Subgroups — C₅×#81871 #14439279

Order 1920.

1144 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#918	C₂	1	2	yes	maximal, complemented
2	C₂×C₅×#914	C₂	1	2	yes	maximal, complemented
3	C₅×#5725	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×D₃×#124	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅×#497	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#5191	C₂	1	2	yes	maximal, complemented
7	C₅×#5168	C₂	1	2	yes	maximal, complemented
8	C₅×#5086	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#5058	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#4712	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#4707	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#3153	—	3	1	no	maximal, Hall
13	C₂×C₅×#239	C₂²	1	2	yes	—
14	C₂×C₅×D₃×Q₈	C₂²	1	1	yes	characteristic
15	C₂×C₅×D₃×D₄	C₂²	1	1	yes	characteristic
16	C₂×C₃×C₅×Q₁₆	C₂²	1	2	yes	complemented
17	C₂×C₃×C₅×SD₁₆	C₂²	1	2	yes	—
18	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
19	C₃×C₅×#124	C₂²	1	1	yes	characteristic
20	C₅×#947	C₂²	1	1	yes	characteristic
21	C₅×#947	C₂²	1	2	yes	complemented
22	C₂×C₅×#216	C₂²	1	2	yes	complemented
23	C₂×C₅×#215	C₂²	1	2	yes	—
24	C₂×C₅×#215	C₂²	1	2	yes	complemented
25	C₅×#936	C₂²	1	1	yes	characteristic
26	C₂×C₅×#213	C₂²	1	2	yes	—
27	C₅×#918	—	2	8	no	—
28	C₅×#914	—	2	8	no	—
29	C₂×C₅×D₂₄	C₂²	1	2	yes	—
30	C₂×C₅×#204	C₂²	1	2	yes	complemented
31	C₂×C₅×ΓL(1,𝔽₂₅)	C₂²	1	2	yes	—
32	C₅×#895	—	2	2	no	—
33	C₅×#893	—	2	2	no	—
34	C₅×#885	—	2	2	no	—
35	C₅×D₃×C₂²⋊C₄	—	2	2	no	—
36	C₅×#875	C₂²	1	1	yes	characteristic
37	C₅×#874	C₂²	1	1	yes	characteristic, complemented
38	C₄²×C₅×D₃	C₂²	1	1	yes	characteristic
39	C₃×C₅×#97	C₂²	1	1	yes	characteristic, complemented
40	C₅×C₈×Dic₃	C₂²	1	2	yes	complemented
41	C₅×#803	C₂²	1	1	yes	characteristic, complemented
42	#81871	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
43	C₂×C₅×#137	—	3	2	no	—
44	C₂×C₅×AGL(1,ℤ/8)	—	3	2	no	—
45	C₅×#532	—	3	1	no	—
46	C₂×C₅×#124	—	3	1	no	—
47	C₅×#497	—	3	1	no	—
48	C₅×#497	D₃	1	1	yes	characteristic, complemented
49	C₅×#496	—	3	1	no	—
50	C₅×#496	—	3	1	no	—
51	C₅×#495	—	3	2	no	—
52	C₅×#495	—	3	2	no	—
53	C₄×C₅×M₁₆	—	3	1	no	—
54	C₂³×C₅×D₃	—	2	1	no	—
55	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
