Subgroups — C₅×#80302 #14458089

Order 1920.

920 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#5837	C₂	1	2	yes	maximal, complemented
2	C₅×#5778	C₂	1	2	yes	maximal, complemented
3	C₃×C₅×#456	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5203	C₂	1	2	yes	maximal, complemented
5	C₅×#5095	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#5085	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#4824	C₂	1	2	yes	maximal, complemented
8	C₅×#4822	C₂	1	2	yes	maximal, complemented
9	C₅×#4754	C₂	1	2	yes	maximal, complemented
10	C₅×#3291	—	3	1	no	maximal, Hall
11	C₃×C₅×2₋¹⁺⁴	C₂²	1	1	yes	characteristic
12	C₅×#1009	C₂²	1	2	yes	complemented
13	C₅×#1007	C₂²	1	1	yes	characteristic
14	C₃×C₅×#137	C₂²	1	2	yes	complemented
15	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
16	C₅×#950	—	2	2	no	—
17	C₅×#950	C₂²	1	2	yes	—
18	C₅×#949	—	2	2	no	—
19	C₅×#949	C₂²	1	2	yes	—
20	C₅×#948	C₂²	1	2	yes	complemented
21	C₅×#942	—	2	2	no	—
22	C₅×#942	C₂²	1	2	yes	complemented
23	C₂×C₅×#215	—	2	2	no	—
24	C₂×C₅×#215	C₂²	1	2	yes	complemented
25	C₂×C₅×#215	C₂²	1	2	yes	complemented
26	C₅×#919	—	2	2	no	—
27	C₅×#918	—	2	2	no	—
28	C₅×#914	—	2	2	no	—
29	C₅×D₃×SD₁₆	—	2	2	no	—
30	C₅×#908	C₂²	1	2	yes	—
31	C₅×#907	C₂²	1	2	yes	complemented
32	C₅×#874	C₂²	1	1	yes	characteristic
33	C₃×C₅×#104	C₂²	1	2	yes	complemented
34	C₃×C₅×#101	C₂²	1	1	yes	characteristic, complemented
35	C₅×#836	C₂²	1	1	yes	characteristic, complemented
36	C₅×#823	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	#80302	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	1	no	—
47	C₅×#456	D₃	1	1	yes	characteristic, complemented
48	C₅×#453	—	3	2	no	—
49	C₅×#443	—	3	2	no	—
50	C₃×C₅×#41	—	2	2	no	—
51	C₃×C₅×#41	—	4	1	no	—
52	C₃×C₅×#41	C₂³	1	2	yes	—
53	C₂×C₃×C₅×Q₈	—	2	2	no	—
54	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
55	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
56	C₅×#239	—	2	2	no	—
57	C₅×#239	—	2	2	no	—
58	C₅×D₃×Q₈	—	2	2	no	—
59	C₅×D₃×D₄	—	2	2	no	—
60	C₅×D₃×D₄	—	4	2	no	—
61	C₅×#235	—	2	2	no	—
62	C₅×#235	—	4	1	no	—
63	C₅×#235	C₂³	1	2	yes	—
64	C₂×C₅×D₁₂	—	2	2	no	—
65	C₂×C₅×D₁₂	—	4	1	no	—
66	C₂×C₅×D₁₂	C₂³	1	2	yes	—
67	C₃×C₅×Q₁₆	—	2	2	no	—
68	C₃×C₅×SD₁₆	—	2	2	no	—
69	C₃×C₅×M₁₆	C₂³	1	2	yes	—
70	C₃×C₅×C₄⋊C₄	—	4	1	no	—
71	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
72	C₅×#216	—	2	2	no	—
73	C₅×#216	D₄	1	2	yes	complemented
74	C₅×#215	—	2	2	no	—
75	C₅×#215	—	2	2	no	—
76	C₅×#215	—	2	2	no	—
77	C₅×#215	—	2	2	no	—
78	C₅×#215	—	2	2	no	—
79	C₅×#215	—	2	2	no	—
80	C₅×#215	D₄	1	2	yes	complemented
81	C₅×#214	D₄	1	2	yes	complemented
82	C₅×#213	—	2	2	no	—
83	C₅×#213	D₄	1	2	yes	complemented
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×D₂₄	—	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	#5837	C₂×C₅	1	2	yes	complemented
93	#5778	C₂×C₅	1	2	yes	complemented
94	C₃×#456	C₂×C₅	1	1	yes	characteristic, complemented
95	#5203	C₂×C₅	1	2	yes	complemented
96	#5095	C₂×C₅	1	1	yes	characteristic, complemented
97	#5085	C₂×C₅	1	1	yes	characteristic, complemented
98	#4824	C₂×C₅	1	2	yes	complemented
99	#4822	C₂×C₅	1	2	yes	complemented
100	#4754	C₂×C₅	1	2	yes	complemented
101	C₅×2₋¹⁺⁴	—	3	1	no	—
102	C₅×2₋¹⁺⁴	C₂×D₃	1	1	yes	characteristic
103	C₅×H(5,𝔽₂)	—	3	2	no	—
104	C₅×#137	—	3	2	no	—
105	C₅×#137	—	6	2	no	—
106	C₅×#137	—	6	2	no	—
107	C₅×#137	C₂×D₃	1	2	yes	complemented
108	C₅×AGL(1,ℤ/8)	—	3	2	no	—
109	C₅×AGL(1,ℤ/8)	—	3	2	no	—
