Subgroups — C₅×#80281 #14458104

Order 1920.

920 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#5836	C₂	1	2	yes	maximal, complemented
2	C₅×#5775	C₂	1	2	yes	maximal, complemented
3	C₃×C₅×#453	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5200	C₂	1	2	yes	maximal, complemented
5	C₅×#5077	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#5076	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#4826	C₂	1	2	yes	maximal, complemented
8	C₅×#4824	C₂	1	2	yes	maximal, complemented
9	C₅×#4748	C₂	1	2	yes	maximal, complemented
10	C₅×#3291	—	3	1	no	maximal, Hall
11	C₃×C₅×H(5,𝔽₂)	C₂²	1	1	yes	characteristic, complemented
12	C₅×#1010	C₂²	1	2	yes	—
13	C₅×#1004	C₂²	1	1	yes	characteristic, complemented
14	C₃×C₅×AGL(1,ℤ/8)	C₂²	1	2	yes	—
15	C₃×C₅×#127	C₂²	1	1	yes	characteristic
16	C₅×#951	—	2	2	no	—
17	C₅×#951	C₂²	1	2	yes	complemented
18	C₅×#950	—	2	2	no	—
19	C₅×#950	C₂²	1	2	yes	—
20	C₅×#948	C₂²	1	2	yes	complemented
21	C₂×C₅×#214	—	2	2	no	—
22	C₂×C₅×#214	C₂²	1	2	yes	complemented
23	C₂×C₅×#214	C₂²	1	2	yes	complemented
24	C₅×#932	—	2	2	no	—
25	C₅×#932	C₂²	1	2	yes	—
26	C₅×#915	—	2	2	no	—
27	C₅×D₃×SD₁₆	—	2	2	no	—
28	C₅×#912	—	2	2	no	—
29	C₅×#911	—	2	2	no	—
30	C₅×#909	C₂²	1	2	yes	complemented
31	C₅×#907	C₂²	1	2	yes	complemented
32	C₅×#869	C₂²	1	1	yes	characteristic, complemented
33	C₃×C₅×#104	C₂²	1	2	yes	complemented
34	C₃×C₅×#100	C₂²	1	1	yes	characteristic, complemented
35	C₅×#833	C₂²	1	1	yes	characteristic, complemented
36	C₅×#824	C₂²	1	2	yes	complemented
37	C₅×#822	C₂²	1	2	yes	complemented
38	C₅×#805	C₂²	1	2	yes	complemented
39	C₄×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
40	#80281	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
41	C₅×#577	—	3	2	no	—
42	C₅×#577	—	3	2	no	—
43	C₅×#492	—	3	1	no	—
44	C₅×#471	—	3	2	no	—
45	C₅×#471	—	3	2	no	—
46	C₅×#456	—	3	2	no	—
47	C₅×#453	—	3	1	no	—
48	C₅×#453	D₃	1	1	yes	characteristic, complemented
49	C₅×#443	—	3	2	no	—
50	C₃×C₅×#41	—	2	2	no	—
51	C₃×C₅×#41	C₂³	1	2	yes	—
52	C₂×C₃×C₅×D₄	—	2	2	no	—
53	C₂×C₃×C₅×D₄	—	4	1	no	—
54	C₂×C₃×C₅×D₄	—	4	1	no	—
55	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
56	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
