Subgroups — C₅×#83940 #14439546

Order 1920.

1192 conjugacy classes of subgroups.

The subgroup lattice has 616 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, complemented
2	C₅×#5830	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×#950	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5805	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×C₅×#213	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₅×#908	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#5176	C₂	1	2	yes	maximal, complemented
8	C₅×#5168	C₂	1	2	yes	maximal, complemented
9	C₅×#5154	C₂	1	2	yes	maximal, complemented
10	C₅×#5151	C₂	1	2	yes	maximal, complemented
11	C₅×#5122	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#3155	—	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	C₂×C₅×#235	C₂²	1	1	yes	characteristic
16	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic
17	C₃×C₅×AGL(1,ℤ/8)	—	2	4	no	—
18	C₂×C₃×C₅×SD₁₆	C₂²	1	2	yes	complemented
19	C₂×C₃×C₅×D₈	C₂²	1	2	yes	complemented
20	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
21	C₅×#953	—	2	2	no	—
22	C₅×#950	—	2	4	no	—
23	C₅×#947	C₂²	1	2	yes	complemented
24	C₂×C₅×#216	C₂²	1	1	yes	characteristic, complemented
25	C₂×C₅×#215	C₂²	1	1	yes	characteristic, complemented
26	C₅×#940	C₂²	1	2	yes	complemented
27	C₅×#940	C₂²	1	2	yes	complemented
28	C₅×#938	—	2	2	no	—
29	C₅×#937	—	2	2	no	—
30	C₅×#936	C₂²	1	2	yes	complemented
31	C₂×C₅×#214	C₂²	1	1	yes	characteristic, complemented
32	C₂×C₅×#213	—	2	4	no	—
33	C₂×C₅×#213	C₂²	1	2	yes	—
34	C₂×C₅×#213	C₂²	1	2	yes	—
35	C₂×C₅×#213	C₂²	1	1	yes	characteristic, complemented
36	C₅×#930	—	2	2	no	—
37	C₅×#926	C₂²	1	1	yes	characteristic
38	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
39	C₅×#908	—	2	4	no	—
40	C₂×C₅×D₂₄	C₂²	1	2	yes	complemented
41	C₂×C₅×#204	C₂²	1	2	yes	complemented
42	C₅×#815	C₂²	1	2	yes	complemented
43	C₅×C₈×Dic₃	C₂²	1	2	yes	complemented
44	#83940	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
45	C₂×C₅×AGL(1,ℤ/8)	—	3	1	no	—
46	C₂×C₅×AGL(1,ℤ/8)	D₃	1	1	yes	characteristic, complemented
47	C₂×C₅×#135	—	3	1	no	—
48	C₂²×C₅×D₈	—	3	1	no	—
49	C₅×#535	—	3	1	no	—
50	C₅×#535	—	3	1	no	—
51	C₅×#496	—	3	2	no	—
52	C₅×#496	—	3	2	no	—
53	C₅×#495	—	3	2	no	—
54	C₅×#493	—	3	2	no	—
55	C₅×#405	—	3	1	no	—
56	C₂⁴×C₃×C₅	—	2	1	no	—
57	C₂³×C₅×D₃	—	2	1	no	—
58	C₃×C₅×#41	—	2	2	no	—
59	C₃×C₅×#41	—	2	2	no	—
60	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
61	C₂×C₃×C₅×D₄	—	2	1	no	—
62	C₂×C₃×C₅×D₄	—	2	2	no	—
63	C₂×C₃×C₅×D₄	—	2	2	no	—
64	C₂×C₃×C₅×D₄	—	2	1	no	—