56	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
57	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
58	C₂×C₅×#67	—	2	1	no	—
59	C₅×#239	—	2	4	no	—
60	C₅×#239	—	2	4	no	—
61	C₅×D₃×Q₈	—	2	4	no	—
62	C₅×D₃×D₄	—	2	4	no	—
63	C₂×C₅×D₁₂	—	2	2	no	—
64	C₂×C₅×D₁₂	—	2	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×C₄×C₅×D₃	—	2	2	no	—
69	C₂×C₄×C₅×D₃	D₄	1	2	yes	—
70	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
71	C₂×C₅×Dic₆	—	2	1	no	—
72	C₂×C₅×Dic₆	C₂³	1	1	yes	characteristic
73	C₃×C₅×Q₁₆	—	2	4	no	—
74	C₃×C₅×SD₁₆	—	2	4	no	—
75	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
76	C₃×C₅×C₄⋊C₄	—	2	2	no	—
77	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
78	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
79	C₅×#217	—	2	2	no	—
80	C₅×#216	—	2	4	no	—
81	C₅×#215	—	2	4	no	—
82	C₅×#215	—	2	4	no	—
83	C₅×#213	—	2	4	no	—
84	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
85	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
86	C₅×(C₂×D₃)⋊C₄	—	2	4	no	—
87	C₄×C₅×Dic₃	D₄	1	2	yes	—
88	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
89	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
90	C₅×D₂₄	—	2	4	no	—
91	C₅×#204	—	2	4	no	—
92	C₅×ΓL(1,𝔽₂₅)	D₄	1	8	yes	complemented
93	C₂×#918	C₂×C₅	1	2	yes	complemented
94	C₂×#914	C₂×C₅	1	2	yes	complemented
95	#5725	C₂×C₅	1	1	yes	characteristic, complemented
96	D₃×#124	C₂×C₅	1	1	yes	characteristic, complemented
97	C₃×#497	C₂×C₅	1	1	yes	characteristic, complemented
98	#5191	C₂×C₅	1	2	yes	complemented
99	#5168	C₂×C₅	1	2	yes	complemented
100	#5086	C₂×C₅	1	1	yes	characteristic, complemented
101	#5058	C₂×C₅	1	1	yes	characteristic, complemented
102	#4712	C₂×C₅	1	1	yes	characteristic, complemented
103	#4707	C₂×C₅	1	1	yes	characteristic, complemented
104	C₂×C₅×#41	—	3	2	no	—
105	C₂²×C₅×Q₈	—	3	1	no	—
106	C₂²×C₅×D₄	—	3	1	no	—
107	C₅×#137	—	6	8	no	—
108	C₅×AGL(1,ℤ/8)	—	6	8	no	—
109	C₂×C₅×Q₁₆	—	3	2	no	—
110	C₂×C₅×Q₁₆	C₂×D₃	1	2	yes	complemented
111	C₂×C₅×SD₁₆	—	3	2	no	—
112	C₂×C₅×SD₁₆	—	3	2	no	—
113	C₂×C₅×SD₁₆	—	3	2	no	—
114	C₂×C₅×SD₁₆	C₂×D₃	1	2	yes	—
115	C₂×C₅×D₈	—	3	2	no	—
116	C₂×C₅×D₈	—	3	2	no	—
117	C₂×C₅×M₁₆	—	3	2	no	—
118	C₅×C₄⋊Q₈	C₂×D₃	1	1	yes	characteristic, complemented
119	C₅×#127	—	3	1	no	—
120	C₅×#124	—	3	1	no	—
121	C₅×#124	—	3	2	no	—