57	C₂×C₅×#67	—	4	1	no	—
58	C₅×D₃×Q₈	—	2	2	no	—
59	C₅×#237	—	2	2	no	—
60	C₅×#237	—	2	2	no	—
61	C₅×#237	—	4	2	no	—
62	C₅×D₃×D₄	—	2	2	no	—
63	C₅×#235	—	2	2	no	—
64	C₅×#235	C₂³	1	2	yes	—
65	C₂×C₅×Dic₆	—	2	2	no	—
66	C₂×C₅×Dic₆	C₂³	1	2	yes	—
67	C₃×C₅×SD₁₆	—	2	2	no	—
68	C₃×C₅×D₈	—	2	2	no	—
69	C₃×C₅×M₁₆	C₂³	1	2	yes	—
70	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
71	C₅×#216	—	2	2	no	—
72	C₅×#216	D₄	1	2	yes	complemented
73	C₅×#215	D₄	1	2	yes	complemented
74	C₅×#214	—	2	2	no	—
75	C₅×#214	—	2	2	no	—
76	C₅×#214	—	2	2	no	—
77	C₅×#214	—	2	2	no	—
78	C₅×#214	—	2	2	no	—
79	C₅×#214	—	2	2	no	—
80	C₅×#214	D₄	1	2	yes	complemented
81	C₅×#213	—	2	2	no	—
82	C₅×#213	D₄	1	2	yes	complemented
83	C₅×C₄⋊Dic₃	—	4	1	no	—
84	C₅×#208	—	2	2	no	—
85	C₅×#208	C₂³	1	2	yes	—
86	C₂×C₅×C₃⋊C₈	—	2	2	no	—
87	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
88	C₅×Dic₁₂	—	2	2	no	—
89	C₅×#204	—	2	2	no	—
90	C₅×ΓL(1,𝔽₂₅)	—	2	2	no	—
91	C₅×D₃×C₈	—	2	2	no	—
92	#5836	C₂×C₅	1	2	yes	complemented
93	#5775	C₂×C₅	1	2	yes	complemented
94	C₃×#453	C₂×C₅	1	1	yes	characteristic, complemented
95	#5200	C₂×C₅	1	2	yes	complemented
96	#5077	C₂×C₅	1	1	yes	characteristic, complemented
97	#5076	C₂×C₅	1	1	yes	characteristic, complemented
98	#4826	C₂×C₅	1	2	yes	complemented
99	#4824	C₂×C₅	1	2	yes	complemented
100	#4748	C₂×C₅	1	2	yes	complemented
101	C₅×2₋¹⁺⁴	—	3	2	no	—
102	C₅×H(5,𝔽₂)	—	3	1	no	—
103	C₅×H(5,𝔽₂)	C₂×D₃	1	1	yes	characteristic, complemented
104	C₅×#137	—	3	2	no	—
105	C₅×#137	—	3	2	no	—
106	C₅×#137	—	6	2	no	—
107	C₅×#137	—	6	2	no	—
108	C₅×AGL(1,ℤ/8)	—	3	2	no	—
109	C₅×AGL(1,ℤ/8)	—	6	2	no	—
110	C₅×AGL(1,ℤ/8)	—	6	2	no	—
111	C₅×AGL(1,ℤ/8)	C₂×D₃	1	2	yes	—
112	C₅×#135	—	3	2	no	—
113	C₅×#135	—	6	2	no	—
114	C₅×#135	—	6	2	no	—
115	C₂×C₅×SD₁₆	—	3	2	no	—
116	C₂×C₅×SD₁₆	—	3	2	no	—
117	C₂×C₅×SD₁₆	—	6	2	no	—
118	C₂×C₅×SD₁₆	—	6	2	no	—
119	C₅×#131	—	3	2	no	—
120	C₅×#131	—	3	2	no	—
121	C₅×C₄⋊Q₈	—	3	1	no	—
122	C₅×#127	C₂×D₃	1	1	yes	characteristic
123	C₅×#108	—	3	2	no	—
124	C₅×#104	—	3	2	no	—
125	C₅×#104	C₂×D₃	1	2	yes	complemented
126	C₅×#101	—	3	2	no	—
127	C₅×#100	—	3	1	no	—
128	C₅×#100	C₂×D₃	1	1	yes	characteristic, complemented
129	C₄×C₅×C₈	—	3	1	no	—
130	#3291	—	3	1	no	Sylow