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	C₂×C₅×#67	—	2	1	no	—
70	C₂×C₅×#67	—	2	4	no	—
71	C₂×C₅×#67	—	2	4	no	—
72	C₅×#235	—	2	2	no	—
73	C₅×#235	—	2	2	no	—
74	C₂×C₅×D₁₂	—	2	2	no	—
75	C₂×C₅×D₁₂	—	2	2	no	—
76	C₂×C₅×D₁₂	—	2	1	no	—
77	C₂×C₅×D₁₂	C₂³	1	2	yes	—
78	C₂×C₅×D₁₂	C₂³	1	1	yes	characteristic
79	C₂×C₄×C₅×D₃	—	2	1	no	—
80	C₂×C₅×Dic₆	C₂³	1	1	yes	characteristic
81	C₃×C₅×SD₁₆	—	2	4	no	—
82	C₃×C₅×D₈	—	2	4	no	—
83	C₃×C₅×M₁₆	D₄	1	4	yes	complemented
84	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
85	C₅×#217	—	2	4	no	—
86	C₅×#217	D₄	1	2	yes	—
87	C₅×#216	—	2	2	no	—
88	C₅×#215	—	2	2	no	—
89	C₅×#214	—	2	2	no	—
90	C₅×#213	—	2	4	no	—
91	C₅×#213	—	2	4	no	—
92	C₅×#213	—	2	2	no	—
93	C₅×(C₂×D₃)⋊C₄	—	2	4	no	—
94	C₅×C₄⋊Dic₃	D₄	1	2	yes	—
95	C₄×C₅×Dic₃	C₂³	1	2	yes	—
96	C₂×C₅×C₃⋊C₈	D₄	1	4	yes	complemented
97	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
98	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
99	C₅×D₂₄	—	2	4	no	—
100	C₅×#204	—	2	4	no	—
101	C₂×C₃×AGL(1,ℤ/8)	C₂×C₅	1	1	yes	characteristic, complemented
102	#5830	C₂×C₅	1	1	yes	characteristic, complemented
103	C₂×#950	C₂×C₅	1	1	yes	characteristic, complemented
104	#5805	C₂×C₅	1	1	yes	characteristic, complemented
105	C₂²×#213	C₂×C₅	1	1	yes	characteristic, complemented
106	C₂×#908	C₂×C₅	1	1	yes	characteristic, complemented
107	#5176	C₂×C₅	1	2	yes	complemented
108	#5168	C₂×C₅	1	2	yes	complemented
109	#5154	C₂×C₅	1	2	yes	complemented
110	#5151	C₂×C₅	1	2	yes	complemented
111	#5122	C₂×C₅	1	1	yes	characteristic, complemented
112	C₂×C₅×#41	—	3	1	no	—
113	C₂×C₅×#41	C₂×D₃	1	1	yes	characteristic
114	C₂²×C₅×D₄	—	3	1	no	—
115	C₂²×C₅×D₄	C₂×D₃	1	1	yes	characteristic
116	C₅×AGL(1,ℤ/8)	—	2	4	no	—
117	C₅×AGL(1,ℤ/8)	—	6	4	no	—
118	C₅×#135	—	6	4	no	—
119	C₂×C₅×Q₁₆	—	3	1	no	—
120	C₂×C₅×SD₁₆	—	3	1	no	—
121	C₂×C₅×SD₁₆	—	3	1	no	—
122	C₂×C₅×SD₁₆	—	3	2	no	—
123	C₂×C₅×SD₁₆	C₂×D₃	1	2	yes	complemented
124	C₂×C₅×D₈	—	3	2	no	—
125	C₂×C₅×D₈	—	3	2	no	—
126	C₂×C₅×D₈	—	3	1	no	—
127	C₂×C₅×D₈	—	3	2	no	—
128	C₂×C₅×D₈	—	6	4	no	—
129	C₂×C₅×D₈	C₂×D₃	1	2	yes	complemented
130	C₂×C₅×M₁₆	C₂×D₃	1	1	yes	characteristic
131	C₂²×C₅×C₈	—	3	1	no	—
132	C₅×#127	—	3	2	no	—
133	C₅×#127	—	3	2	no	—
134	C₅×#124	—	3	2	no	—
135	C₅×#124	—	3	2	no	—
136	C₅×#121	—	6	2	no	—
137	C₅×#121	—	6	2	no	—
138	C₅×#120	—	6	2	no	—
139	C₅×#120	—	6	2	no	—
140	C₅×#117	—	3	1	no	—
141	C₅×#97	—	3	2	no	—
142	C₄×C₅×C₈	—	3	2	no	—
143	#3155	—	3	1	no	Sylow
144	C₂³×C₃×C₅	—	2	2	no	—
145	C₂³×C₃×C₅	—	2	1	no	—
146	C₂³×C₃×C₅	—	4	2	no	—
147	C₂³×C₃×C₅	—	8	2	no	—
148	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
