Subgroups — C₅×#79439 #14458455

Order 1920.

924 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×D₄×D₁₂	C₂	1	1	yes	maximal, characteristic
2	C₅×#5543	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×C₈×D₄	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5114	C₂	1	2	yes	maximal, complemented
5	C₂×C₅×#821	C₂	1	2	yes	maximal, complemented
6	C₅×#4848	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#4842	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#4735	C₂	1	2	yes	maximal, complemented
9	C₅×#4731	C₂	1	2	yes	maximal, complemented
10	C₅×#4694	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₅×#204	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#3295	—	3	1	no	maximal, Hall
13	C₂×C₅×D₃×D₄	—	2	1	no	—
14	C₂²×C₅×D₁₂	C₂²	1	2	yes	—
15	C₂²×C₃×C₅×C₈	C₂²	1	2	yes	complemented
16	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
17	C₅×D₄×Dic₃	—	2	1	no	—
18	C₅×#930	C₂²	1	2	yes	—
19	C₂×C₅×C₄⋊Dic₃	C₂²	1	2	yes	complemented
20	C₅×#924	C₂²	1	2	yes	complemented
21	C₂×C₅×#204	C₂²	1	1	yes	characteristic
22	C₂×C₅×#204	C₂²	1	2	yes	complemented
23	C₅×#895	—	2	1	no	—
24	C₅×#890	—	2	1	no	—
25	C₅×#882	—	2	2	no	—
26	C₅×#878	—	2	2	no	—
27	C₅×#874	C₂²	1	1	yes	characteristic
28	C₄×C₅×D₁₂	C₂²	1	1	yes	characteristic
29	C₅×#869	C₂²	1	1	yes	characteristic, complemented
30	C₄×C₅×Dic₆	C₂²	1	1	yes	characteristic, complemented
31	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
32	C₃×C₅×C₂²⋊C₈	C₂²	1	2	yes	complemented
33	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic, complemented
34	C₅×#821	C₂²	1	1	yes	characteristic
35	C₅×#821	C₂²	1	2	yes	—
36	C₅×#821	C₂²	1	2	yes	complemented
37	C₅×#821	C₂²	1	2	yes	complemented
38	C₅×#821	C₂²	1	2	yes	complemented
39	C₅×#817	C₂²	1	1	yes	characteristic, complemented
40	C₅×#817	C₂²	1	2	yes	complemented
41	C₅×#816	C₂²	1	1	yes	characteristic, complemented
42	#79439	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
43	C₅×#554	—	3	1	no	—
44	C₅×D₄²	—	3	1	no	—
45	C₅×#486	—	3	1	no	—
46	C₅×#481	—	3	2	no	—
47	C₅×#476	—	3	1	no	—
48	C₅×#465	—	3	2	no	—
49	C₅×#460	—	3	1	no	—
50	C₅×#450	—	3	2	no	—
51	C₄×C₅×SD₁₆	—	3	1	no	—
52	C₅×C₈×D₄	D₃	1	1	yes	characteristic, complemented
53	C₂×C₅×#102	—	3	2	no	—
54	C₂³×C₅×D₃	—	2	2	no	—
55	C₂×C₃×C₅×D₄	D₄	1	1	yes	characteristic
56	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
57	C₂×C₅×#67	—	2	2	no	—
58	C₂²×C₅×Dic₃	—	2	2	no	—
59	C₅×D₃×D₄	—	4	4	no	—
60	C₂×C₅×D₁₂	—	2	4	no	—
61	C₂×C₅×D₁₂	—	2	1	no	—
62	C₂×C₅×D₁₂	—	2	2	no	—