131	C₂³×C₃×C₅	—	2	1	no	—
132	C₂³×C₃×C₅	—	2	1	no	—
133	C₂³×C₃×C₅	—	4	1	no	—
134	C₂²×C₅×D₃	—	4	1	no	—
135	C₃×C₅×Q₈	C₂×D₄	1	2	yes	—
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	—	4	2	no	—
140	C₃×C₅×D₄	—	8	2	no	—
141	C₃×C₅×D₄	C₂×D₄	1	2	yes	—
142	C₂×C₃×C₄×C₅	—	2	1	no	—
143	C₂×C₃×C₄×C₅	—	2	2	no	—
144	C₂×C₃×C₄×C₅	—	4	1	no	—
145	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
146	C₅×#67	—	2	2	no	—
147	C₅×#67	—	4	2	no	—
148	C₅×#67	—	4	2	no	—
149	C₂×C₅×Dic₃	—	2	2	no	—
150	C₂×C₅×Dic₃	—	4	1	no	—
151	C₂×C₅×Dic₃	—	4	2	no	—
152	C₅×D₁₂	C₂×D₄	1	2	yes	—
153	C₄×C₅×D₃	—	2	2	no	—
154	C₄×C₅×D₃	—	4	2	no	—
155	C₅×Dic₆	—	2	2	no	—
156	C₅×Dic₆	—	2	2	no	—
157	C₅×Dic₆	—	4	2	no	—
158	C₅×Dic₆	C₂×D₄	1	2	yes	—
159	C₃×C₅×C₈	—	2	2	no	—
160	C₅×C₃⋊C₈	—	2	2	no	—
161	C₅×C₃⋊C₈	C₂×D₄	1	2	yes	—
162	C₅×C₃⋊C₈	C₂×D₄	1	2	yes	—
163	C₃×H(5,𝔽₂)	C₂²×C₅	1	1	yes	characteristic, complemented
164	#1010	C₂²×C₅	1	2	yes	—
165	#1004	C₂²×C₅	1	1	yes	characteristic, complemented
166	C₃×AGL(1,ℤ/8)	C₂²×C₅	1	2	yes	—
167	C₃×#127	C₂²×C₅	1	1	yes	characteristic
168	#951	—	2	2	no	—
169	#951	C₂²×C₅	1	2	yes	complemented
170	#950	—	2	2	no	—
171	#950	C₂²×C₅	1	2	yes	—
172	#948	C₂²×C₅	1	2	yes	complemented
173	C₂×#214	—	2	2	no	—
174	C₂×#214	C₂²×C₅	1	2	yes	complemented
175	C₂×#214	C₂²×C₅	1	2	yes	complemented
176	#932	—	2	2	no	—
177	#932	C₂²×C₅	1	2	yes	—
178	#915	—	2	2	no	—
179	D₃×SD₁₆	—	2	2	no	—
180	#912	—	2	2	no	—
181	#911	—	2	2	no	—
182	#909	C₂²×C₅	1	2	yes	complemented
183	#907	C₂²×C₅	1	2	yes	complemented
184	#869	C₂²×C₅	1	1	yes	characteristic, complemented
185	C₃×#104	C₂²×C₅	1	2	yes	complemented
186	C₃×#100	C₂²×C₅	1	1	yes	characteristic, complemented
187	#833	C₂²×C₅	1	1	yes	characteristic, complemented
188	#824	C₂²×C₅	1	2	yes	complemented
189	#822	C₂²×C₅	1	2	yes	complemented
190	#805	C₂²×C₅	1	2	yes	complemented
191	C₄×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
192	C₅×#41	—	2	2	no	—
193	C₅×#41	—	3	2	no	—
194	C₅×#41	—	6	2	no	—
195	C₅×#41	—	6	2	no	—
196	C₅×#41	—	6	2	no	—
197	C₅×#41	—	12	2	no	—
198	C₅×#41	C₂²×D₃	1	2	yes	—
199	C₂×C₅×Q₈	—	3	2	no	—
200	C₂×C₅×Q₈	—	6	2	no	—
201	C₂×C₅×Q₈	—	6	2	no	—
202	C₂×C₅×D₄	—	2	2	no	—
203	C₂×C₅×D₄	—	4	1	no	—
204	C₂×C₅×D₄	—	4	1	no	—
