Subgroups — C₅×#81784 #14439531

Order 1920.

1192 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#912	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅×#911	C₂	1	2	yes	maximal, complemented
3	C₂×C₅×D₃×D₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5715	C₂	1	2	yes	maximal, complemented
5	C₃×C₅×#493	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#5155	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#5154	C₂	1	2	yes	maximal, complemented
8	C₅×#5151	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#5074	C₂	1	2	yes	maximal, complemented
10	C₅×#4696	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#4689	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#3155	—	3	1	no	maximal, Hall
13	C₂×C₅×#237	C₂²	1	2	yes	—
14	C₂×C₅×D₃×D₄	C₂²	1	2	yes	—
15	C₂×C₃×C₅×D₈	C₂²	1	1	yes	characteristic
16	C₂×C₃×C₅×D₈	C₂²	1	2	yes	complemented
17	C₂×C₃×C₅×D₈	C₂²	1	1	yes	characteristic, complemented
18	C₃×C₅×#127	C₂²	1	2	yes	complemented
19	C₅×#940	C₂²	1	2	yes	complemented
20	C₅×#939	—	2	4	no	—
21	C₅×#937	—	2	4	no	—
22	C₅×#936	C₂²	1	2	yes	complemented
23	C₂×C₅×#214	C₂²	1	2	yes	complemented
24	C₂×C₅×#214	C₂²	1	2	yes	complemented
25	C₂×C₅×#213	C₂²	1	2	yes	—
26	C₂×C₅×#213	C₂²	1	2	yes	complemented
27	C₅×#912	—	2	4	no	—
28	C₅×#911	—	2	8	no	—
29	C₅×D₃×D₈	—	2	4	no	—
30	C₂×C₅×Dic₁₂	C₂²	1	1	yes	characteristic, complemented
31	C₂×C₅×D₂₄	C₂²	1	1	yes	characteristic
32	C₂×C₅×#204	C₂²	1	2	yes	complemented
33	C₂×C₅×ΓL(1,𝔽₂₅)	C₂²	1	1	yes	characteristic
34	C₂×C₅×D₃×C₈	C₂²	1	1	yes	characteristic
35	C₅×#875	C₂²	1	2	yes	complemented
36	C₅×#872	C₂²	1	1	yes	characteristic
37	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic, complemented
38	C₅×#815	C₂²	1	1	yes	characteristic, complemented
39	C₅×C₈×Dic₃	C₂²	1	1	yes	characteristic, complemented
40	C₅×#803	C₂²	1	1	yes	characteristic, complemented
41	#81784	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
42	C₂×C₅×AGL(1,ℤ/8)	—	3	2	no	—
43	C₂×C₅×#135	—	3	1	no	—
44	C₂²×C₅×D₈	—	3	1	no	—
45	C₅×#535	—	3	2	no	—
46	C₅×#496	—	3	2	no	—
47	C₅×#496	—	3	2	no	—
48	C₅×#495	—	3	1	no	—
49	C₅×#495	—	3	1	no	—
50	C₅×#493	—	3	1	no	—
51	C₅×#493	D₃	1	1	yes	characteristic, complemented
52	C₅×#405	—	3	1	no	—
53	C₂³×C₅×D₃	—	2	2	no	—
54	C₂×C₃×C₅×D₄	—	2	4	no	—
55	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