63	C₂×C₅×D₁₂	—	2	1	no	—
64	C₂×C₅×D₁₂	—	4	2	no	—
65	C₂×C₅×D₁₂	C₂³	1	2	yes	—
66	C₂×C₅×D₁₂	C₂³	1	1	yes	characteristic
67	C₂×C₄×C₅×D₃	—	2	1	no	—
68	C₂×C₅×Dic₆	—	2	1	no	—
69	C₂×C₅×Dic₆	C₂³	1	1	yes	characteristic
70	C₂×C₃×C₅×C₈	—	4	2	no	—
71	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
72	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
73	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
74	C₃×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
75	C₃×C₅×C₂²⋊C₄	D₄	1	2	yes	—
76	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
77	C₅×#217	—	2	2	no	—
78	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
79	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
80	C₅×C₄⋊Dic₃	—	2	1	no	—
81	C₅×C₄⋊Dic₃	—	2	2	no	—
82	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
83	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
84	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
85	C₅×Dic₃⋊C₄	—	2	1	no	—
86	C₅×Dic₃⋊C₄	—	2	2	no	—
87	C₄×C₅×Dic₃	—	2	1	no	—
88	C₅×#204	—	2	2	no	—
89	C₅×#204	—	4	2	no	—
90	D₄×D₁₂	C₂×C₅	1	1	yes	characteristic
91	#5543	C₂×C₅	1	1	yes	characteristic, complemented
92	C₃×C₈×D₄	C₂×C₅	1	1	yes	characteristic, complemented
93	#5114	C₂×C₅	1	2	yes	complemented
94	C₂×#821	C₂×C₅	1	2	yes	complemented
95	#4848	C₂×C₅	1	1	yes	characteristic, complemented
96	#4842	C₂×C₅	1	1	yes	characteristic, complemented
97	#4735	C₂×C₅	1	2	yes	complemented
98	#4731	C₂×C₅	1	2	yes	complemented
99	#4694	C₂×C₅	1	1	yes	characteristic, complemented
100	C₄×#204	C₂×C₅	1	1	yes	characteristic, complemented
101	C₂²×C₅×D₄	—	3	2	no	—
102	C₂²×C₅×D₄	—	6	1	no	—
103	C₂×C₅×SD₁₆	—	3	1	no	—
104	C₂×C₅×SD₁₆	—	3	2	no	—
105	C₂²×C₅×C₈	C₂×D₃	1	2	yes	complemented
106	C₅×C₄⋊Q₈	—	3	1	no	—
107	C₅×#127	—	3	1	no	—
108	C₅×#125	—	6	1	no	—
109	C₅×C₂²⋊Q₈	—	3	2	no	—
110	C₅×C₂²⋊Q₈	—	6	2	no	—
111	C₅×#121	—	3	2	no	—
112	C₅×#121	—	6	1	no	—
113	C₅×#120	—	6	2	no	—
114	C₄×C₅×Q₈	—	3	1	no	—
115	C₄×C₅×D₄	—	3	1	no	—
116	C₄×C₅×D₄	—	6	1	no	—
117	C₄×C₅×D₄	C₂×D₃	1	1	yes	characteristic
118	C₂×C₅×C₄⋊C₄	—	3	2	no	—
119	C₅×#106	—	3	1	no	—
120	C₅×#106	—	3	2	no	—
121	C₅×C₄⋊C₈	C₂×D₃	1	1	yes	characteristic, complemented
122	C₅×#103	—	3	1	no	—
123	C₅×#102	—	3	1	no	—
124	C₅×#102	—	3	2	no	—
125	C₅×#102	—	3	2	no	—
126	C₅×#102	—	3	2	no	—
127	C₅×#102	—	3	2	no	—
128	C₅×C₂²⋊C₈	C₂×D₃	1	2	yes	complemented
129	C₄×C₅×C₈	C₂×D₃	1	1	yes	characteristic, complemented
130	#3295	—	3	1	no	Sylow
131	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
