₂²×C₅	semidirect
234. #833	C₂²×C₅	semidirect
235. #823	C₂²×C₅	semidirect
236. #823	C₂²×C₅	semidirect
237. #822	C₂²×C₅	semidirect
238. #819	C₂²×C₅	semidirect
302. #472	C₅×D₃	direct (N × H)
428. AGL(1,ℤ/8)	C₂×C₅×D₃	semidirect
437. C₂×D₈	C₂×C₅×D₃	semidirect
443. #131	C₂×C₅×D₃	semidirect
451. #108	C₂×C₅×D₃	semidirect
455. #100	C₂×C₅×D₃	semidirect
463. C₅×D₃	#472	direct (N × H)
580. C₃×C₅	C₂×#472	semidirect
657. D₃	C₅×#472	direct (N × H)
658. C₅	D₃×#472	direct (N × H)
678. C₃	C₂×C₅×#472	semidirect

Maximal subgroups

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

subgroup	index
C₅×D₃×AGL(1,ℤ/8)	2
C₂×C₅×D₃×D₈	2
C₅×D₃×#131	2
C₃×C₅×#472	2
C₅×#5199	2
C₅×#5160	2
C₅×#5142	2
C₅×#4897	2
C₅×D₃×#108	2
C₅×#4749	2
C₅×D₃×#100	2
C₂×C₅×#472	3
D₃×#472	5

Subgroups — C5×D3×#472 #14429367

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×D₃×#472 #14429367