205	C₂×C₅×D₄	—	6	2	no	—
206	C₂×C₅×D₄	—	12	1	no	—
207	C₂×C₅×D₄	C₂²×D₃	1	1	yes	characteristic
208	C₂×C₅×D₄	C₂²×D₃	1	1	yes	characteristic
209	C₅×Q₁₆	—	3	2	no	—
210	C₅×Q₁₆	—	6	2	no	—
211	C₅×Q₁₆	—	6	2	no	—
212	C₅×SD₁₆	—	2	2	no	—
213	C₅×SD₁₆	—	3	2	no	—
214	C₅×SD₁₆	—	3	2	no	—
215	C₅×SD₁₆	—	6	2	no	—
216	C₅×SD₁₆	—	6	2	no	—
217	C₅×SD₁₆	—	6	2	no	—
218	C₅×SD₁₆	—	6	2	no	—
219	C₅×SD₁₆	—	6	2	no	—
220	C₅×SD₁₆	—	6	2	no	—
221	C₅×SD₁₆	—	6	2	no	—
222	C₅×D₈	—	2	2	no	—
223	C₅×D₈	—	3	2	no	—
224	C₅×D₈	—	6	2	no	—
225	C₅×M₁₆	—	3	2	no	—
226	C₅×M₁₆	—	6	2	no	—
227	C₅×M₁₆	—	6	2	no	—
228	C₅×M₁₆	C₂²×D₃	1	2	yes	—
229	C₂×C₅×C₈	—	3	2	no	—
230	C₂×C₅×C₈	—	6	2	no	—
231	C₂×C₅×C₈	—	6	2	no	—
232	C₅×C₄⋊C₄	—	12	1	no	—
233	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
234	#577	—	3	2	no	—
235	#577	—	3	2	no	—
236	#492	—	3	1	no	—
237	#471	—	3	2	no	—
238	#471	—	3	2	no	—
239	#456	—	3	2	no	—
240	#453	—	3	1	no	—
241	#453	C₅×D₃	1	1	yes	characteristic, complemented
242	#443	—	3	2	no	—
243	C₂²×C₃×C₅	—	2	2	no	—
244	C₂²×C₃×C₅	—	4	1	no	—
245	C₂²×C₃×C₅	—	4	1	no	—
246	C₂²×C₃×C₅	—	8	1	no	—
247	C₂²×C₃×C₅	—	8	1	no	—
248	C₂²×C₃×C₅	—	16	1	no	—
249	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
250	C₂×C₅×D₃	—	2	2	no	—
251	C₂×C₅×D₃	—	16	1	no	—
252	C₃×C₄×C₅	—	2	2	no	—
253	C₃×C₄×C₅	—	2	2	no	—
254	C₃×C₄×C₅	C₂²×D₄	1	2	yes	—
255	C₅×Dic₃	—	2	2	no	—
256	C₅×Dic₃	—	4	2	no	—
257	C₃×#41	—	2	2	no	—
258	C₃×#41	C₂³×C₅	1	2	yes	—
259	C₂×C₃×D₄	—	2	2	no	—
260	C₂×C₃×D₄	—	4	1	no	—
261	C₂×C₃×D₄	—	4	1	no	—
262	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
263	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
264	C₂×#67	—	4	1	no	—
265	D₃×Q₈	—	2	2	no	—
266	#237	—	2	2	no	—
267	#237	—	2	2	no	—
268	#237	—	4	2	no	—
269	D₃×D₄	—	2	2	no	—
270	#235	—	2	2	no	—
271	#235	C₂³×C₅	1	2	yes	—
272	C₂×Dic₆	—	2	2	no	—
273	C₂×Dic₆	C₂³×C₅	1	2	yes	—
274	C₃×SD₁₆	—	2	2	no	—
275	C₃×D₈	—	2	2	no	—
276	C₃×M₁₆	C₂³×C₅	1	2	yes	—
277	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
278	#216	—	2	2	no	—
279	#216	C₅×D₄	1	2	yes	complemented
280	#215	C₅×D₄	1	2	yes	complemented
281	#214	—	2	2	no	—
282	#214	—	2	2	no	—
283	#214	—	2	2	no	—
284	#214	—	2	2	no	—
285	#214	—	2	2	no	—
286	#214	—	2	2	no	—