132	C₂²×C₅×D₃	—	2	1	no	—
133	C₂²×C₅×D₃	—	2	2	no	—
134	C₂²×C₅×D₃	—	4	4	no	—
135	C₂²×C₅×D₃	—	4	4	no	—
136	C₂²×C₅×D₃	—	8	2	no	—
137	C₃×C₅×D₄	SD₁₆	1	4	yes	complemented
138	C₂×C₃×C₄×C₅	—	2	2	no	—
139	C₂×C₃×C₄×C₅	—	2	2	no	—
140	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
141	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
142	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
143	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
144	C₅×#67	—	4	4	no	—
145	C₂×C₅×Dic₃	—	2	1	no	—
146	C₂×C₅×Dic₃	—	2	1	no	—
147	C₂×C₅×Dic₃	—	2	2	no	—
148	C₂×C₅×Dic₃	—	2	1	no	—
149	C₂×C₅×Dic₃	—	8	2	no	—
150	C₅×D₁₂	—	2	2	no	—
151	C₅×D₁₂	—	2	1	no	—
152	C₅×D₁₂	—	2	2	no	—
153	C₅×D₁₂	—	4	4	no	—
154	C₅×D₁₂	—	4	2	no	—
155	C₅×D₁₂	—	8	1	no	—
156	C₅×D₁₂	#41	1	2	yes	—
157	C₄×C₅×D₃	—	4	2	no	—
158	C₅×Dic₆	—	2	1	no	—
159	C₅×Dic₆	—	2	1	no	—
160	C₅×Dic₆	—	8	1	no	—
161	C₃×C₅×C₈	—	2	1	no	—
162	C₃×C₅×C₈	—	2	2	no	—
163	C₃×C₅×C₈	—	2	1	no	—
164	C₂×D₃×D₄	—	2	1	no	—
165	C₂²×D₁₂	C₂²×C₅	1	2	yes	—
166	C₂²×C₃×C₈	C₂²×C₅	1	2	yes	complemented
167	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
168	D₄×Dic₃	—	2	1	no	—
169	#930	C₂²×C₅	1	2	yes	—
170	C₂×C₄⋊Dic₃	C₂²×C₅	1	2	yes	complemented
171	#924	C₂²×C₅	1	2	yes	complemented
172	C₂×#204	C₂²×C₅	1	1	yes	characteristic
173	C₂×#204	C₂²×C₅	1	2	yes	complemented
174	#895	—	2	1	no	—
175	#890	—	2	1	no	—
176	#882	—	2	2	no	—
177	#878	—	2	2	no	—
178	#874	C₂²×C₅	1	1	yes	characteristic
179	C₄×D₁₂	C₂²×C₅	1	1	yes	characteristic
180	#869	C₂²×C₅	1	1	yes	characteristic, complemented
181	C₄×Dic₆	C₂²×C₅	1	1	yes	characteristic, complemented
182	C₃×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
183	C₃×C₂²⋊C₈	C₂²×C₅	1	2	yes	complemented
184	C₃×C₄×C₈	C₂²×C₅	1	1	yes	characteristic, complemented
185	#821	C₂²×C₅	1	1	yes	characteristic
186	#821	C₂²×C₅	1	2	yes	—
187	#821	C₂²×C₅	1	2	yes	complemented
188	#821	C₂²×C₅	1	2	yes	complemented
189	#821	C₂²×C₅	1	2	yes	complemented
190	#817	C₂²×C₅	1	1	yes	characteristic, complemented
191	#817	C₂²×C₅	1	2	yes	complemented
192	#816	C₂²×C₅	1	1	yes	characteristic, complemented
193	C₂⁴×C₅	—	6	2	no	—
194	C₂×C₅×Q₈	—	3	1	no	—
195	C₂×C₅×Q₈	—	6	1	no	—
196	C₂×C₅×D₄	—	3	1	no	—
197	C₂×C₅×D₄	—	3	2	no	—
198	C₂×C₅×D₄	—	6	4	no	—
199	C₂×C₅×D₄	—	6	2	no	—
200	C₂×C₅×D₄	—	6	2	no	—
201	C₂×C₅×D₄	—	6	1	no	—
202	C₂×C₅×D₄	—	6	1	no	—
203	C₂×C₅×D₄	—	12	2	no	—
204	C₂×C₅×D₄	—	12	4	no	—
205	C₂×C₅×D₄	D₁₂	1	1	yes	characteristic
206	C₂²×C₄×C₅	—	6	2	no	—
207	C₂²×C₄×C₅	—	6	1	no	—