56	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
57	C₂×C₅×#67	—	2	2	no	—
58	C₂×C₅×#67	—	2	2	no	—
59	C₂×C₅×#67	—	2	4	no	—
60	C₂²×C₅×Dic₃	—	2	2	no	—
61	C₅×#237	—	2	4	no	—
62	C₅×#237	—	2	4	no	—
63	C₅×D₃×D₄	—	2	4	no	—
64	C₅×D₃×D₄	—	2	4	no	—
65	C₂×C₅×D₁₂	C₂³	1	2	yes	—
66	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
67	C₂×C₅×Dic₆	C₂³	1	2	yes	—
68	C₃×C₅×D₈	—	2	2	no	—
69	C₃×C₅×D₈	—	2	4	no	—
70	C₃×C₅×D₈	—	2	2	no	—
71	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
72	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
73	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
74	C₅×#217	—	2	4	no	—
75	C₅×#214	—	2	4	no	—
76	C₅×#214	—	2	4	no	—
77	C₅×#213	—	2	4	no	—
78	C₅×#213	—	2	4	no	—
79	C₅×(C₂×D₃)⋊C₄	—	2	4	no	—
80	C₅×(C₂×D₃)⋊C₄	D₄	1	2	yes	—
81	C₅×Dic₃⋊C₄	D₄	1	2	yes	—
82	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
83	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
84	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
85	C₅×Dic₁₂	—	2	2	no	—
86	C₅×D₂₄	—	2	2	no	—
87	C₅×#204	—	2	4	no	—
88	C₅×ΓL(1,𝔽₂₅)	D₄	1	4	yes	complemented
89	C₅×D₃×C₈	D₄	1	4	yes	complemented
90	C₂×#912	C₂×C₅	1	1	yes	characteristic, complemented
91	C₂×#911	C₂×C₅	1	2	yes	complemented
92	C₂×D₃×D₈	C₂×C₅	1	1	yes	characteristic, complemented
93	#5715	C₂×C₅	1	2	yes	complemented
94	C₃×#493	C₂×C₅	1	1	yes	characteristic, complemented
95	#5155	C₂×C₅	1	1	yes	characteristic, complemented
96	#5154	C₂×C₅	1	2	yes	complemented
97	#5151	C₂×C₅	1	1	yes	characteristic, complemented
98	#5074	C₂×C₅	1	2	yes	complemented
99	#4696	C₂×C₅	1	1	yes	characteristic, complemented
100	#4689	C₂×C₅	1	1	yes	characteristic, complemented
101	C₂×C₅×#41	—	3	2	no	—
102	C₂²×C₅×D₄	—	3	2	no	—
103	C₅×AGL(1,ℤ/8)	—	6	8	no	—
104	C₅×#135	—	6	4	no	—
105	C₂×C₅×Q₁₆	—	3	1	no	—
106	C₂×C₅×SD₁₆	—	3	2	no	—
107	C₂×C₅×SD₁₆	—	3	2	no	—
108	C₂×C₅×SD₁₆	—	3	2	no	—
109	C₂×C₅×D₈	—	3	2	no	—
110	C₂×C₅×D₈	—	3	2	no	—
111	C₂×C₅×D₈	—	3	1	no	—
112	C₂×C₅×D₈	—	6	4	no	—
113	C₂×C₅×D₈	C₂×D₃	1	1	yes	characteristic
114	C₂×C₅×D₈	C₂×D₃	1	1	yes	characteristic, complemented
115	C₂×C₅×D₈	C₂×D₃	1	2	yes	complemented
116	C₂×C₅×M₁₆	—	3	1	no	—
117	C₂²×C₅×C₈	—	3	1	no	—
118	C₅×#127	—	3	2	no	—
119	C₅×#127	C₂×D₃	1	2	yes	complemented
120	C₅×#124	—	3	2	no	—
121	C₅×#124	—	3	2	no	—
122	C₅×#121	—	6	4	no	—
123	C₅×#120	—	6	4	no	—