287	#214	C₅×D₄	1	2	yes	complemented
288	#213	—	2	2	no	—
289	#213	C₅×D₄	1	2	yes	complemented
290	C₄⋊Dic₃	—	4	1	no	—
291	#208	—	2	2	no	—
292	#208	C₂³×C₅	1	2	yes	—
293	C₂×C₃⋊C₈	—	2	2	no	—
294	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
295	Dic₁₂	—	2	2	no	—
296	#204	—	2	2	no	—
297	ΓL(1,𝔽₂₅)	—	2	2	no	—
298	D₃×C₈	—	2	2	no	—
299	C₂³×C₅	—	2	1	no	—
300	C₂³×C₅	—	2	1	no	—
301	C₂³×C₅	—	4	1	no	—
302	C₂³×C₅	—	12	1	no	—
303	C₅×Q₈	—	3	2	no	—
304	C₅×Q₈	—	6	2	no	—
305	C₅×Q₈	—	6	2	no	—
306	C₅×Q₈	—	12	2	no	—
307	C₅×Q₈	D₃×D₄	1	2	yes	—
308	C₅×D₄	—	2	2	no	—
309	C₅×D₄	—	2	2	no	—
310	C₅×D₄	—	2	2	no	—
311	C₅×D₄	—	3	2	no	—
312	C₅×D₄	—	4	2	no	—
313	C₅×D₄	—	6	2	no	—
314	C₅×D₄	—	8	2	no	—
315	C₅×D₄	—	12	2	no	—
316	C₅×D₄	—	12	2	no	—
317	C₅×D₄	D₃×D₄	1	2	yes	—
318	C₂×C₄×C₅	—	2	1	no	—
319	C₂×C₄×C₅	—	2	2	no	—
320	C₂×C₄×C₅	—	4	1	no	—
321	C₂×C₄×C₅	—	6	2	no	—
322	C₂×C₄×C₅	—	6	2	no	—
323	C₂×C₄×C₅	—	12	2	no	—
324	C₂×C₄×C₅	—	12	1	no	—
325	C₂×C₄×C₅	—	12	2	no	—
326	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
327	C₅×C₈	—	2	2	no	—
328	C₅×C₈	—	3	2	no	—
329	C₅×C₈	—	3	2	no	—
330	C₅×C₈	—	6	2	no	—
331	2₋¹⁺⁴	—	3	2	no	—
332	H(5,𝔽₂)	—	3	1	no	—
333	H(5,𝔽₂)	C₂×C₅×D₃	1	1	yes	characteristic, complemented
334	#137	—	3	2	no	—
335	#137	—	3	2	no	—
336	#137	—	6	2	no	—
337	#137	—	6	2	no	—
338	AGL(1,ℤ/8)	—	3	2	no	—
339	AGL(1,ℤ/8)	—	6	2	no	—
340	AGL(1,ℤ/8)	—	6	2	no	—
341	AGL(1,ℤ/8)	C₂×C₅×D₃	1	2	yes	—
342	#135	—	3	2	no	—
343	#135	—	6	2	no	—
344	#135	—	6	2	no	—
345	C₂×SD₁₆	—	3	2	no	—
346	C₂×SD₁₆	—	3	2	no	—
347	C₂×SD₁₆	—	6	2	no	—
348	C₂×SD₁₆	—	6	2	no	—
349	#131	—	3	2	no	—
350	#131	—	3	2	no	—
351	C₄⋊Q₈	—	3	1	no	—
352	#127	C₂×C₅×D₃	1	1	yes	characteristic
353	#108	—	3	2	no	—
354	#104	—	3	2	no	—
355	#104	C₂×C₅×D₃	1	2	yes	complemented
356	#101	—	3	2	no	—
357	#100	—	3	1	no	—
358	#100	C₂×C₅×D₃	1	1	yes	characteristic, complemented
359	C₄×C₈	—	3	1	no	—
360	C₂×C₃×C₅	—	2	1	no	—
361	C₂×C₃×C₅	—	4	2	no	—
362	C₂×C₃×C₅	—	8	1	no	—
363	C₂×C₃×C₅	—	8	1	no	—
364	C₂×C₃×C₅	D₄²	1	1	yes	characteristic
365	C₅×D₃	—	4	2	no	—
366	C₂³×C₃	—	2	1	no	—
367	C₂³×C₃	—	2	1	no	—
368	C₂³×C₃	—	4	1	no	—
369	C₂²×D₃	—	4	1	no	—
370	C₃×Q₈	C₂×C₅×D₄	1	2	yes	—
371	C₃×D₄	—	2	2	no	—
372	C₃×D₄	—	2	2	no	—