208	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
209	C₅×SD₁₆	—	6	2	no	—
210	C₅×SD₁₆	—	12	2	no	—
211	C₂×C₅×C₈	—	4	2	no	—
212	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
213	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
214	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
215	C₅×C₄⋊C₄	—	3	1	no	—
216	C₅×C₄⋊C₄	—	3	2	no	—
217	C₅×C₄⋊C₄	—	3	1	no	—
218	C₅×C₄⋊C₄	—	6	2	no	—
219	C₅×C₄⋊C₄	—	6	1	no	—
220	C₅×C₄⋊C₄	—	6	1	no	—
221	C₅×C₄⋊C₄	—	6	2	no	—
222	C₅×C₄⋊C₄	D₁₂	1	1	yes	characteristic
223	C₅×C₂²⋊C₄	—	6	2	no	—
224	C₅×C₂²⋊C₄	—	6	1	no	—
225	C₅×C₂²⋊C₄	—	6	2	no	—
226	C₅×C₂²⋊C₄	D₁₂	1	2	yes	—
227	C₄²×C₅	—	6	1	no	—
228	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
229	#554	—	3	1	no	—
230	D₄²	—	3	1	no	—
231	#486	—	3	1	no	—
232	#481	—	3	2	no	—
233	#476	—	3	1	no	—
234	#465	—	3	2	no	—
235	#460	—	3	1	no	—
236	#450	—	3	2	no	—
237	C₄×SD₁₆	—	3	1	no	—
238	C₈×D₄	C₅×D₃	1	1	yes	characteristic, complemented
239	C₂×#102	—	3	2	no	—
240	C₂²×C₃×C₅	—	2	2	no	—
241	C₂²×C₃×C₅	—	2	2	no	—
242	C₂²×C₃×C₅	C₂×SD₁₆	1	4	yes	—
243	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
244	C₂×C₅×D₃	—	2	2	no	—
245	C₂×C₅×D₃	—	4	1	no	—
246	C₂×C₅×D₃	—	4	1	no	—
247	C₂×C₅×D₃	—	4	2	no	—
248	C₂×C₅×D₃	—	4	2	no	—
249	C₂×C₅×D₃	—	4	2	no	—
250	C₂×C₅×D₃	—	8	8	no	—
251	C₃×C₄×C₅	—	2	2	no	—
252	C₃×C₄×C₅	—	2	1	no	—
253	C₃×C₄×C₅	C₂×SD₁₆	1	2	yes	—
254	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
255	C₃×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
256	C₅×Dic₃	—	4	1	no	—
257	C₅×Dic₃	—	4	1	no	—
258	C₅×Dic₃	—	4	2	no	—
259	C₅×Dic₃	—	4	1	no	—
260	C₂³×D₃	—	2	2	no	—
261	C₂×C₃×D₄	C₅×D₄	1	1	yes	characteristic
262	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
263	C₂×#67	—	2	2	no	—
264	C₂²×Dic₃	—	2	2	no	—
265	D₃×D₄	—	4	4	no	—
266	C₂×D₁₂	—	2	4	no	—
267	C₂×D₁₂	—	2	1	no	—
268	C₂×D₁₂	—	2	2	no	—
269	C₂×D₁₂	—	2	1	no	—
270	C₂×D₁₂	—	4	2	no	—
271	C₂×D₁₂	C₂³×C₅	1	2	yes	—
272	C₂×D₁₂	C₂³×C₅	1	1	yes	characteristic
273	C₂×C₄×D₃	—	2	1	no	—
274	C₂×Dic₆	—	2	1	no	—
275	C₂×Dic₆	C₂³×C₅	1	1	yes	characteristic
276	C₂×C₃×C₈	—	4	2	no	—
277	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
278	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
279	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
280	C₃×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
281	C₃×C₂²⋊C₄	C₅×D₄	1	2	yes	—
282	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
283	#217	—	2	2	no	—
284	(C₂×D₃)⋊C₄	—	2	1	no	—
285	(C₂×D₃)⋊C₄	—	2	2	no	—