149	C₂²×C₅×D₃	—	2	2	no	—
150	C₂²×C₅×D₃	—	2	1	no	—
151	C₂²×C₅×D₃	—	4	2	no	—
152	C₂²×C₅×D₃	—	8	2	no	—
153	C₃×C₅×Q₈	—	2	1	no	—
154	C₃×C₅×Q₈	—	2	1	no	—
155	C₃×C₅×D₄	—	2	2	no	—
156	C₃×C₅×D₄	—	2	1	no	—
157	C₃×C₅×D₄	—	2	1	no	—
158	C₃×C₅×D₄	—	2	2	no	—
159	C₃×C₅×D₄	—	4	2	no	—
160	C₃×C₅×D₄	—	4	2	no	—
161	C₂×C₃×C₄×C₅	—	2	1	no	—
162	C₂×C₃×C₄×C₅	—	4	2	no	—
163	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
164	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
165	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
166	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
167	C₅×#67	—	4	2	no	—
168	C₅×#67	—	8	4	no	—
169	C₅×#67	—	8	4	no	—
170	C₂×C₅×Dic₃	—	2	1	no	—
171	C₂×C₅×Dic₃	C₂×D₄	1	4	yes	—
172	C₅×D₁₂	—	2	2	no	—
173	C₅×D₁₂	—	2	1	no	—
174	C₅×D₁₂	—	2	2	no	—
175	C₅×D₁₂	—	2	1	no	—
176	C₅×D₁₂	—	4	2	no	—
177	C₄×C₅×D₃	—	4	2	no	—
178	C₅×Dic₆	—	2	1	no	—
179	C₅×Dic₆	—	2	1	no	—
180	C₃×C₅×C₈	C₂×D₄	1	4	yes	—
181	C₅×C₃⋊C₈	C₂×D₄	1	2	yes	—
182	C₅×C₃⋊C₈	C₂×D₄	1	2	yes	—
183	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
184	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
185	C₂×#235	C₂²×C₅	1	1	yes	characteristic
186	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic
187	C₃×AGL(1,ℤ/8)	—	2	4	no	—
188	C₂×C₃×SD₁₆	C₂²×C₅	1	2	yes	complemented
189	C₂×C₃×D₈	C₂²×C₅	1	2	yes	complemented
190	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
191	#953	—	2	2	no	—
192	#950	—	2	4	no	—
193	#947	C₂²×C₅	1	2	yes	complemented
194	C₂×#216	C₂²×C₅	1	1	yes	characteristic, complemented
195	C₂×#215	C₂²×C₅	1	1	yes	characteristic, complemented
196	#940	C₂²×C₅	1	2	yes	complemented
197	#940	C₂²×C₅	1	2	yes	complemented
198	#938	—	2	2	no	—
199	#937	—	2	2	no	—
200	#936	C₂²×C₅	1	2	yes	complemented
201	C₂×#214	C₂²×C₅	1	1	yes	characteristic, complemented
202	C₂×#213	—	2	4	no	—
203	C₂×#213	C₂²×C₅	1	2	yes	—
204	C₂×#213	C₂²×C₅	1	2	yes	—
205	C₂×#213	C₂²×C₅	1	1	yes	characteristic, complemented
206	#930	—	2	2	no	—
207	#926	C₂²×C₅	1	1	yes	characteristic
208	C₂²×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
209	#908	—	2	4	no	—
210	C₂×D₂₄	C₂²×C₅	1	2	yes	complemented
211	C₂×#204	C₂²×C₅	1	2	yes	complemented
212	#815	C₂²×C₅	1	2	yes	complemented
213	C₈×Dic₃	C₂²×C₅	1	2	yes	complemented
214	C₂⁴×C₅	—	2	1	no	—
215	C₂⁴×C₅	—	6	1	no	—
216	C₅×#41	—	2	2	no	—
217	C₅×#41	—	2	2	no	—
218	C₅×#41	—	6	2	no	—
219	C₅×#41	—	6	2	no	—
220	C₂×C₅×Q₈	—	3	1	no	—
221	C₂×C₅×Q₈	C₂²×D₃	1	1	yes	characteristic
222	C₂×C₅×D₄	—	2	1	no	—
223	C₂×C₅×D₄	—	2	2	no	—
224	C₂×C₅×D₄	—	2	1	no	—
225	C₂×C₅×D₄	—	2	2	no	—