124	C₅×#117	—	3	1	no	—
125	C₅×#97	—	3	1	no	—
126	C₅×#97	—	3	1	no	—
127	C₄×C₅×C₈	—	3	1	no	—
128	C₄×C₅×C₈	C₂×D₃	1	1	yes	characteristic, complemented
129	#3155	—	3	1	no	Sylow
130	C₂³×C₃×C₅	—	2	2	no	—
131	C₂³×C₃×C₅	—	2	2	no	—
132	C₂²×C₅×D₃	—	2	2	no	—
133	C₂²×C₅×D₃	—	4	4	no	—
134	C₂²×C₅×D₃	—	8	4	no	—
135	C₂²×C₅×D₃	C₂×D₄	1	1	yes	characteristic
136	C₃×C₅×D₄	—	2	2	no	—
137	C₃×C₅×D₄	—	2	2	no	—
138	C₃×C₅×D₄	—	2	2	no	—
139	C₃×C₅×D₄	—	2	2	no	—
140	C₃×C₅×D₄	—	8	4	no	—
141	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
142	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
143	C₅×#67	—	4	4	no	—
144	C₅×#67	—	4	4	no	—
145	C₅×#67	—	8	4	no	—
146	C₂×C₅×Dic₃	—	2	2	no	—
147	C₂×C₅×Dic₃	—	4	4	no	—
148	C₂×C₅×Dic₃	C₂×D₄	1	2	yes	—
149	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
150	C₅×D₁₂	—	2	2	no	—
151	C₅×D₁₂	—	2	2	no	—
152	C₄×C₅×D₃	C₂×D₄	1	2	yes	—
153	C₄×C₅×D₃	C₂×D₄	1	2	yes	—
154	C₅×Dic₆	—	2	2	no	—
155	C₅×Dic₆	—	2	2	no	—
156	C₃×C₅×C₈	C₂×D₄	1	2	yes	—
157	C₃×C₅×C₈	C₂×D₄	1	2	yes	—
158	C₅×C₃⋊C₈	C₂×D₄	1	2	yes	—
159	C₅×C₃⋊C₈	C₂×D₄	1	2	yes	—
160	C₂×#237	C₂²×C₅	1	2	yes	—
161	C₂×D₃×D₄	C₂²×C₅	1	2	yes	—
162	C₂×C₃×D₈	C₂²×C₅	1	1	yes	characteristic
163	C₂×C₃×D₈	C₂²×C₅	1	1	yes	characteristic, complemented
164	C₂×C₃×D₈	C₂²×C₅	1	2	yes	complemented
165	C₃×#127	C₂²×C₅	1	2	yes	complemented
166	#940	C₂²×C₅	1	2	yes	complemented
167	#939	—	2	4	no	—
168	#937	—	2	4	no	—
169	#936	C₂²×C₅	1	2	yes	complemented
170	C₂×#214	C₂²×C₅	1	2	yes	complemented
171	C₂×#214	C₂²×C₅	1	2	yes	complemented
172	C₂×#213	C₂²×C₅	1	2	yes	—
173	C₂×#213	C₂²×C₅	1	2	yes	complemented
174	#912	—	2	4	no	—
175	#911	—	2	8	no	—
176	D₃×D₈	—	2	4	no	—
177	C₂×Dic₁₂	C₂²×C₅	1	1	yes	characteristic, complemented
178	C₂×D₂₄	C₂²×C₅	1	1	yes	characteristic
179	C₂×#204	C₂²×C₅	1	2	yes	complemented
180	C₂×ΓL(1,𝔽₂₅)	C₂²×C₅	1	1	yes	characteristic
181	C₂×D₃×C₈	C₂²×C₅	1	1	yes	characteristic
182	#875	C₂²×C₅	1	2	yes	complemented
183	#872	C₂²×C₅	1	1	yes	characteristic
184	C₃×C₄×C₈	C₂²×C₅	1	1	yes	characteristic, complemented
185	#815	C₂²×C₅	1	1	yes	characteristic, complemented
186	C₈×Dic₃	C₂²×C₅	1	1	yes	characteristic, complemented
187	#803	C₂²×C₅	1	1	yes	characteristic, complemented
188	C₂⁴×C₅	—	6	2	no	—
189	C₅×#41	—	6	4	no	—
190	C₅×#41	—	6	4	no	—
191	C₂×C₅×Q₈	—	3	2	no	—
192	C₂×C₅×D₄	—	2	4	no	—