286	C₄⋊Dic₃	—	2	1	no	—
287	C₄⋊Dic₃	—	2	2	no	—
288	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
289	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
290	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
291	Dic₃⋊C₄	—	2	1	no	—
292	Dic₃⋊C₄	—	2	2	no	—
293	C₄×Dic₃	—	2	1	no	—
294	#204	—	2	2	no	—
295	#204	—	4	2	no	—
296	C₂³×C₅	—	6	1	no	—
297	C₂³×C₅	—	6	2	no	—
298	C₂³×C₅	—	12	4	no	—
299	C₂³×C₅	—	12	4	no	—
300	C₂³×C₅	—	24	2	no	—
301	C₂³×C₅	C₂×D₁₂	1	2	yes	—
302	C₅×Q₈	—	6	1	no	—
303	C₅×Q₈	—	6	1	no	—
304	C₅×Q₈	—	24	1	no	—
305	C₅×D₄	—	3	2	no	—
306	C₅×D₄	—	6	1	no	—
307	C₅×D₄	—	6	2	no	—
308	C₅×D₄	—	6	2	no	—
309	C₅×D₄	—	12	4	no	—
310	C₅×D₄	—	12	4	no	—
311	C₅×D₄	—	12	2	no	—
312	C₅×D₄	—	24	1	no	—
313	C₅×D₄	#204	1	4	yes	complemented
314	C₂×C₄×C₅	—	2	2	no	—
315	C₂×C₄×C₅	—	2	2	no	—
316	C₂×C₄×C₅	—	6	1	no	—
317	C₂×C₄×C₅	—	6	1	no	—
318	C₂×C₄×C₅	—	6	1	no	—
319	C₂×C₄×C₅	—	6	2	no	—
320	C₂×C₄×C₅	—	12	2	no	—
321	C₂×C₄×C₅	—	24	2	no	—
322	C₂×C₄×C₅	C₂×D₁₂	1	1	yes	characteristic
323	C₂×C₄×C₅	C₂×D₁₂	1	2	yes	—
324	C₂×C₄×C₅	C₂×D₁₂	1	1	yes	characteristic
325	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
326	C₅×C₈	—	2	1	no	—
327	C₅×C₈	—	2	2	no	—
328	C₅×C₈	—	2	1	no	—
329	C₂²×D₄	—	3	2	no	—
330	C₂²×D₄	—	6	1	no	—
331	C₂×SD₁₆	—	3	1	no	—
332	C₂×SD₁₆	—	3	2	no	—
333	C₂²×C₈	C₂×C₅×D₃	1	2	yes	complemented
334	C₄⋊Q₈	—	3	1	no	—
335	#127	—	3	1	no	—
336	#125	—	6	1	no	—
337	C₂²⋊Q₈	—	3	2	no	—
338	C₂²⋊Q₈	—	6	2	no	—
339	#121	—	3	2	no	—
340	#121	—	6	1	no	—
341	#120	—	6	2	no	—
342	C₄×Q₈	—	3	1	no	—
343	C₄×D₄	—	3	1	no	—
344	C₄×D₄	—	6	1	no	—
345	C₄×D₄	C₂×C₅×D₃	1	1	yes	characteristic
346	C₂×C₄⋊C₄	—	3	2	no	—
347	#106	—	3	1	no	—
348	#106	—	3	2	no	—
349	C₄⋊C₈	C₂×C₅×D₃	1	1	yes	characteristic, complemented
350	#103	—	3	1	no	—
351	#102	—	3	1	no	—
352	#102	—	3	2	no	—
353	#102	—	3	2	no	—
354	#102	—	3	2	no	—
355	#102	—	3	2	no	—
356	C₂²⋊C₈	C₂×C₅×D₃	1	2	yes	complemented
357	C₄×C₈	C₂×C₅×D₃	1	1	yes	characteristic, complemented
358	C₂×C₃×C₅	—	2	4	no	—
359	C₂×C₃×C₅	#546	1	1	yes	characteristic
360	C₂×C₃×C₅	C₂²×SD₁₆	1	1	yes	characteristic
361	C₂×C₃×C₅	#576	1	1	yes	characteristic
362	C₅×D₃	—	4	2	no	—
363	C₅×D₃	—	8	2	no	—
364	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
365	C₂²×D₃	—	2	1	no	—
366	C₂²×D₃	—	2	2	no	—
367	C₂²×D₃	—	4	4	no	—
368	C₂²×D₃	—	4	4	no	—
369	C₂²×D₃	—	8	2	no	—
370	C₃×D₄	C₅×SD₁₆	1	4	yes	complemented
371	C₂×C₃×C₄	—	2	2	no	—
372	C₂×C₃×C₄	—	2	2	no	—
373	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