122	C₅×#124	—	3	1	no	—
123	C₅×#124	—	3	1	no	—
124	C₅×#124	—	6	2	no	—
125	C₅×#124	C₂×D₃	1	1	yes	characteristic
126	C₅×#121	—	6	2	no	—
127	C₄×C₅×D₄	—	6	2	no	—
128	C₂×C₅×C₂²⋊C₄	—	6	2	no	—
129	C₂×C₄²×C₅	—	3	1	no	—
130	C₅×#97	—	3	1	no	—
131	C₅×#97	C₂×D₃	1	1	yes	characteristic, complemented
132	C₄×C₅×C₈	—	3	2	no	—
133	#3153	—	3	1	no	Sylow
134	C₂³×C₃×C₅	—	2	1	no	—
135	C₂²×C₅×D₃	—	2	1	no	—
136	C₂²×C₅×D₃	—	2	2	no	—
137	C₂²×C₅×D₃	—	4	4	no	—
138	C₂²×C₅×D₃	—	4	2	no	—
139	C₂²×C₅×D₃	C₂×D₄	1	1	yes	characteristic
140	C₃×C₅×Q₈	—	2	2	no	—
141	C₃×C₅×Q₈	—	2	2	no	—
142	C₃×C₅×Q₈	—	2	2	no	—
143	C₃×C₅×D₄	—	2	2	no	—
144	C₂×C₃×C₄×C₅	—	2	1	no	—
145	C₂×C₃×C₄×C₅	—	2	2	no	—
146	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
147	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
148	C₅×#67	—	4	2	no	—
149	C₂×C₅×Dic₃	—	2	1	no	—
150	C₂×C₅×Dic₃	C₂×D₄	1	2	yes	—
151	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
152	C₅×D₁₂	—	2	2	no	—
153	C₅×D₁₂	—	2	2	no	—
154	C₅×D₁₂	—	2	2	no	—
155	C₅×D₁₂	—	4	4	no	—
156	C₅×D₁₂	—	4	4	no	—
157	C₄×C₅×D₃	—	4	2	no	—
158	C₄×C₅×D₃	—	4	2	no	—
159	C₄×C₅×D₃	—	4	4	no	—
160	C₄×C₅×D₃	C₂×D₄	1	4	yes	—
161	C₅×Dic₆	—	2	2	no	—
162	C₅×Dic₆	—	4	2	no	—
163	C₃×C₅×C₈	C₂×D₄	1	4	yes	—
164	C₅×C₃⋊C₈	C₂×D₄	1	4	yes	—
165	C₂×#239	C₂²×C₅	1	2	yes	—
166	C₂×D₃×Q₈	C₂²×C₅	1	1	yes	characteristic
167	C₂×D₃×D₄	C₂²×C₅	1	1	yes	characteristic
168	C₂×C₃×Q₁₆	C₂²×C₅	1	2	yes	complemented
169	C₂×C₃×SD₁₆	C₂²×C₅	1	2	yes	—
170	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
171	C₃×#124	C₂²×C₅	1	1	yes	characteristic
172	#947	C₂²×C₅	1	1	yes	characteristic
173	#947	C₂²×C₅	1	2	yes	complemented
174	C₂×#216	C₂²×C₅	1	2	yes	complemented
175	C₂×#215	C₂²×C₅	1	2	yes	—
176	C₂×#215	C₂²×C₅	1	2	yes	complemented
177	#936	C₂²×C₅	1	1	yes	characteristic
178	C₂×#213	C₂²×C₅	1	2	yes	—
179	#918	—	2	8	no	—
180	#914	—	2	8	no	—
181	C₂×D₂₄	C₂²×C₅	1	2	yes	—
182	C₂×#204	C₂²×C₅	1	2	yes	complemented
183	C₂×ΓL(1,𝔽₂₅)	C₂²×C₅	1	2	yes	—
184	#895	—	2	2	no	—
185	#893	—	2	2	no	—
186	#885	—	2	2	no	—
187	D₃×C₂²⋊C₄	—	2	2	no	—
188	#875	C₂²×C₅	1	1	yes	characteristic
189	#874	C₂²×C₅	1	1	yes	characteristic, complemented
190	C₄²×D₃	C₂²×C₅	1	1	yes	characteristic
191	C₃×#97	C₂²×C₅	1	1	yes	characteristic, complemented
192	C₈×Dic₃	C₂²×C₅	1	2	yes	complemented