193	C₂×C₅×D₄	—	3	2	no	—
194	C₂×C₅×D₄	—	6	4	no	—
195	C₂×C₅×D₄	—	6	4	no	—
196	C₂×C₅×D₄	—	6	2	no	—
197	C₂×C₅×D₄	—	6	4	no	—
198	C₂×C₅×D₄	—	6	2	no	—
199	C₂×C₅×D₄	C₂²×D₃	1	2	yes	—
200	C₂×C₅×D₄	C₂²×D₃	1	2	yes	—
201	C₂²×C₄×C₅	—	3	1	no	—
202	C₂²×C₄×C₅	—	6	2	no	—
203	C₅×Q₁₆	—	6	2	no	—
204	C₅×SD₁₆	—	6	4	no	—
205	C₅×SD₁₆	—	6	4	no	—
206	C₅×SD₁₆	—	6	4	no	—
207	C₅×D₈	—	2	2	no	—
208	C₅×D₈	—	2	2	no	—
209	C₅×D₈	—	2	4	no	—
210	C₅×D₈	—	6	4	no	—
211	C₅×D₈	—	6	4	no	—
212	C₅×D₈	—	6	2	no	—
213	C₅×M₁₆	—	3	4	no	—
214	C₂×C₅×C₈	—	3	1	no	—
215	C₂×C₅×C₈	—	3	1	no	—
216	C₂×C₅×C₈	—	3	4	no	—
217	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
218	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
219	C₅×C₄⋊C₄	—	3	2	no	—
220	C₅×C₂²⋊C₄	—	3	2	no	—
221	C₅×C₂²⋊C₄	—	6	4	no	—
222	C₅×C₂²⋊C₄	—	6	4	no	—
223	C₄²×C₅	—	3	1	no	—
224	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
225	C₂×AGL(1,ℤ/8)	—	3	2	no	—
226	C₂×#135	—	3	1	no	—
227	C₂²×D₈	—	3	1	no	—
228	#535	—	3	2	no	—
229	#496	—	3	2	no	—
230	#496	—	3	2	no	—
231	#495	—	3	1	no	—
232	#495	—	3	1	no	—
233	#493	—	3	1	no	—
234	#493	C₅×D₃	1	1	yes	characteristic, complemented
235	#405	—	3	1	no	—
236	C₂²×C₃×C₅	—	4	2	no	—
237	C₂²×C₃×C₅	—	4	2	no	—
238	C₂²×C₃×C₅	—	4	4	no	—
239	C₂²×C₃×C₅	—	4	4	no	—
240	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
241	C₂×C₅×D₃	—	2	2	no	—
242	C₂×C₅×D₃	—	4	2	no	—
243	C₂×C₅×D₃	—	4	4	no	—
244	C₂×C₅×D₃	—	8	8	no	—
245	C₂×C₅×D₃	#127	1	2	yes	—
246	C₃×C₄×C₅	—	2	2	no	—
247	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
248	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
249	C₅×Dic₃	—	2	2	no	—
250	C₅×Dic₃	—	4	2	no	—
251	C₅×Dic₃	#127	1	2	yes	—
252	C₂³×D₃	—	2	2	no	—
253	C₂×C₃×D₄	—	2	4	no	—
254	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
255	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
256	C₂×#67	—	2	2	no	—
257	C₂×#67	—	2	2	no	—
258	C₂×#67	—	2	4	no	—
259	C₂²×Dic₃	—	2	2	no	—
260	#237	—	2	4	no	—
261	#237	—	2	4	no	—
262	D₃×D₄	—	2	4	no	—
263	D₃×D₄	—	2	4	no	—
264	C₂×D₁₂	C₂³×C₅	1	2	yes	—
265	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
266	C₂×Dic₆	C₂³×C₅	1	2	yes	—
267	C₃×D₈	—	2	2	no	—
268	C₃×D₈	—	2	4	no	—
269	C₃×D₈	—	2	2	no	—
270	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
271	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