374	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
375	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
376	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
377	#67	—	4	4	no	—
378	C₂×Dic₃	—	2	1	no	—
379	C₂×Dic₃	—	2	1	no	—
380	C₂×Dic₃	—	2	2	no	—
381	C₂×Dic₃	—	2	1	no	—
382	C₂×Dic₃	—	8	2	no	—
383	D₁₂	—	2	2	no	—
384	D₁₂	—	2	1	no	—
385	D₁₂	—	2	2	no	—
386	D₁₂	—	4	4	no	—
387	D₁₂	—	4	2	no	—
388	D₁₂	—	8	1	no	—
389	D₁₂	C₅×#41	1	2	yes	—
390	C₄×D₃	—	4	2	no	—
391	Dic₆	—	2	1	no	—
392	Dic₆	—	2	1	no	—
393	Dic₆	—	8	1	no	—
394	C₃×C₈	—	2	1	no	—
395	C₃×C₈	—	2	2	no	—
396	C₃×C₈	—	2	1	no	—
397	C₂²×C₅	—	2	2	no	—
398	C₂²×C₅	—	2	2	no	—
399	C₂²×C₅	—	6	2	no	—
400	C₂²×C₅	—	12	1	no	—
401	C₂²×C₅	—	12	1	no	—
402	C₂²×C₅	—	12	2	no	—
403	C₂²×C₅	—	12	2	no	—
404	C₂²×C₅	—	12	2	no	—
405	C₂²×C₅	—	24	8	no	—
406	C₂²×C₅	C₂×#204	1	4	yes	—
407	C₂²×C₅	C₂²×D₁₂	1	1	yes	characteristic
408	C₄×C₅	—	2	1	no	—
409	C₄×C₅	—	2	2	no	—
410	C₄×C₅	—	12	1	no	—
411	C₄×C₅	—	12	1	no	—
412	C₄×C₅	—	12	2	no	—
413	C₄×C₅	—	12	1	no	—
414	C₄×C₅	C₂×#204	1	2	yes	—
415	C₄×C₅	#1004	1	1	yes	characteristic
416	C₄×C₅	D₃×#41	1	1	yes	characteristic
417	C₂⁴	—	6	2	no	—
418	C₂×Q₈	—	3	1	no	—
419	C₂×Q₈	—	6	1	no	—
420	C₂×D₄	—	3	1	no	—
421	C₂×D₄	—	3	2	no	—
422	C₂×D₄	—	6	4	no	—
423	C₂×D₄	—	6	2	no	—
424	C₂×D₄	—	6	2	no	—
425	C₂×D₄	—	6	1	no	—
426	C₂×D₄	—	6	1	no	—
427	C₂×D₄	—	12	2	no	—
428	C₂×D₄	—	12	4	no	—
429	C₂×D₄	C₅×D₁₂	1	1	yes	characteristic
430	C₂²×C₄	—	6	2	no	—
431	C₂²×C₄	—	6	1	no	—
432	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
433	SD₁₆	—	6	2	no	—
434	SD₁₆	—	12	2	no	—
435	C₂×C₈	—	4	2	no	—
436	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
437	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
438	C₂×C₈	C₂²×C₅×D₃	1	2	yes	—
439	C₄⋊C₄	—	3	1	no	—
440	C₄⋊C₄	—	3	2	no	—
441	C₄⋊C₄	—	3	1	no	—
442	C₄⋊C₄	—	6	2	no	—
443	C₄⋊C₄	—	6	1	no	—
444	C₄⋊C₄	—	6	1	no	—
445	C₄⋊C₄	—	6	2	no	—
446	C₄⋊C₄	C₅×D₁₂	1	1	yes	characteristic
447	C₂²⋊C₄	—	6	2	no	—
448	C₂²⋊C₄	—	6	1	no	—
449	C₂²⋊C₄	—	6	2	no	—
450	C₂²⋊C₄	C₅×D₁₂	1	2	yes	—
451	C₄²	—	6	1	no	—
452	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
453	C₃×C₅	#3295	1	1	yes	characteristic, complemented, Hall
454	C₂²×C₃	—	2	2	no	—
455	C₂²×C₃	—	2	2	no	—
456	C₂²×C₃	C₂×C₅×SD₁₆	1	4	yes	—
457	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
458	C₂×D₃	—	2	2	no	—
459	C₂×D₃	—	4	1	no	—
460	C₂×D₃	—	4	1	no	—
461	C₂×D₃	—	4	2	no	—
462	C₂×D₃	—	4	2	no	—
463	C₂×D₃	—	4	2	no	—
464	C₂×D₃	—	8	8	no	—
465	C₃×C₄	—	2	2	no	—
466	C₃×C₄	—	2	1	no	—