193	#803	C₂²×C₅	1	1	yes	characteristic, complemented
194	C₂⁴×C₅	—	6	1	no	—
195	C₅×#41	—	6	4	no	—
196	C₅×#41	—	6	4	no	—
197	C₂×C₅×Q₈	—	3	1	no	—
198	C₂×C₅×Q₈	—	6	1	no	—
199	C₂×C₅×Q₈	—	6	4	no	—
200	C₂×C₅×Q₈	C₂²×D₃	1	1	yes	characteristic
201	C₂×C₅×Q₈	C₂²×D₃	1	2	yes	—
202	C₂×C₅×D₄	—	3	1	no	—
203	C₂×C₅×D₄	—	3	2	no	—
204	C₂×C₅×D₄	—	6	2	no	—
205	C₂×C₅×D₄	—	6	4	no	—
206	C₂×C₅×D₄	—	6	1	no	—
207	C₂×C₅×D₄	—	6	2	no	—
208	C₂×C₅×D₄	C₂²×D₃	1	1	yes	characteristic
209	C₂²×C₄×C₅	—	3	1	no	—
210	C₂²×C₄×C₅	—	3	2	no	—
211	C₂²×C₄×C₅	—	6	2	no	—
212	C₂²×C₄×C₅	—	6	1	no	—
213	C₅×Q₁₆	—	2	4	no	—
214	C₅×Q₁₆	—	6	4	no	—
215	C₅×SD₁₆	—	2	4	no	—
216	C₅×SD₁₆	—	6	4	no	—
217	C₅×SD₁₆	—	6	4	no	—
218	C₅×SD₁₆	—	6	4	no	—
219	C₅×D₈	—	6	4	no	—
220	C₅×D₈	—	6	4	no	—
221	C₅×M₁₆	—	3	8	no	—
222	C₂×C₅×C₈	—	3	2	no	—
223	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
224	C₅×C₄⋊C₄	—	2	2	no	—
225	C₅×C₂²⋊C₄	—	2	2	no	—
226	C₅×C₂²⋊C₄	—	6	2	no	—
227	C₅×C₂²⋊C₄	—	6	4	no	—
228	C₅×C₂²⋊C₄	—	6	2	no	—
229	C₅×C₂²⋊C₄	—	6	2	no	—
230	C₄²×C₅	—	3	2	no	—
231	C₄²×C₅	—	3	1	no	—
232	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
233	C₂×#137	—	3	2	no	—
234	C₂×AGL(1,ℤ/8)	—	3	2	no	—
235	#532	—	3	1	no	—
236	C₂×#124	—	3	1	no	—
237	#497	—	3	1	no	—
238	#497	C₅×D₃	1	1	yes	characteristic, complemented
239	#496	—	3	1	no	—
240	#496	—	3	1	no	—
241	#495	—	3	2	no	—
242	#495	—	3	2	no	—
243	C₄×M₁₆	—	3	1	no	—
244	C₂²×C₃×C₅	—	4	1	no	—
245	C₂²×C₃×C₅	—	4	2	no	—
246	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
247	C₂×C₅×D₃	—	2	2	no	—
248	C₂×C₅×D₃	—	4	2	no	—
249	C₂×C₅×D₃	—	4	1	no	—
250	C₂×C₅×D₃	—	4	4	no	—
251	C₂×C₅×D₃	—	4	2	no	—
252	C₂×C₅×D₃	—	8	4	no	—
253	C₂×C₅×D₃	#127	1	2	yes	—
254	C₃×C₄×C₅	—	2	2	no	—
255	C₃×C₄×C₅	—	4	1	no	—
256	C₃×C₄×C₅	—	4	2	no	—
257	C₃×C₄×C₅	C₂²×D₄	1	2	yes	—
258	C₅×Dic₃	—	2	2	no	—
259	C₅×Dic₃	—	4	1	no	—
260	C₅×Dic₃	#127	1	2	yes	—
261	C₂³×D₃	—	2	1	no	—
262	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
263	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
264	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
265	C₂×#67	—	2	1	no	—
266	#239	—	2	4	no	—
267	#239	—	2	4	no	—
268	D₃×Q₈	—	2	4	no	—
269	D₃×D₄	—	2	4	no	—
270	C₂×D₁₂	—	2	2	no	—
271	C₂×D₁₂	—	2	2	no	—
272	C₂×D₁₂	C₂³×C₅	1	2	yes	—