226	C₂×C₅×D₄	—	3	2	no	—
227	C₂×C₅×D₄	—	3	1	no	—
228	C₂×C₅×D₄	—	6	4	no	—
229	C₂×C₅×D₄	—	6	4	no	—
230	C₂×C₅×D₄	—	6	1	no	—
231	C₂×C₅×D₄	—	6	2	no	—
232	C₂×C₅×D₄	—	6	1	no	—
233	C₂×C₅×D₄	—	6	2	no	—
234	C₂×C₅×D₄	C₂²×D₃	1	2	yes	—
235	C₂×C₅×D₄	C₂²×D₃	1	1	yes	characteristic
236	C₂²×C₄×C₅	—	2	1	no	—
237	C₂²×C₄×C₅	—	6	1	no	—
238	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
239	C₅×Q₁₆	—	6	2	no	—
240	C₅×SD₁₆	—	2	4	no	—
241	C₅×SD₁₆	—	6	2	no	—
242	C₅×SD₁₆	—	6	2	no	—
243	C₅×SD₁₆	—	6	4	no	—
244	C₅×D₈	—	2	4	no	—
245	C₅×D₈	—	6	4	no	—
246	C₅×D₈	—	6	4	no	—
247	C₅×D₈	—	6	2	no	—
248	C₅×D₈	—	6	4	no	—
249	C₅×M₁₆	#67	1	4	yes	complemented
250	C₂×C₅×C₈	—	3	4	no	—
251	C₂×C₅×C₈	—	3	1	no	—
252	C₂×C₅×C₈	—	3	1	no	—
253	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
254	C₅×C₄⋊C₄	—	3	2	no	—
255	C₅×C₂²⋊C₄	—	3	2	no	—
256	C₅×C₂²⋊C₄	—	6	4	no	—
257	C₅×C₂²⋊C₄	—	6	4	no	—
258	C₄²×C₅	—	3	2	no	—
259	C₂×AGL(1,ℤ/8)	—	3	1	no	—
260	C₂×AGL(1,ℤ/8)	C₅×D₃	1	1	yes	characteristic, complemented
261	C₂×#135	—	3	1	no	—
262	C₂²×D₈	—	3	1	no	—
263	#535	—	3	1	no	—
264	#535	—	3	1	no	—
265	#496	—	3	2	no	—
266	#496	—	3	2	no	—
267	#495	—	3	2	no	—
268	#493	—	3	2	no	—
269	#405	—	3	1	no	—
270	C₂²×C₃×C₅	—	2	2	no	—
271	C₂²×C₃×C₅	—	4	1	no	—
272	C₂²×C₃×C₅	—	4	2	no	—
273	C₂²×C₃×C₅	—	4	2	no	—
274	C₂²×C₃×C₅	—	4	4	no	—
275	C₂²×C₃×C₅	—	8	4	no	—
276	C₂²×C₃×C₅	#127	1	2	yes	—
277	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
278	C₂×C₅×D₃	—	4	1	no	—
279	C₂×C₅×D₃	—	4	2	no	—
280	C₂×C₅×D₃	—	4	2	no	—
281	C₂×C₅×D₃	—	4	4	no	—
282	C₂×C₅×D₃	—	8	4	no	—
283	C₃×C₄×C₅	—	4	1	no	—
284	C₃×C₄×C₅	#127	1	2	yes	—
285	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
286	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
287	C₅×Dic₃	—	2	4	no	—
288	C₅×Dic₃	—	4	1	no	—
289	C₂⁴×C₃	—	2	1	no	—
290	C₂³×D₃	—	2	1	no	—
291	C₃×#41	—	2	2	no	—
292	C₃×#41	—	2	2	no	—
293	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
294	C₂×C₃×D₄	—	2	1	no	—
295	C₂×C₃×D₄	—	2	2	no	—
296	C₂×C₃×D₄	—	2	2	no	—
297	C₂×C₃×D₄	—	2	1	no	—
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	C₂×#67	—	2	1	no	—
303	C₂×#67	—	2	4	no	—
304	C₂×#67	—	2	4	no	—
305	#235	—	2	2	no	—
306	#235	—	2	2	no	—
307	C₂×D₁₂	—	2	2	no	—
308	C₂×D₁₂	—	2	2	no	—
309	C₂×D₁₂	—	2	1	no	—
310	C₂×D₁₂	C₂³×C₅	1	2	yes	—
311	C₂×D₁₂	C₂³×C₅	1	1	yes	characteristic
312	C₂×C₄×D₃	—	2	1	no	—
313	C₂×Dic₆	C₂³×C₅	1	1	yes	characteristic
314	C₃×SD₁₆	—	2	4	no	—
315	C₃×D₈	—	2	4	no	—
316	C₃×M₁₆	C₅×D₄	1	4	yes	complemented
317	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
318	#217	—	2	4	no	—
319	#217	C₅×D₄	1	2	yes	—