467	C₃×C₄	C₂×C₅×SD₁₆	1	2	yes	—
468	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
469	C₃×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
470	Dic₃	—	4	1	no	—
471	Dic₃	—	4	1	no	—
472	Dic₃	—	4	2	no	—
473	Dic₃	—	4	1	no	—
474	C₂×C₅	—	2	4	no	—
475	C₂×C₅	—	12	2	no	—
476	C₂×C₅	—	24	2	no	—
477	C₂×C₅	#5554	1	1	yes	characteristic
478	C₂×C₅	C₂²×#204	1	1	yes	characteristic
479	C₂×C₅	#5752	1	1	yes	characteristic
480	C₂³	—	6	1	no	—
481	C₂³	—	6	2	no	—
482	C₂³	—	12	4	no	—
483	C₂³	—	12	4	no	—
484	C₂³	—	24	2	no	—
485	C₂³	C₂×C₅×D₁₂	1	2	yes	—
486	Q₈	—	6	1	no	—
487	Q₈	—	6	1	no	—
488	Q₈	—	24	1	no	—
489	D₄	—	3	2	no	—
490	D₄	—	6	1	no	—
491	D₄	—	6	2	no	—
492	D₄	—	6	2	no	—
493	D₄	—	12	4	no	—
494	D₄	—	12	4	no	—
495	D₄	—	12	2	no	—
496	D₄	—	24	1	no	—
497	D₄	C₅×#204	1	4	yes	complemented
498	C₂×C₄	—	2	2	no	—
499	C₂×C₄	—	2	2	no	—
500	C₂×C₄	—	6	1	no	—
501	C₂×C₄	—	6	1	no	—
502	C₂×C₄	—	6	1	no	—
503	C₂×C₄	—	6	2	no	—
504	C₂×C₄	—	12	2	no	—
505	C₂×C₄	—	24	2	no	—
506	C₂×C₄	C₂×C₅×D₁₂	1	1	yes	characteristic
507	C₂×C₄	C₂×C₅×D₁₂	1	2	yes	—
508	C₂×C₄	C₂×C₅×D₁₂	1	1	yes	characteristic
509	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
510	C₈	—	2	1	no	—
511	C₈	—	2	2	no	—
512	C₈	—	2	1	no	—
513	C₂×C₃	—	2	4	no	—
514	C₂×C₃	C₅×#546	1	1	yes	characteristic
515	C₂×C₃	C₂²×C₅×SD₁₆	1	1	yes	characteristic
516	C₂×C₃	C₅×#576	1	1	yes	characteristic
517	D₃	—	4	2	no	—
518	D₃	—	8	2	no	—
519	C₅	#79439	1	1	yes	characteristic, direct product factor, Sylow
520	C₂²	—	2	2	no	—
521	C₂²	—	2	2	no	—
522	C₂²	—	6	2	no	—
523	C₂²	—	12	1	no	—
524	C₂²	—	12	1	no	—
525	C₂²	—	12	2	no	—
526	C₂²	—	12	2	no	—
527	C₂²	—	12	2	no	—
528	C₂²	—	24	8	no	—
529	C₂²	C₂×C₅×#204	1	4	yes	—
530	C₂²	C₂²×C₅×D₁₂	1	1	yes	characteristic
531	C₄	—	2	1	no	—
532	C₄	—	2	2	no	—
533	C₄	—	12	1	no	—
534	C₄	—	12	1	no	—
535	C₄	—	12	2	no	—
536	C₄	—	12	1	no	—
537	C₄	C₂×C₅×#204	1	2	yes	—
538	C₄	C₅×#1004	1	1	yes	characteristic
539	C₄	C₅×D₃×#41	1	1	yes	characteristic
540	C₃	C₅×#3295	1	1	yes	characteristic, complemented, Sylow
541	C₂	—	2	4	no	—
542	C₂	—	12	2	no	—
543	C₂	—	24	2	no	—
544	C₂	C₅×#5554	1	1	yes	characteristic
545	C₂	C₂²×C₅×#204	1	1	yes	characteristic
546	C₂	C₅×#5752	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₅	C₂²×D₁₂
commutator, cosocle	C₂×C₃×C₄	C₂⁴×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₃×C₅×C₈×D₄	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₅×D₄×D₁₂	C₂
hypercenter	C₅×C₈×D₄	D₃
hypocenter	C₃	C₅×#3295
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₄×C₅×D₄ ◁ C₅×C₈×D₄