273	C₂×D₁₂	C₂³×C₅	1	1	yes	characteristic
274	C₂×C₄×D₃	—	2	1	no	—
275	C₂×C₄×D₃	—	2	2	no	—
276	C₂×C₄×D₃	C₅×D₄	1	2	yes	—
277	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
278	C₂×Dic₆	—	2	1	no	—
279	C₂×Dic₆	C₂³×C₅	1	1	yes	characteristic
280	C₃×Q₁₆	—	2	4	no	—
281	C₃×SD₁₆	—	2	4	no	—
282	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
283	C₃×C₄⋊C₄	—	2	2	no	—
284	C₃×C₂²⋊C₄	—	2	2	no	—
285	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
286	#217	—	2	2	no	—
287	#216	—	2	4	no	—
288	#215	—	2	4	no	—
289	#215	—	2	4	no	—
290	#213	—	2	4	no	—
291	(C₂×D₃)⋊C₄	—	2	2	no	—
292	(C₂×D₃)⋊C₄	—	2	2	no	—
293	(C₂×D₃)⋊C₄	—	2	4	no	—
294	C₄×Dic₃	C₅×D₄	1	2	yes	—
295	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
296	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
297	D₂₄	—	2	4	no	—
298	#204	—	2	4	no	—
299	ΓL(1,𝔽₂₅)	C₅×D₄	1	8	yes	complemented
300	C₂³×C₅	—	2	1	no	—
301	C₂³×C₅	—	3	1	no	—
302	C₂³×C₅	—	6	1	no	—
303	C₂³×C₅	—	6	2	no	—
304	C₂³×C₅	—	12	2	no	—
305	C₂³×C₅	—	12	4	no	—
306	C₅×Q₈	—	2	2	no	—
307	C₅×Q₈	—	2	2	no	—
308	C₅×Q₈	—	2	2	no	—
309	C₅×Q₈	—	6	2	no	—
310	C₅×Q₈	—	12	2	no	—
311	C₅×D₄	—	2	2	no	—
312	C₅×D₄	—	6	2	no	—
313	C₅×D₄	—	6	2	no	—
314	C₅×D₄	—	6	2	no	—
315	C₅×D₄	—	12	4	no	—
316	C₅×D₄	—	12	2	no	—
317	C₅×D₄	—	12	4	no	—
318	C₂×C₄×C₅	—	2	1	no	—
319	C₂×C₄×C₅	—	2	2	no	—
320	C₂×C₄×C₅	—	3	1	no	—
321	C₂×C₄×C₅	—	3	4	no	—
322	C₂×C₄×C₅	—	3	2	no	—
323	C₂×C₄×C₅	—	6	1	no	—
324	C₂×C₄×C₅	—	12	2	no	—
325	C₂×C₄×C₅	—	12	4	no	—
326	C₂×C₄×C₅	—	12	2	no	—
327	C₂×C₄×C₅	D₃×D₄	1	2	yes	—
328	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
329	C₅×C₈	—	3	4	no	—
330	C₅×C₈	D₃×D₄	1	4	yes	—
331	C₂×#41	—	3	2	no	—
332	C₂²×Q₈	—	3	1	no	—
333	C₂²×D₄	—	3	1	no	—
334	#137	—	6	8	no	—
335	AGL(1,ℤ/8)	—	6	8	no	—
336	C₂×Q₁₆	—	3	2	no	—
337	C₂×Q₁₆	C₂×C₅×D₃	1	2	yes	complemented
338	C₂×SD₁₆	—	3	2	no	—
339	C₂×SD₁₆	—	3	2	no	—
340	C₂×SD₁₆	—	3	2	no	—
341	C₂×SD₁₆	C₂×C₅×D₃	1	2	yes	—
342	C₂×D₈	—	3	2	no	—
343	C₂×D₈	—	3	2	no	—
344	C₂×M₁₆	—	3	2	no	—
345	C₄⋊Q₈	C₂×C₅×D₃	1	1	yes	characteristic, complemented
346	#127	—	3	1	no	—
347	#124	—	3	1	no	—
348	#124	—	3	2	no	—
349	#124	—	3	1	no	—
350	#124	—	3	1	no	—
351	#124	—	6	2	no	—
352	#124	C₂×C₅×D₃	1	1	yes	characteristic
353	#121	—	6	2	no	—
354	C₄×D₄	—	6	2	no	—
355	C₂×C₂²⋊C₄	—	6	2	no	—
356	C₂×C₄²	—	3	1	no	—