320	#216	—	2	2	no	—
321	#215	—	2	2	no	—
322	#214	—	2	2	no	—
323	#213	—	2	4	no	—
324	#213	—	2	4	no	—
325	#213	—	2	2	no	—
326	(C₂×D₃)⋊C₄	—	2	4	no	—
327	C₄⋊Dic₃	C₅×D₄	1	2	yes	—
328	C₄×Dic₃	C₂³×C₅	1	2	yes	—
329	C₂×C₃⋊C₈	C₅×D₄	1	4	yes	complemented
330	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
331	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
332	D₂₄	—	2	4	no	—
333	#204	—	2	4	no	—
334	C₂³×C₅	—	2	2	no	—
335	C₂³×C₅	—	2	1	no	—
336	C₂³×C₅	—	4	2	no	—
337	C₂³×C₅	—	6	2	no	—
338	C₂³×C₅	—	6	1	no	—
339	C₂³×C₅	—	8	2	no	—
340	C₂³×C₅	—	12	2	no	—
341	C₂³×C₅	—	24	2	no	—
342	C₂³×C₅	D₃×D₄	1	1	yes	characteristic
343	C₅×Q₈	—	2	1	no	—
344	C₅×Q₈	—	2	1	no	—
345	C₅×Q₈	—	6	1	no	—
346	C₅×Q₈	—	6	1	no	—
347	C₅×D₄	—	2	2	no	—
348	C₅×D₄	—	2	1	no	—
349	C₅×D₄	—	2	1	no	—
350	C₅×D₄	—	2	2	no	—
351	C₅×D₄	—	4	2	no	—
352	C₅×D₄	—	4	2	no	—
353	C₅×D₄	—	6	2	no	—
354	C₅×D₄	—	6	1	no	—
355	C₅×D₄	—	6	1	no	—
356	C₅×D₄	—	6	2	no	—
357	C₅×D₄	—	12	2	no	—
358	C₅×D₄	—	12	2	no	—
359	C₅×D₄	—	24	4	no	—
360	C₅×D₄	—	24	4	no	—
361	C₂×C₄×C₅	—	2	1	no	—
362	C₂×C₄×C₅	—	3	4	no	—
363	C₂×C₄×C₅	—	4	2	no	—
364	C₂×C₄×C₅	—	6	1	no	—
365	C₂×C₄×C₅	—	12	2	no	—
366	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
367	C₂×C₄×C₅	D₃×D₄	1	2	yes	—
368	C₂×C₄×C₅	C₂×#67	1	2	yes	—
369	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
370	C₅×C₈	—	3	2	no	—
371	C₅×C₈	—	3	2	no	—
372	C₅×C₈	C₂×#67	1	4	yes	—
373	C₂×#41	—	3	1	no	—
374	C₂×#41	C₂×C₅×D₃	1	1	yes	characteristic
375	C₂²×D₄	—	3	1	no	—
376	C₂²×D₄	C₂×C₅×D₃	1	1	yes	characteristic
377	AGL(1,ℤ/8)	—	2	4	no	—
378	AGL(1,ℤ/8)	—	6	4	no	—
379	#135	—	6	4	no	—
380	C₂×Q₁₆	—	3	1	no	—
381	C₂×SD₁₆	—	3	1	no	—
382	C₂×SD₁₆	—	3	1	no	—
383	C₂×SD₁₆	—	3	2	no	—
384	C₂×SD₁₆	C₂×C₅×D₃	1	2	yes	complemented
385	C₂×D₈	—	3	2	no	—
386	C₂×D₈	—	3	2	no	—
387	C₂×D₈	—	3	1	no	—
388	C₂×D₈	—	3	2	no	—
389	C₂×D₈	—	6	4	no	—
390	C₂×D₈	C₂×C₅×D₃	1	2	yes	complemented
391	C₂×M₁₆	C₂×C₅×D₃	1	1	yes	characteristic
392	C₂²×C₈	—	3	1	no	—
393	#127	—	3	2	no	—
394	#127	—	3	2	no	—
395	#124	—	3	2	no	—
396	#124	—	3	2	no	—
397	#121	—	6	2	no	—
398	#121	—	6	2	no	—
399	#120	—	6	2	no	—
400	#120	—	6	2	no	—
401	#117	—	3	1	no	—
402	#97	—	3	2	no	—
403	C₄×C₈	—	3	2	no	—
404	C₂×C₃×C₅	—	2	2	no	—
405	C₂×C₃×C₅	—	8	1	no	—
406	C₂×C₃×C₅	—	8	2	no	—
407	C₂×C₃×C₅	C₂×#127	1	1	yes	characteristic
408	C₂×C₃×C₅	#576	1	2	yes	—
409	C₅×D₃	—	8	1	no	—
410	C₅×D₃	—	8	2	no	—
411	C₂³×C₃	—	2	2	no	—
412	C₂³×C₃	—	2	1	no	—
413	C₂³×C₃	—	4	2	no	—
414	C₂³×C₃	—	8	2	no	—
415	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
416	C₂²×D₃	—	2	2	no	—