Complements

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

N	H ≅ G/N	type
2. C₅×#5543	C₂	semidirect
3. C₃×C₅×C₈×D₄	C₂	semidirect
4. C₅×#5114	C₂	semidirect
5. C₂×C₅×#821	C₂	semidirect
6. C₅×#4848	C₂	semidirect
7. C₅×#4842	C₂	semidirect
8. C₅×#4735	C₂	semidirect
9. C₅×#4731	C₂	semidirect
10. C₅×#4694	C₂	semidirect
11. C₄×C₅×#204	C₂	semidirect
15. C₂²×C₃×C₅×C₈	C₂²	semidirect
19. C₂×C₅×C₄⋊Dic₃	C₂²	semidirect
20. C₅×#924	C₂²	semidirect
22. C₂×C₅×#204	C₂²	semidirect
29. C₅×#869	C₂²	semidirect
30. C₄×C₅×Dic₆	C₂²	semidirect
31. C₃×C₅×C₄⋊C₈	C₂²	semidirect
32. C₃×C₅×C₂²⋊C₈	C₂²	semidirect
33. C₃×C₄×C₅×C₈	C₂²	semidirect
36. C₅×#821	C₂²	semidirect
37. C₅×#821	C₂²	semidirect
38. C₅×#821	C₂²	semidirect
39. C₅×#817	C₂²	semidirect
40. C₅×#817	C₂²	semidirect
41. C₅×#816	C₂²	semidirect
42. #79439	C₅	direct (N × H)
52. C₅×C₈×D₄	D₃	semidirect
91. #5543	C₂×C₅	semidirect
92. C₃×C₈×D₄	C₂×C₅	semidirect
93. #5114	C₂×C₅	semidirect
94. C₂×#821	C₂×C₅	semidirect
95. #4848	C₂×C₅	semidirect
96. #4842	C₂×C₅	semidirect
97. #4735	C₂×C₅	semidirect
98. #4731	C₂×C₅	semidirect
99. #4694	C₂×C₅	semidirect
100. C₄×#204	C₂×C₅	semidirect
105. C₂²×C₅×C₈	C₂×D₃	semidirect
121. C₅×C₄⋊C₈	C₂×D₃	semidirect
128. C₅×C₂²⋊C₈	C₂×D₃	semidirect
129. C₄×C₅×C₈	C₂×D₃	semidirect
137. C₃×C₅×D₄	SD₁₆	semidirect
166. C₂²×C₃×C₈	C₂²×C₅	semidirect
170. C₂×C₄⋊Dic₃	C₂²×C₅	semidirect
171. #924	C₂²×C₅	semidirect
173. C₂×#204	C₂²×C₅	semidirect
180. #869	C₂²×C₅	semidirect
181. C₄×Dic₆	C₂²×C₅	semidirect
182. C₃×C₄⋊C₈	C₂²×C₅	semidirect
183. C₃×C₂²⋊C₈	C₂²×C₅	semidirect
184. C₃×C₄×C₈	C₂²×C₅	semidirect
187. #821	C₂²×C₅	semidirect
188. #821	C₂²×C₅	semidirect
189. #821	C₂²×C₅	semidirect
190. #817	C₂²×C₅	semidirect
191. #817	C₂²×C₅	semidirect
192. #816	C₂²×C₅	semidirect
238. C₈×D₄	C₅×D₃	semidirect
313. C₅×D₄	#204	semidirect
333. C₂²×C₈	C₂×C₅×D₃	semidirect
349. C₄⋊C₈	C₂×C₅×D₃	semidirect
356. C₂²⋊C₈	C₂×C₅×D₃	semidirect
357. C₄×C₈	C₂×C₅×D₃	semidirect
370. C₃×D₄	C₅×SD₁₆	semidirect
453. C₃×C₅	#3295	semidirect
497. D₄	C₅×#204	semidirect
519. C₅	#79439	direct (N × H)
540. C₃	C₅×#3295	semidirect

Maximal subgroups

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

subgroup	index
C₅×D₄×D₁₂	2
C₅×#5543	2
C₃×C₅×C₈×D₄	2
C₅×#5114	2
C₂×C₅×#821	2
C₅×#4848	2
C₅×#4842	2
C₅×#4735	2
C₅×#4731	2
C₅×#4694	2
C₄×C₅×#204	2
C₅×#3295	3
#79439	5

Subgroups — C5×#79439 #14458455

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#79439 #14458455