357	#97	—	3	1	no	—
358	#97	C₂×C₅×D₃	1	1	yes	characteristic, complemented
359	C₄×C₈	—	3	2	no	—
360	C₂×C₃×C₅	—	8	1	no	—
361	C₂×C₃×C₅	C₂×#127	1	1	yes	characteristic
362	C₂×C₃×C₅	#575	1	2	yes	—
363	C₅×D₃	—	2	2	no	—
364	C₅×D₃	—	8	2	no	—
365	C₅×D₃	—	8	1	no	—
366	C₂³×C₃	—	2	1	no	—
367	C₂²×D₃	—	2	1	no	—
368	C₂²×D₃	—	2	2	no	—
369	C₂²×D₃	—	4	4	no	—
370	C₂²×D₃	—	4	2	no	—
371	C₂²×D₃	C₂×C₅×D₄	1	1	yes	characteristic
372	C₃×Q₈	—	2	2	no	—
373	C₃×Q₈	—	2	2	no	—
374	C₃×Q₈	—	2	2	no	—
375	C₃×D₄	—	2	2	no	—
376	C₂×C₃×C₄	—	2	1	no	—
377	C₂×C₃×C₄	—	2	2	no	—
378	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
379	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
380	#67	—	4	2	no	—
381	C₂×Dic₃	—	2	1	no	—
382	C₂×Dic₃	C₂×C₅×D₄	1	2	yes	—
383	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
384	D₁₂	—	2	2	no	—
385	D₁₂	—	2	2	no	—
386	D₁₂	—	2	2	no	—
387	D₁₂	—	4	4	no	—
388	D₁₂	—	4	4	no	—
389	C₄×D₃	—	4	2	no	—
390	C₄×D₃	—	4	2	no	—
391	C₄×D₃	—	4	4	no	—
392	C₄×D₃	C₂×C₅×D₄	1	4	yes	—
393	Dic₆	—	2	2	no	—
394	Dic₆	—	4	2	no	—
395	C₃×C₈	C₂×C₅×D₄	1	4	yes	—
396	C₃⋊C₈	C₂×C₅×D₄	1	4	yes	—
397	C₂²×C₅	—	3	2	no	—
398	C₂²×C₅	—	4	1	no	—
399	C₂²×C₅	—	4	2	no	—
400	C₂²×C₅	—	6	2	no	—
401	C₂²×C₅	—	12	2	no	—
402	C₂²×C₅	—	12	1	no	—
403	C₂²×C₅	—	12	4	no	—
404	C₂²×C₅	—	12	2	no	—
405	C₂²×C₅	—	24	4	no	—
406	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
407	C₄×C₅	—	2	2	no	—
408	C₄×C₅	—	3	2	no	—
409	C₄×C₅	—	4	2	no	—
410	C₄×C₅	—	4	1	no	—
411	C₄×C₅	—	6	2	no	—
412	C₄×C₅	—	12	1	no	—
413	C₄×C₅	C₂×D₃×D₄	1	2	yes	—
414	C₂⁴	—	6	1	no	—
415	#41	—	6	4	no	—
416	#41	—	6	4	no	—
417	C₂×Q₈	—	3	1	no	—
418	C₂×Q₈	—	6	1	no	—
419	C₂×Q₈	—	6	4	no	—
420	C₂×Q₈	C₂²×C₅×D₃	1	1	yes	characteristic
421	C₂×Q₈	C₂²×C₅×D₃	1	2	yes	—
422	C₂×D₄	—	3	1	no	—
423	C₂×D₄	—	3	2	no	—
424	C₂×D₄	—	6	2	no	—
425	C₂×D₄	—	6	4	no	—
426	C₂×D₄	—	6	1	no	—
427	C₂×D₄	—	6	2	no	—
428	C₂×D₄	C₂²×C₅×D₃	1	1	yes	characteristic
429	C₂²×C₄	—	3	1	no	—
430	C₂²×C₄	—	3	2	no	—
431	C₂²×C₄	—	6	2	no	—
432	C₂²×C₄	—	6	1	no	—
433	Q₁₆	—	2	4	no	—
434	Q₁₆	—	6	4	no	—
435	SD₁₆	—	2	4	no	—
436	SD₁₆	—	6	4	no	—
437	SD₁₆	—	6	4	no	—
438	SD₁₆	—	6	4	no	—
439	D₈	—	6	4	no	—
440	D₈	—	6	4	no	—
441	M₁₆	—	3	8	no	—
442	C₂×C₈	—	3	2	no	—
443	C₂×C₈	C₂²×C₅×D₃	1	2	yes	—
444	C₄⋊C₄	—	2	2	no	—
445	C₂²⋊C₄	—	2	2	no	—