373	C₃×D₄	—	2	2	no	—
374	C₃×D₄	—	4	2	no	—
375	C₃×D₄	—	8	2	no	—
376	C₃×D₄	C₂×C₅×D₄	1	2	yes	—
377	C₂×C₃×C₄	—	2	1	no	—
378	C₂×C₃×C₄	—	2	2	no	—
379	C₂×C₃×C₄	—	4	1	no	—
380	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
381	#67	—	2	2	no	—
382	#67	—	4	2	no	—
383	#67	—	4	2	no	—
384	C₂×Dic₃	—	2	2	no	—
385	C₂×Dic₃	—	4	1	no	—
386	C₂×Dic₃	—	4	2	no	—
387	D₁₂	C₂×C₅×D₄	1	2	yes	—
388	C₄×D₃	—	2	2	no	—
389	C₄×D₃	—	4	2	no	—
390	Dic₆	—	2	2	no	—
391	Dic₆	—	2	2	no	—
392	Dic₆	—	4	2	no	—
393	Dic₆	C₂×C₅×D₄	1	2	yes	—
394	C₃×C₈	—	2	2	no	—
395	C₃⋊C₈	—	2	2	no	—
396	C₃⋊C₈	C₂×C₅×D₄	1	2	yes	—
397	C₃⋊C₈	C₂×C₅×D₄	1	2	yes	—
398	C₂²×C₅	—	2	2	no	—
399	C₂²×C₅	—	4	1	no	—
400	C₂²×C₅	—	4	1	no	—
401	C₂²×C₅	—	6	2	no	—
402	C₂²×C₅	—	8	1	no	—
403	C₂²×C₅	—	8	1	no	—
404	C₂²×C₅	—	16	1	no	—
405	C₂²×C₅	—	48	1	no	—
406	C₂²×C₅	#1004	1	1	yes	characteristic
407	C₄×C₅	—	2	2	no	—
408	C₄×C₅	—	2	2	no	—
409	C₄×C₅	—	6	2	no	—
410	C₄×C₅	—	12	2	no	—
411	C₄×C₅	C₂×D₃×D₄	1	2	yes	—
412	#41	—	2	2	no	—
413	#41	—	3	2	no	—
414	#41	—	6	2	no	—
415	#41	—	6	2	no	—
416	#41	—	6	2	no	—
417	#41	—	12	2	no	—
418	#41	C₂²×C₅×D₃	1	2	yes	—
419	C₂×Q₈	—	3	2	no	—
420	C₂×Q₈	—	6	2	no	—
421	C₂×Q₈	—	6	2	no	—
422	C₂×D₄	—	2	2	no	—
423	C₂×D₄	—	4	1	no	—
424	C₂×D₄	—	4	1	no	—
425	C₂×D₄	—	6	2	no	—
426	C₂×D₄	—	12	1	no	—
427	C₂×D₄	C₂²×C₅×D₃	1	1	yes	characteristic
428	C₂×D₄	C₂²×C₅×D₃	1	1	yes	characteristic
429	Q₁₆	—	3	2	no	—
430	Q₁₆	—	6	2	no	—
431	Q₁₆	—	6	2	no	—
432	SD₁₆	—	2	2	no	—
433	SD₁₆	—	3	2	no	—
434	SD₁₆	—	3	2	no	—
435	SD₁₆	—	6	2	no	—
436	SD₁₆	—	6	2	no	—
437	SD₁₆	—	6	2	no	—
438	SD₁₆	—	6	2	no	—
439	SD₁₆	—	6	2	no	—
440	SD₁₆	—	6	2	no	—
441	SD₁₆	—	6	2	no	—
442	D₈	—	2	2	no	—
443	D₈	—	3	2	no	—
444	D₈	—	6	2	no	—
445	M₁₆	—	3	2	no	—
446	M₁₆	—	6	2	no	—
447	M₁₆	—	6	2	no	—
448	M₁₆	C₂²×C₅×D₃	1	2	yes	—
449	C₂×C₈	—	3	2	no	—
450	C₂×C₈	—	6	2	no	—
451	C₂×C₈	—	6	2	no	—
452	C₄⋊C₄	—	12	1	no	—
453	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
454	C₃×C₅	#3291	1	1	yes	characteristic, complemented, Hall
455	C₂²×C₃	—	2	2	no	—
456	C₂²×C₃	—	4	1	no	—
457	C₂²×C₃	—	4	1	no	—
458	C₂²×C₃	—	8	1	no	—
459	C₂²×C₃	—	8	1	no	—
460	C₂²×C₃	—	16	1	no	—
461	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
462	C₂×D₃	—	2	2	no	—