272	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
273	#217	—	2	4	no	—
274	#214	—	2	4	no	—
275	#214	—	2	4	no	—
276	#213	—	2	4	no	—
277	#213	—	2	4	no	—
278	(C₂×D₃)⋊C₄	—	2	4	no	—
279	(C₂×D₃)⋊C₄	C₅×D₄	1	2	yes	—
280	Dic₃⋊C₄	C₅×D₄	1	2	yes	—
281	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
282	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
283	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
284	Dic₁₂	—	2	2	no	—
285	D₂₄	—	2	2	no	—
286	#204	—	2	4	no	—
287	ΓL(1,𝔽₂₅)	C₅×D₄	1	4	yes	complemented
288	D₃×C₈	C₅×D₄	1	4	yes	complemented
289	C₂³×C₅	—	2	2	no	—
290	C₂³×C₅	—	2	2	no	—
291	C₂³×C₅	—	3	1	no	—
292	C₂³×C₅	—	6	2	no	—
293	C₂³×C₅	—	12	4	no	—
294	C₂³×C₅	—	24	4	no	—
295	C₅×Q₈	—	6	2	no	—
296	C₅×Q₈	—	6	2	no	—
297	C₅×D₄	—	2	2	no	—
298	C₅×D₄	—	2	2	no	—
299	C₅×D₄	—	2	2	no	—
300	C₅×D₄	—	2	2	no	—
301	C₅×D₄	—	6	2	no	—
302	C₅×D₄	—	6	2	no	—
303	C₅×D₄	—	8	4	no	—
304	C₅×D₄	—	12	4	no	—
305	C₅×D₄	—	12	4	no	—
306	C₅×D₄	—	24	4	no	—
307	C₂×C₄×C₅	—	3	1	no	—
308	C₂×C₄×C₅	—	3	2	no	—
309	C₂×C₄×C₅	—	3	2	no	—
310	C₂×C₄×C₅	—	3	2	no	—
311	C₂×C₄×C₅	—	6	2	no	—
312	C₂×C₄×C₅	—	12	4	no	—
313	C₂×C₄×C₅	D₃×D₄	1	2	yes	—
314	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
315	C₅×C₈	—	3	2	no	—
316	C₅×C₈	—	3	2	no	—
317	C₅×C₈	D₃×D₄	1	2	yes	—
318	C₅×C₈	D₃×D₄	1	2	yes	—
319	C₂×#41	—	3	2	no	—
320	C₂²×D₄	—	3	2	no	—
321	AGL(1,ℤ/8)	—	6	8	no	—
322	#135	—	6	4	no	—
323	C₂×Q₁₆	—	3	1	no	—
324	C₂×SD₁₆	—	3	2	no	—
325	C₂×SD₁₆	—	3	2	no	—
326	C₂×SD₁₆	—	3	2	no	—
327	C₂×D₈	—	3	2	no	—
328	C₂×D₈	—	3	2	no	—
329	C₂×D₈	—	3	1	no	—
330	C₂×D₈	—	6	4	no	—
331	C₂×D₈	C₂×C₅×D₃	1	1	yes	characteristic
332	C₂×D₈	C₂×C₅×D₃	1	1	yes	characteristic, complemented
333	C₂×D₈	C₂×C₅×D₃	1	2	yes	complemented
334	C₂×M₁₆	—	3	1	no	—
335	C₂²×C₈	—	3	1	no	—
336	#127	—	3	2	no	—
337	#127	C₂×C₅×D₃	1	2	yes	complemented
338	#124	—	3	2	no	—
339	#124	—	3	2	no	—
340	#121	—	6	4	no	—
341	#120	—	6	4	no	—
342	#117	—	3	1	no	—
343	#97	—	3	1	no	—
344	#97	—	3	1	no	—
345	C₄×C₈	—	3	1	no	—
346	C₄×C₈	C₂×C₅×D₃	1	1	yes	characteristic, complemented
347	C₂×C₃×C₅	—	8	2	no	—
348	C₂×C₃×C₅	—	8	2	no	—
349	C₂×C₃×C₅	C₂×#127	1	1	yes	characteristic
350	C₂×C₃×C₅	#576	1	2	yes	—
351	C₅×D₃	—	2	2	no	—
352	C₅×D₃	—	8	2	no	—
353	C₂³×C₃	—	2	2	no	—
354	C₂³×C₃	—	2	2	no	—
355	C₂²×D₃	—	2	2	no	—
356	C₂²×D₃	—	4	4	no	—
357	C₂²×D₃	—	8	4	no	—
358	C₂²×D₃	C₂×C₅×D₄	1	1	yes	characteristic