446	C₂²⋊C₄	—	6	2	no	—
447	C₂²⋊C₄	—	6	4	no	—
448	C₂²⋊C₄	—	6	2	no	—
449	C₂²⋊C₄	—	6	2	no	—
450	C₄²	—	3	2	no	—
451	C₄²	—	3	1	no	—
452	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
453	C₃×C₅	#3153	1	1	yes	characteristic, complemented, Hall
454	C₂²×C₃	—	4	1	no	—
455	C₂²×C₃	—	4	2	no	—
456	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
457	C₂×D₃	—	2	2	no	—
458	C₂×D₃	—	4	2	no	—
459	C₂×D₃	—	4	1	no	—
460	C₂×D₃	—	4	4	no	—
461	C₂×D₃	—	4	2	no	—
462	C₂×D₃	—	8	4	no	—
463	C₂×D₃	C₅×#127	1	2	yes	—
464	C₃×C₄	—	2	2	no	—
465	C₃×C₄	—	4	1	no	—
466	C₃×C₄	—	4	2	no	—
467	C₃×C₄	C₂²×C₅×D₄	1	2	yes	—
468	Dic₃	—	2	2	no	—
469	Dic₃	—	4	1	no	—
470	Dic₃	C₅×#127	1	2	yes	—
471	C₂×C₅	—	6	2	no	—
472	C₂×C₅	—	8	1	no	—
473	C₂×C₅	—	24	1	no	—
474	C₂×C₅	—	24	2	no	—
475	C₂×C₅	D₃×#127	1	1	yes	characteristic
476	C₂×C₅	#5777	1	2	yes	—
477	C₂³	—	2	1	no	—
478	C₂³	—	3	1	no	—
479	C₂³	—	6	1	no	—
480	C₂³	—	6	2	no	—
481	C₂³	—	12	2	no	—
482	C₂³	—	12	4	no	—
483	Q₈	—	2	2	no	—
484	Q₈	—	2	2	no	—
485	Q₈	—	2	2	no	—
486	Q₈	—	6	2	no	—
487	Q₈	—	12	2	no	—
488	D₄	—	2	2	no	—
489	D₄	—	6	2	no	—
490	D₄	—	6	2	no	—
491	D₄	—	6	2	no	—
492	D₄	—	12	4	no	—
493	D₄	—	12	2	no	—
494	D₄	—	12	4	no	—
495	C₂×C₄	—	2	1	no	—
496	C₂×C₄	—	2	2	no	—
497	C₂×C₄	—	3	1	no	—
498	C₂×C₄	—	3	4	no	—
499	C₂×C₄	—	3	2	no	—
500	C₂×C₄	—	6	1	no	—
501	C₂×C₄	—	12	2	no	—
502	C₂×C₄	—	12	4	no	—
503	C₂×C₄	—	12	2	no	—
504	C₂×C₄	C₅×D₃×D₄	1	2	yes	—
505	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
506	C₈	—	3	4	no	—
507	C₈	C₅×D₃×D₄	1	4	yes	—
508	C₂×C₃	—	8	1	no	—
509	C₂×C₃	C₂×C₅×#127	1	1	yes	characteristic
510	C₂×C₃	C₅×#575	1	2	yes	—
511	D₃	—	2	2	no	—
512	D₃	—	8	1	no	—
513	D₃	—	8	2	no	—
514	C₅	#81871	1	1	yes	characteristic, direct product factor, Sylow
515	C₂²	—	3	2	no	—
516	C₂²	—	4	1	no	—
517	C₂²	—	4	2	no	—
518	C₂²	—	6	2	no	—
519	C₂²	—	12	2	no	—
520	C₂²	—	12	1	no	—
521	C₂²	—	12	4	no	—
522	C₂²	—	12	2	no	—
523	C₂²	—	24	4	no	—
524	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
525	C₄	—	2	2	no	—
526	C₄	—	3	2	no	—
527	C₄	—	4	2	no	—
528	C₄	—	4	1	no	—
529	C₄	—	6	2	no	—
530	C₄	—	12	1	no	—
531	C₄	C₂×C₅×D₃×D₄	1	2	yes	—
532	C₃	C₅×#3153	1	1	yes	characteristic, complemented, Sylow
533	C₂	—	6	2	no	—
534	C₂	—	8	1	no	—
535	C₂	—	24	1	no	—
536	C₂	—	24	2	no	—
537	C₂	C₅×D₃×#127	1	1	yes	characteristic