463	C₂×D₃	—	16	1	no	—
464	C₃×C₄	—	2	2	no	—
465	C₃×C₄	—	2	2	no	—
466	C₃×C₄	C₂²×C₅×D₄	1	2	yes	—
467	Dic₃	—	2	2	no	—
468	Dic₃	—	4	2	no	—
469	C₂×C₅	—	2	1	no	—
470	C₂×C₅	—	4	2	no	—
471	C₂×C₅	—	8	1	no	—
472	C₂×C₅	—	8	1	no	—
473	C₂×C₅	—	12	2	no	—
474	C₂×C₅	#5590	1	1	yes	characteristic
475	C₂³	—	2	1	no	—
476	C₂³	—	2	1	no	—
477	C₂³	—	4	1	no	—
478	C₂³	—	12	1	no	—
479	Q₈	—	3	2	no	—
480	Q₈	—	6	2	no	—
481	Q₈	—	6	2	no	—
482	Q₈	—	12	2	no	—
483	Q₈	C₅×D₃×D₄	1	2	yes	—
484	D₄	—	2	2	no	—
485	D₄	—	2	2	no	—
486	D₄	—	2	2	no	—
487	D₄	—	3	2	no	—
488	D₄	—	4	2	no	—
489	D₄	—	6	2	no	—
490	D₄	—	8	2	no	—
491	D₄	—	12	2	no	—
492	D₄	—	12	2	no	—
493	D₄	C₅×D₃×D₄	1	2	yes	—
494	C₂×C₄	—	2	1	no	—
495	C₂×C₄	—	2	2	no	—
496	C₂×C₄	—	4	1	no	—
497	C₂×C₄	—	6	2	no	—
498	C₂×C₄	—	6	2	no	—
499	C₂×C₄	—	12	2	no	—
500	C₂×C₄	—	12	1	no	—
501	C₂×C₄	—	12	2	no	—
502	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
503	C₈	—	2	2	no	—
504	C₈	—	3	2	no	—
505	C₈	—	3	2	no	—
506	C₈	—	6	2	no	—
507	C₂×C₃	—	2	1	no	—
508	C₂×C₃	—	4	2	no	—
509	C₂×C₃	—	8	1	no	—
510	C₂×C₃	—	8	1	no	—
511	C₂×C₃	C₅×D₄²	1	1	yes	characteristic
512	D₃	—	4	2	no	—
513	C₅	#80281	1	1	yes	characteristic, direct product factor, Sylow
514	C₂²	—	2	2	no	—
515	C₂²	—	4	1	no	—
516	C₂²	—	4	1	no	—
517	C₂²	—	6	2	no	—
518	C₂²	—	8	1	no	—
519	C₂²	—	8	1	no	—
520	C₂²	—	16	1	no	—
521	C₂²	—	48	1	no	—
522	C₂²	C₅×#1004	1	1	yes	characteristic
523	C₄	—	2	2	no	—
524	C₄	—	2	2	no	—
525	C₄	—	6	2	no	—
526	C₄	—	12	2	no	—
527	C₄	C₂×C₅×D₃×D₄	1	2	yes	—
528	C₃	C₅×#3291	1	1	yes	characteristic, complemented, Sylow
529	C₂	—	2	1	no	—
530	C₂	—	4	2	no	—
531	C₂	—	8	1	no	—
532	C₂	—	8	1	no	—
533	C₂	—	12	2	no	—
534	C₂	C₅×#5590	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₅	#5590
commutator, cosocle	C₂×C₃×C₄	C₂⁴×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₃×C₅×#453	C₂
socle	C₂×C₃×C₅	D₄²
hypercenter	C₅×#453	D₃
hypocenter	C₃	C₅×#3291
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₅ ◁ C₂×C₄×C₅ ◁ C₅×#453

Complements

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

N	H ≅ G/N	type
1. C₅×#5836	C₂	semidirect
2. C₅×#5775	C₂	semidirect
3. C₃×C₅×#453	C₂	semidirect
4. C₅×#5200	C₂	semidirect
5. C₅×#5077	C₂	semidirect