359	C₃×D₄	—	2	2	no	—
360	C₃×D₄	—	2	2	no	—
361	C₃×D₄	—	2	2	no	—
362	C₃×D₄	—	2	2	no	—
363	C₃×D₄	—	8	4	no	—
364	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
365	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
366	#67	—	4	4	no	—
367	#67	—	4	4	no	—
368	#67	—	8	4	no	—
369	C₂×Dic₃	—	2	2	no	—
370	C₂×Dic₃	—	4	4	no	—
371	C₂×Dic₃	C₂×C₅×D₄	1	2	yes	—
372	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
373	D₁₂	—	2	2	no	—
374	D₁₂	—	2	2	no	—
375	C₄×D₃	C₂×C₅×D₄	1	2	yes	—
376	C₄×D₃	C₂×C₅×D₄	1	2	yes	—
377	Dic₆	—	2	2	no	—
378	Dic₆	—	2	2	no	—
379	C₃×C₈	C₂×C₅×D₄	1	2	yes	—
380	C₃×C₈	C₂×C₅×D₄	1	2	yes	—
381	C₃⋊C₈	C₂×C₅×D₄	1	2	yes	—
382	C₃⋊C₈	C₂×C₅×D₄	1	2	yes	—
383	C₂²×C₅	—	3	2	no	—
384	C₂²×C₅	—	4	2	no	—
385	C₂²×C₅	—	4	2	no	—
386	C₂²×C₅	—	4	4	no	—
387	C₂²×C₅	—	4	4	no	—
388	C₂²×C₅	—	6	2	no	—
389	C₂²×C₅	—	12	2	no	—
390	C₂²×C₅	—	12	4	no	—
391	C₂²×C₅	—	24	8	no	—
392	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
393	C₄×C₅	—	2	2	no	—
394	C₄×C₅	—	3	2	no	—
395	C₄×C₅	—	6	2	no	—
396	C₄×C₅	—	12	2	no	—
397	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
398	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
399	C₂⁴	—	6	2	no	—
400	#41	—	6	4	no	—
401	#41	—	6	4	no	—
402	C₂×Q₈	—	3	2	no	—
403	C₂×D₄	—	2	4	no	—
404	C₂×D₄	—	3	2	no	—
405	C₂×D₄	—	6	4	no	—
406	C₂×D₄	—	6	4	no	—
407	C₂×D₄	—	6	2	no	—
408	C₂×D₄	—	6	4	no	—
409	C₂×D₄	—	6	2	no	—
410	C₂×D₄	C₂²×C₅×D₃	1	2	yes	—
411	C₂×D₄	C₂²×C₅×D₃	1	2	yes	—
412	C₂²×C₄	—	3	1	no	—
413	C₂²×C₄	—	6	2	no	—
414	Q₁₆	—	6	2	no	—
415	SD₁₆	—	6	4	no	—
416	SD₁₆	—	6	4	no	—
417	SD₁₆	—	6	4	no	—
418	D₈	—	2	2	no	—
419	D₈	—	2	2	no	—
420	D₈	—	2	4	no	—
421	D₈	—	6	4	no	—
422	D₈	—	6	4	no	—
423	D₈	—	6	2	no	—
424	M₁₆	—	3	4	no	—
425	C₂×C₈	—	3	1	no	—
426	C₂×C₈	—	3	1	no	—
427	C₂×C₈	—	3	4	no	—
428	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
429	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
430	C₄⋊C₄	—	3	2	no	—
431	C₂²⋊C₄	—	3	2	no	—
432	C₂²⋊C₄	—	6	4	no	—
433	C₂²⋊C₄	—	6	4	no	—
434	C₄²	—	3	1	no	—
435	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
436	C₃×C₅	#3155	1	1	yes	characteristic, complemented, Hall
437	C₂²×C₃	—	4	2	no	—
438	C₂²×C₃	—	4	2	no	—
439	C₂²×C₃	—	4	4	no	—
440	C₂²×C₃	—	4	4	no	—
441	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
442	C₂×D₃	—	2	2	no	—
443	C₂×D₃	—	4	2	no	—