538	C₂	C₅×#5777	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×#497	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
hypercenter	C₅×#497	D₃
hypocenter	C₃	C₅×#3153
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₄²×C₅ ◁ C₅×#497

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×#918	C₂	semidirect
2. C₂×C₅×#914	C₂	semidirect
3. C₅×#5725	C₂	semidirect
4. C₅×D₃×#124	C₂	semidirect
5. C₃×C₅×#497	C₂	semidirect
6. C₅×#5191	C₂	semidirect
7. C₅×#5168	C₂	semidirect
8. C₅×#5086	C₂	semidirect
9. C₅×#5058	C₂	semidirect
10. C₅×#4712	C₂	semidirect
11. C₅×#4707	C₂	semidirect
16. C₂×C₃×C₅×Q₁₆	C₂²	semidirect
18. C₃×C₅×C₄⋊Q₈	C₂²	semidirect
21. C₅×#947	C₂²	semidirect
22. C₂×C₅×#216	C₂²	semidirect
24. C₂×C₅×#215	C₂²	semidirect
30. C₂×C₅×#204	C₂²	semidirect
37. C₅×#874	C₂²	semidirect
39. C₃×C₅×#97	C₂²	semidirect
40. C₅×C₈×Dic₃	C₂²	semidirect
41. C₅×#803	C₂²	semidirect
42. #81871	C₅	direct (N × H)
48. C₅×#497	D₃	semidirect
92. C₅×ΓL(1,𝔽₂₅)	D₄	semidirect
93. C₂×#918	C₂×C₅	semidirect
94. C₂×#914	C₂×C₅	semidirect
95. #5725	C₂×C₅	semidirect
96. D₃×#124	C₂×C₅	semidirect
97. C₃×#497	C₂×C₅	semidirect
98. #5191	C₂×C₅	semidirect
99. #5168	C₂×C₅	semidirect
100. #5086	C₂×C₅	semidirect
101. #5058	C₂×C₅	semidirect
102. #4712	C₂×C₅	semidirect
103. #4707	C₂×C₅	semidirect
110. C₂×C₅×Q₁₆	C₂×D₃	semidirect
118. C₅×C₄⋊Q₈	C₂×D₃	semidirect
131. C₅×#97	C₂×D₃	semidirect
168. C₂×C₃×Q₁₆	C₂²×C₅	semidirect
170. C₃×C₄⋊Q₈	C₂²×C₅	semidirect
173. #947	C₂²×C₅	semidirect
174. C₂×#216	C₂²×C₅	semidirect
176. C₂×#215	C₂²×C₅	semidirect
182. C₂×#204	C₂²×C₅	semidirect
189. #874	C₂²×C₅	semidirect
191. C₃×#97	C₂²×C₅	semidirect
192. C₈×Dic₃	C₂²×C₅	semidirect
193. #803	C₂²×C₅	semidirect
238. #497	C₅×D₃	semidirect
299. ΓL(1,𝔽₂₅)	C₅×D₄	semidirect
337. C₂×Q₁₆	C₂×C₅×D₃	semidirect
345. C₄⋊Q₈	C₂×C₅×D₃	semidirect
358. #97	C₂×C₅×D₃	semidirect
453. C₃×C₅	#3153	semidirect
514. C₅	#81871	direct (N × H)
532. C₃	C₅×#3153	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×#918	2
C₂×C₅×#914	2
C₅×#5725	2
C₅×D₃×#124	2
C₃×C₅×#497	2
C₅×#5191	2
C₅×#5168	2
C₅×#5086	2
C₅×#5058	2
C₅×#4712	2
C₅×#4707	2
C₅×#3153	3
#81871	5

Subgroups — C5×#81871 #14439279

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#81871 #14439279