417	C₂²×D₃	—	2	1	no	—
418	C₂²×D₃	—	4	2	no	—
419	C₂²×D₃	—	8	2	no	—
420	C₃×Q₈	—	2	1	no	—
421	C₃×Q₈	—	2	1	no	—
422	C₃×D₄	—	2	2	no	—
423	C₃×D₄	—	2	1	no	—
424	C₃×D₄	—	2	1	no	—
425	C₃×D₄	—	2	2	no	—
426	C₃×D₄	—	4	2	no	—
427	C₃×D₄	—	4	2	no	—
428	C₂×C₃×C₄	—	2	1	no	—
429	C₂×C₃×C₄	—	4	2	no	—
430	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
431	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
432	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
433	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
434	#67	—	4	2	no	—
435	#67	—	8	4	no	—
436	#67	—	8	4	no	—
437	C₂×Dic₃	—	2	1	no	—
438	C₂×Dic₃	C₂×C₅×D₄	1	4	yes	—
439	D₁₂	—	2	2	no	—
440	D₁₂	—	2	1	no	—
441	D₁₂	—	2	2	no	—
442	D₁₂	—	2	1	no	—
443	D₁₂	—	4	2	no	—
444	C₄×D₃	—	4	2	no	—
445	Dic₆	—	2	1	no	—
446	Dic₆	—	2	1	no	—
447	C₃×C₈	C₂×C₅×D₄	1	4	yes	—
448	C₃⋊C₈	C₂×C₅×D₄	1	2	yes	—
449	C₃⋊C₈	C₂×C₅×D₄	1	2	yes	—
450	C₂²×C₅	—	2	2	no	—
451	C₂²×C₅	—	4	2	no	—
452	C₂²×C₅	—	4	4	no	—
453	C₂²×C₅	—	4	1	no	—
454	C₂²×C₅	—	4	2	no	—
455	C₂²×C₅	—	8	4	no	—
456	C₂²×C₅	—	12	2	no	—
457	C₂²×C₅	—	12	4	no	—
458	C₂²×C₅	—	12	1	no	—
459	C₂²×C₅	—	12	2	no	—
460	C₂²×C₅	—	24	4	no	—
461	C₂²×C₅	#940	1	2	yes	—
462	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
463	C₄×C₅	—	4	1	no	—
464	C₄×C₅	—	6	4	no	—
465	C₄×C₅	—	12	1	no	—
466	C₄×C₅	#940	1	2	yes	—
467	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
468	C₄×C₅	C₂²×#67	1	1	yes	characteristic
469	C₂⁴	—	2	1	no	—
470	C₂⁴	—	6	1	no	—
471	#41	—	2	2	no	—
472	#41	—	2	2	no	—
473	#41	—	6	2	no	—
474	#41	—	6	2	no	—
475	C₂×Q₈	—	3	1	no	—
476	C₂×Q₈	C₂²×C₅×D₃	1	1	yes	characteristic
477	C₂×D₄	—	2	1	no	—
478	C₂×D₄	—	2	2	no	—
479	C₂×D₄	—	2	1	no	—
480	C₂×D₄	—	2	2	no	—
481	C₂×D₄	—	3	2	no	—
482	C₂×D₄	—	3	1	no	—
483	C₂×D₄	—	6	4	no	—
484	C₂×D₄	—	6	4	no	—
485	C₂×D₄	—	6	1	no	—
486	C₂×D₄	—	6	2	no	—
487	C₂×D₄	—	6	1	no	—
488	C₂×D₄	—	6	2	no	—
489	C₂×D₄	C₂²×C₅×D₃	1	2	yes	—
490	C₂×D₄	C₂²×C₅×D₃	1	1	yes	characteristic
491	C₂²×C₄	—	2	1	no	—
492	C₂²×C₄	—	6	1	no	—
493	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
494	Q₁₆	—	6	2	no	—
495	SD₁₆	—	2	4	no	—
496	SD₁₆	—	6	2	no	—
497	SD₁₆	—	6	2	no	—
498	SD₁₆	—	6	4	no	—
499	D₈	—	2	4	no	—
500	D₈	—	6	4	no	—
501	D₈	—	6	4	no	—
502	D₈	—	6	2	no	—
503	D₈	—	6	4	no	—
504	M₁₆	C₅×#67	1	4	yes	complemented
505	C₂×C₈	—	3	4	no	—
506	C₂×C₈	—	3	1	no	—
507	C₂×C₈	—	3	1	no	—
508	C₂×C₈	C₂²×C₅×D₃	1	2	yes	—
509	C₄⋊C₄	—	3	2	no	—
510	C₂²⋊C₄	—	3	2	no	—
511	C₂²⋊C₄	—	6	4	no	—
512	C₂²⋊C₄	—	6	4	no	—
513	C₄²	—	3	2	no	—
514	C₃×C₅	#3155	1	1	yes	characteristic, complemented, Hall
515	C₂²×C₃	—	2	2	no	—