444	C₂×D₃	—	4	4	no	—
445	C₂×D₃	—	8	8	no	—
446	C₂×D₃	C₅×#127	1	2	yes	—
447	C₃×C₄	—	2	2	no	—
448	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
449	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
450	Dic₃	—	2	2	no	—
451	Dic₃	—	4	2	no	—
452	Dic₃	C₅×#127	1	2	yes	—
453	C₂×C₅	—	6	2	no	—
454	C₂×C₅	—	8	2	no	—
455	C₂×C₅	—	8	2	no	—
456	C₂×C₅	—	24	2	no	—
457	C₂×C₅	D₃×#127	1	1	yes	characteristic
458	C₂×C₅	#5757	1	2	yes	—
459	C₂³	—	2	2	no	—
460	C₂³	—	2	2	no	—
461	C₂³	—	3	1	no	—
462	C₂³	—	6	2	no	—
463	C₂³	—	12	4	no	—
464	C₂³	—	24	4	no	—
465	Q₈	—	6	2	no	—
466	Q₈	—	6	2	no	—
467	D₄	—	2	2	no	—
468	D₄	—	2	2	no	—
469	D₄	—	2	2	no	—
470	D₄	—	2	2	no	—
471	D₄	—	6	2	no	—
472	D₄	—	6	2	no	—
473	D₄	—	8	4	no	—
474	D₄	—	12	4	no	—
475	D₄	—	12	4	no	—
476	D₄	—	24	4	no	—
477	C₂×C₄	—	3	1	no	—
478	C₂×C₄	—	3	2	no	—
479	C₂×C₄	—	3	2	no	—
480	C₂×C₄	—	3	2	no	—
481	C₂×C₄	—	6	2	no	—
482	C₂×C₄	—	12	4	no	—
483	C₂×C₄	C₅×D₃×D₄	1	2	yes	—
484	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
485	C₈	—	3	2	no	—
486	C₈	—	3	2	no	—
487	C₈	C₅×D₃×D₄	1	2	yes	—
488	C₈	C₅×D₃×D₄	1	2	yes	—
489	C₂×C₃	—	8	2	no	—
490	C₂×C₃	—	8	2	no	—
491	C₂×C₃	C₂×C₅×#127	1	1	yes	characteristic
492	C₂×C₃	C₅×#576	1	2	yes	—
493	D₃	—	2	2	no	—
494	D₃	—	8	2	no	—
495	C₅	#81784	1	1	yes	characteristic, direct product factor, Sylow
496	C₂²	—	3	2	no	—
497	C₂²	—	4	2	no	—
498	C₂²	—	4	2	no	—
499	C₂²	—	4	4	no	—
500	C₂²	—	4	4	no	—
501	C₂²	—	6	2	no	—
502	C₂²	—	12	2	no	—
503	C₂²	—	12	4	no	—
504	C₂²	—	24	8	no	—
505	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
506	C₄	—	2	2	no	—
507	C₄	—	3	2	no	—
508	C₄	—	6	2	no	—
509	C₄	—	12	2	no	—
510	C₄	C₂×C₅×D₃×D₄	1	1	yes	characteristic
511	C₄	C₂×C₅×D₃×D₄	1	1	yes	characteristic
512	C₃	C₅×#3155	1	1	yes	characteristic, complemented, Sylow
513	C₂	—	6	2	no	—
514	C₂	—	8	2	no	—
515	C₂	—	8	2	no	—
516	C₂	—	24	2	no	—
517	C₂	C₅×D₃×#127	1	1	yes	characteristic
518	C₂	C₅×#5757	1	2	yes	—

	subgroup	G/H
center	C₂²×C₅	C₂×D₃×D₄
commutator, cosocle	C₂×C₃×C₄	C₂⁴×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₃×C₅×#493	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
hypercenter	C₅×#493	D₃
hypocenter	C₃	C₅×#3155
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₄²×C₅ ◁ C₅×#493

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×#912	C₂	semidirect
2. C₂×C₅×#911	C₂	semidirect