6. C₅×#5076	C₂	semidirect
7. C₅×#4826	C₂	semidirect
8. C₅×#4824	C₂	semidirect
9. C₅×#4748	C₂	semidirect
11. C₃×C₅×H(5,𝔽₂)	C₂²	semidirect
13. C₅×#1004	C₂²	semidirect
17. C₅×#951	C₂²	semidirect
20. C₅×#948	C₂²	semidirect
22. C₂×C₅×#214	C₂²	semidirect
23. C₂×C₅×#214	C₂²	semidirect
30. C₅×#909	C₂²	semidirect
31. C₅×#907	C₂²	semidirect
32. C₅×#869	C₂²	semidirect
33. C₃×C₅×#104	C₂²	semidirect
34. C₃×C₅×#100	C₂²	semidirect
35. C₅×#833	C₂²	semidirect
36. C₅×#824	C₂²	semidirect
37. C₅×#822	C₂²	semidirect
38. C₅×#805	C₂²	semidirect
39. C₄×C₅×C₃⋊C₈	C₂²	semidirect
40. #80281	C₅	direct (N × H)
48. C₅×#453	D₃	semidirect
72. C₅×#216	D₄	semidirect
73. C₅×#215	D₄	semidirect
80. C₅×#214	D₄	semidirect
82. C₅×#213	D₄	semidirect
92. #5836	C₂×C₅	semidirect
93. #5775	C₂×C₅	semidirect
94. C₃×#453	C₂×C₅	semidirect
95. #5200	C₂×C₅	semidirect
96. #5077	C₂×C₅	semidirect
97. #5076	C₂×C₅	semidirect
98. #4826	C₂×C₅	semidirect
99. #4824	C₂×C₅	semidirect
100. #4748	C₂×C₅	semidirect
103. C₅×H(5,𝔽₂)	C₂×D₃	semidirect
125. C₅×#104	C₂×D₃	semidirect
128. C₅×#100	C₂×D₃	semidirect
163. C₃×H(5,𝔽₂)	C₂²×C₅	semidirect
165. #1004	C₂²×C₅	semidirect
169. #951	C₂²×C₅	semidirect
172. #948	C₂²×C₅	semidirect
174. C₂×#214	C₂²×C₅	semidirect
175. C₂×#214	C₂²×C₅	semidirect
182. #909	C₂²×C₅	semidirect
183. #907	C₂²×C₅	semidirect
184. #869	C₂²×C₅	semidirect
185. C₃×#104	C₂²×C₅	semidirect
186. C₃×#100	C₂²×C₅	semidirect
187. #833	C₂²×C₅	semidirect
188. #824	C₂²×C₅	semidirect
189. #822	C₂²×C₅	semidirect
190. #805	C₂²×C₅	semidirect
191. C₄×C₃⋊C₈	C₂²×C₅	semidirect
241. #453	C₅×D₃	semidirect
279. #216	C₅×D₄	semidirect
280. #215	C₅×D₄	semidirect
287. #214	C₅×D₄	semidirect
289. #213	C₅×D₄	semidirect
333. H(5,𝔽₂)	C₂×C₅×D₃	semidirect
355. #104	C₂×C₅×D₃	semidirect
358. #100	C₂×C₅×D₃	semidirect
454. C₃×C₅	#3291	semidirect
513. C₅	#80281	direct (N × H)
528. C₃	C₅×#3291	semidirect

Maximal subgroups

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

subgroup	index
C₅×#5836	2
C₅×#5775	2
C₃×C₅×#453	2
C₅×#5200	2
C₅×#5077	2
C₅×#5076	2
C₅×#4826	2
C₅×#4824	2
C₅×#4748	2
C₅×#3291	3
#80281	5

Subgroups — C5×#80281 #14458104

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#80281 #14458104