516	C₂²×C₃	—	4	1	no	—
517	C₂²×C₃	—	4	2	no	—
518	C₂²×C₃	—	4	2	no	—
519	C₂²×C₃	—	4	4	no	—
520	C₂²×C₃	—	8	4	no	—
521	C₂²×C₃	C₅×#127	1	2	yes	—
522	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
523	C₂×D₃	—	4	1	no	—
524	C₂×D₃	—	4	2	no	—
525	C₂×D₃	—	4	2	no	—
526	C₂×D₃	—	4	4	no	—
527	C₂×D₃	—	8	4	no	—
528	C₃×C₄	—	4	1	no	—
529	C₃×C₄	C₅×#127	1	2	yes	—
530	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
531	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
532	Dic₃	—	2	4	no	—
533	Dic₃	—	4	1	no	—
534	C₂×C₅	—	2	2	no	—
535	C₂×C₅	—	8	2	no	—
536	C₂×C₅	—	8	1	no	—
537	C₂×C₅	—	24	2	no	—
538	C₂×C₅	—	24	1	no	—
539	C₂×C₅	#5774	1	2	yes	—
540	C₂×C₅	C₂×#940	1	1	yes	characteristic
541	C₂³	—	2	2	no	—
542	C₂³	—	2	1	no	—
543	C₂³	—	4	2	no	—
544	C₂³	—	6	2	no	—
545	C₂³	—	6	1	no	—
546	C₂³	—	8	2	no	—
547	C₂³	—	12	2	no	—
548	C₂³	—	24	2	no	—
549	C₂³	C₅×D₃×D₄	1	1	yes	characteristic
550	Q₈	—	2	1	no	—
551	Q₈	—	2	1	no	—
552	Q₈	—	6	1	no	—
553	Q₈	—	6	1	no	—
554	D₄	—	2	2	no	—
555	D₄	—	2	1	no	—
556	D₄	—	2	1	no	—
557	D₄	—	2	2	no	—
558	D₄	—	4	2	no	—
559	D₄	—	4	2	no	—
560	D₄	—	6	2	no	—
561	D₄	—	6	1	no	—
562	D₄	—	6	1	no	—
563	D₄	—	6	2	no	—
564	D₄	—	12	2	no	—
565	D₄	—	12	2	no	—
566	D₄	—	24	4	no	—
567	D₄	—	24	4	no	—
568	C₂×C₄	—	2	1	no	—
569	C₂×C₄	—	3	4	no	—
570	C₂×C₄	—	4	2	no	—
571	C₂×C₄	—	6	1	no	—
572	C₂×C₄	—	12	2	no	—
573	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
574	C₂×C₄	C₅×D₃×D₄	1	2	yes	—
575	C₂×C₄	C₂×C₅×#67	1	2	yes	—
576	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
577	C₈	—	3	2	no	—
578	C₈	—	3	2	no	—
579	C₈	C₂×C₅×#67	1	4	yes	—
580	C₂×C₃	—	2	2	no	—
581	C₂×C₃	—	8	2	no	—
582	C₂×C₃	—	8	1	no	—
583	C₂×C₃	C₂×C₅×#127	1	1	yes	characteristic
584	C₂×C₃	C₅×#576	1	2	yes	—
585	D₃	—	8	2	no	—
586	D₃	—	8	1	no	—
587	C₅	#83940	1	1	yes	characteristic, direct product factor, Sylow
588	C₂²	—	2	2	no	—
589	C₂²	—	4	2	no	—
590	C₂²	—	4	4	no	—
591	C₂²	—	4	1	no	—
592	C₂²	—	4	2	no	—
593	C₂²	—	8	4	no	—
594	C₂²	—	12	2	no	—
595	C₂²	—	12	4	no	—
596	C₂²	—	12	1	no	—
597	C₂²	—	12	2	no	—
598	C₂²	—	24	4	no	—
599	C₂²	C₅×#940	1	2	yes	—
600	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
601	C₄	—	4	1	no	—
602	C₄	—	6	4	no	—
603	C₄	—	12	1	no	—
604	C₄	C₅×#940	1	2	yes	—
605	C₄	C₂×C₅×D₃×D₄	1	1	yes	characteristic
606	C₄	C₂²×C₅×#67	1	1	yes	characteristic
607	C₃	C₅×#3155	1	1	yes	characteristic, complemented, Sylow
608	C₂	—	2	2	no	—
609	C₂	—	8	2	no	—
610	C₂	—	8	1	no	—
611	C₂	—	24	2	no	—
612	C₂	—	24	1	no	—
613	C₂	C₅×#5774	1	2	yes	—
614	C₂	C₂×C₅×#940	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₅	C₂×D₃×D₄