3. C₂×C₅×D₃×D₈	C₂	semidirect
4. C₅×#5715	C₂	semidirect
5. C₃×C₅×#493	C₂	semidirect
6. C₅×#5155	C₂	semidirect
7. C₅×#5154	C₂	semidirect
8. C₅×#5151	C₂	semidirect
9. C₅×#5074	C₂	semidirect
10. C₅×#4696	C₂	semidirect
11. C₅×#4689	C₂	semidirect
16. C₂×C₃×C₅×D₈	C₂²	semidirect
17. C₂×C₃×C₅×D₈	C₂²	semidirect
18. C₃×C₅×#127	C₂²	semidirect
19. C₅×#940	C₂²	semidirect
22. C₅×#936	C₂²	semidirect
23. C₂×C₅×#214	C₂²	semidirect
24. C₂×C₅×#214	C₂²	semidirect
26. C₂×C₅×#213	C₂²	semidirect
30. C₂×C₅×Dic₁₂	C₂²	semidirect
32. C₂×C₅×#204	C₂²	semidirect
35. C₅×#875	C₂²	semidirect
37. C₃×C₄×C₅×C₈	C₂²	semidirect
38. C₅×#815	C₂²	semidirect
39. C₅×C₈×Dic₃	C₂²	semidirect
40. C₅×#803	C₂²	semidirect
41. #81784	C₅	direct (N × H)
51. C₅×#493	D₃	semidirect
88. C₅×ΓL(1,𝔽₂₅)	D₄	semidirect
89. C₅×D₃×C₈	D₄	semidirect
90. C₂×#912	C₂×C₅	semidirect
91. C₂×#911	C₂×C₅	semidirect
92. C₂×D₃×D₈	C₂×C₅	semidirect
93. #5715	C₂×C₅	semidirect
94. C₃×#493	C₂×C₅	semidirect
95. #5155	C₂×C₅	semidirect
96. #5154	C₂×C₅	semidirect
97. #5151	C₂×C₅	semidirect
98. #5074	C₂×C₅	semidirect
99. #4696	C₂×C₅	semidirect
100. #4689	C₂×C₅	semidirect
114. C₂×C₅×D₈	C₂×D₃	semidirect
115. C₂×C₅×D₈	C₂×D₃	semidirect
119. C₅×#127	C₂×D₃	semidirect
128. C₄×C₅×C₈	C₂×D₃	semidirect
163. C₂×C₃×D₈	C₂²×C₅	semidirect
164. C₂×C₃×D₈	C₂²×C₅	semidirect
165. C₃×#127	C₂²×C₅	semidirect
166. #940	C₂²×C₅	semidirect
169. #936	C₂²×C₅	semidirect
170. C₂×#214	C₂²×C₅	semidirect
171. C₂×#214	C₂²×C₅	semidirect
173. C₂×#213	C₂²×C₅	semidirect
177. C₂×Dic₁₂	C₂²×C₅	semidirect
179. C₂×#204	C₂²×C₅	semidirect
182. #875	C₂²×C₅	semidirect
184. C₃×C₄×C₈	C₂²×C₅	semidirect
185. #815	C₂²×C₅	semidirect
186. C₈×Dic₃	C₂²×C₅	semidirect
187. #803	C₂²×C₅	semidirect
234. #493	C₅×D₃	semidirect
287. ΓL(1,𝔽₂₅)	C₅×D₄	semidirect
288. D₃×C₈	C₅×D₄	semidirect
332. C₂×D₈	C₂×C₅×D₃	semidirect
333. C₂×D₈	C₂×C₅×D₃	semidirect
337. #127	C₂×C₅×D₃	semidirect
346. C₄×C₈	C₂×C₅×D₃	semidirect
436. C₃×C₅	#3155	semidirect
495. C₅	#81784	direct (N × H)
512. 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×C₅×#912	2
C₂×C₅×#911	2
C₂×C₅×D₃×D₈	2
C₅×#5715	2
C₃×C₅×#493	2
C₅×#5155	2
C₅×#5154	2
C₅×#5151	2
C₅×#5074	2
C₅×#4696	2
C₅×#4689	2
C₅×#3155	3
#81784	5

Subgroups — C5×#81784 #14439531

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#81784 #14439531