commutator, cosocle	C₂×C₃×C₄	C₂⁴×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₂×C₃×C₅×AGL(1,ℤ/8)	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
hypercenter	C₂×C₅×AGL(1,ℤ/8)	D₃
hypocenter	C₃	C₅×#3155
LCS	G ▷ C₂×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
1. C₂×C₃×C₅×AGL(1,ℤ/8)	C₂	semidirect
2. C₅×#5830	C₂	semidirect
3. C₂×C₅×#950	C₂	semidirect
4. C₅×#5805	C₂	semidirect
5. C₂²×C₅×#213	C₂	semidirect
6. C₂×C₅×#908	C₂	semidirect
7. C₅×#5176	C₂	semidirect
8. C₅×#5168	C₂	semidirect
9. C₅×#5154	C₂	semidirect
10. C₅×#5151	C₂	semidirect
11. C₅×#5122	C₂	semidirect
18. C₂×C₃×C₅×SD₁₆	C₂²	semidirect
19. C₂×C₃×C₅×D₈	C₂²	semidirect
23. C₅×#947	C₂²	semidirect
24. C₂×C₅×#216	C₂²	semidirect
25. C₂×C₅×#215	C₂²	semidirect
26. C₅×#940	C₂²	semidirect
27. C₅×#940	C₂²	semidirect
30. C₅×#936	C₂²	semidirect
31. C₂×C₅×#214	C₂²	semidirect
35. C₂×C₅×#213	C₂²	semidirect
40. C₂×C₅×D₂₄	C₂²	semidirect
41. C₂×C₅×#204	C₂²	semidirect
42. C₅×#815	C₂²	semidirect
43. C₅×C₈×Dic₃	C₂²	semidirect
44. #83940	C₅	direct (N × H)
46. C₂×C₅×AGL(1,ℤ/8)	D₃	semidirect
83. C₃×C₅×M₁₆	D₄	semidirect
96. C₂×C₅×C₃⋊C₈	D₄	semidirect
101. C₂×C₃×AGL(1,ℤ/8)	C₂×C₅	semidirect
102. #5830	C₂×C₅	semidirect
103. C₂×#950	C₂×C₅	semidirect
104. #5805	C₂×C₅	semidirect
105. C₂²×#213	C₂×C₅	semidirect
106. C₂×#908	C₂×C₅	semidirect
107. #5176	C₂×C₅	semidirect
108. #5168	C₂×C₅	semidirect
109. #5154	C₂×C₅	semidirect
110. #5151	C₂×C₅	semidirect
111. #5122	C₂×C₅	semidirect
123. C₂×C₅×SD₁₆	C₂×D₃	semidirect
129. C₂×C₅×D₈	C₂×D₃	semidirect
188. C₂×C₃×SD₁₆	C₂²×C₅	semidirect
189. C₂×C₃×D₈	C₂²×C₅	semidirect
193. #947	C₂²×C₅	semidirect
194. C₂×#216	C₂²×C₅	semidirect
195. C₂×#215	C₂²×C₅	semidirect
196. #940	C₂²×C₅	semidirect
197. #940	C₂²×C₅	semidirect
200. #936	C₂²×C₅	semidirect
201. C₂×#214	C₂²×C₅	semidirect
205. C₂×#213	C₂²×C₅	semidirect
210. C₂×D₂₄	C₂²×C₅	semidirect
211. C₂×#204	C₂²×C₅	semidirect
212. #815	C₂²×C₅	semidirect
213. C₈×Dic₃	C₂²×C₅	semidirect
249. C₅×M₁₆	#67	semidirect
260. C₂×AGL(1,ℤ/8)	C₅×D₃	semidirect
316. C₃×M₁₆	C₅×D₄	semidirect
329. C₂×C₃⋊C₈	C₅×D₄	semidirect
384. C₂×SD₁₆	C₂×C₅×D₃	semidirect
390. C₂×D₈	C₂×C₅×D₃	semidirect
504. M₁₆	C₅×#67	semidirect
514. C₃×C₅	#3155	semidirect
587. C₅	#83940	direct (N × H)
607. C₃	C₅×#3155	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×#5830	2
C₂×C₅×#950	2
C₅×#5805	2
C₂²×C₅×#213	2
C₂×C₅×#908	2
C₅×#5176	2
C₅×#5168	2
C₅×#5154	2
C₅×#5151	2
C₅×#5122	2
C₅×#3155	3
#83940	5

Subgroups — C5×#83940 #14439546

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#83940 #14439546