110	C₅×AGL(1,ℤ/8)	—	6	2	no	—
111	C₅×AGL(1,ℤ/8)	—	6	2	no	—
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	C₂×D₃	1	1	yes	characteristic, complemented
122	C₅×#127	—	3	1	no	—
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	1	no	—
127	C₅×#101	C₂×D₃	1	1	yes	characteristic, complemented
128	C₅×#100	—	3	2	no	—
129	C₄×C₅×C₈	—	3	1	no	—
130	#3291	—	3	1	no	Sylow
131	C₂²×C₅×D₃	—	2	2	no	—
132	C₂²×C₅×D₃	—	4	2	no	—
133	C₃×C₅×Q₈	—	2	2	no	—
134	C₃×C₅×Q₈	—	2	2	no	—
135	C₃×C₅×Q₈	—	4	1	no	—
136	C₃×C₅×Q₈	C₂×D₄	1	2	yes	—
137	C₃×C₅×D₄	—	2	2	no	—
138	C₃×C₅×D₄	—	4	1	no	—
139	C₃×C₅×D₄	C₂×D₄	1	2	yes	—
140	C₂×C₃×C₄×C₅	—	2	1	no	—
141	C₂×C₃×C₄×C₅	—	2	2	no	—
142	C₂×C₃×C₄×C₅	—	2	1	no	—
143	C₂×C₃×C₄×C₅	—	2	1	no	—
144	C₂×C₃×C₄×C₅	—	4	2	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×D₁₂	—	2	2	no	—
149	C₅×D₁₂	—	2	2	no	—
150	C₅×D₁₂	—	4	2	no	—
151	C₅×D₁₂	—	4	1	no	—
152	C₅×D₁₂	—	8	2	no	—
153	C₅×D₁₂	C₂×D₄	1	2	yes	—
154	C₄×C₅×D₃	—	2	2	no	—
155	C₄×C₅×D₃	—	4	2	no	—
156	C₄×C₅×D₃	—	4	2	no	—
157	C₅×Dic₆	—	4	1	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	C₃×2₋¹⁺⁴	C₂²×C₅	1	1	yes	characteristic
164	#1009	C₂²×C₅	1	2	yes	complemented
165	#1007	C₂²×C₅	1	1	yes	characteristic
166	C₃×#137	C₂²×C₅	1	2	yes	complemented
167	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
168	#950	—	2	2	no	—
169	#950	C₂²×C₅	1	2	yes	—
170	#949	—	2	2	no	—
171	#949	C₂²×C₅	1	2	yes	—
172	#948	C₂²×C₅	1	2	yes	complemented
173	#942	—	2	2	no	—
174	#942	C₂²×C₅	1	2	yes	complemented
175	C₂×#215	—	2	2	no	—
176	C₂×#215	C₂²×C₅	1	2	yes	complemented
177	C₂×#215	C₂²×C₅	1	2	yes	complemented
178	#919	—	2	2	no	—
179	#918	—	2	2	no	—
180	#914	—	2	2	no	—
181	D₃×SD₁₆	—	2	2	no	—
182	#908	C₂²×C₅	1	2	yes	—
183	#907	C₂²×C₅	1	2	yes	complemented
184	#874	C₂²×C₅	1	1	yes	characteristic
185	C₃×#104	C₂²×C₅	1	2	yes	complemented
186	C₃×#101	C₂²×C₅	1	1	yes	characteristic, complemented
187	#836	C₂²×C₅	1	1	yes	characteristic, complemented
188	#823	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	—	4	1	no	—
195	C₅×#41	—	6	2	no	—
196	C₅×#41	—	6	2	no	—
197	C₅×#41	—	6	2	no	—
198	C₅×#41	—	12	1	no	—
199	C₅×#41	C₂²×D₃	1	2	yes	—
200	C₂×C₅×Q₈	—	2	2	no	—
201	C₂×C₅×Q₈	—	6	2	no	—
202	C₂×C₅×Q₈	C₂²×D₃	1	1	yes	characteristic
203	C₂×C₅×Q₈	C₂²×D₃	1	1	yes	characteristic
204	C₂×C₅×D₄	—	3	2	no	—
205	C₂×C₅×D₄	—	6	2	no	—
206	C₂×C₅×D₄	—	6	2	no	—
207	C₂×C₅×D₄	—	12	1	no	—
208	C₂×C₅×D₄	—	12	2	no	—
209	C₅×Q₁₆	—	2	2	no	—
210	C₅×Q₁₆	—	3	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	—	3	2	no	—
223	C₅×D₈	—	6	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	—	4	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	1	no	—
240	#456	C₅×D₃	1	1	yes	characteristic, complemented
241	#453	—	3	2	no	—
242	#443	—	3	2	no	—
243	C₂²×C₃×C₅	—	2	2	no	—
244	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
245	C₂×C₅×D₃	—	2	2	no	—
246	C₂×C₅×D₃	—	4	2	no	—
247	C₂×C₅×D₃	—	8	2	no	—
248	C₂×C₅×D₃	—	16	2	no	—
249	C₃×C₄×C₅	—	2	2	no	—
250	C₃×C₄×C₅	—	2	2	no	—
251	C₃×C₄×C₅	—	4	1	no	—
252	C₃×C₄×C₅	—	4	1	no	—
253	C₃×C₄×C₅	C₂²×D₄	1	2	yes	—
254	C₅×Dic₃	—	2	2	no	—
255	C₃×#41	—	2	2	no	—
256	C₃×#41	—	4	1	no	—
257	C₃×#41	C₂³×C₅	1	2	yes	—
258	C₂×C₃×Q₈	—	2	2	no	—
259	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
260	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
261	#239	—	2	2	no	—
262	#239	—	2	2	no	—
263	D₃×Q₈	—	2	2	no	—
264	D₃×D₄	—	2	2	no	—
265	D₃×D₄	—	4	2	no	—
266	#235	—	2	2	no	—
267	#235	—	4	1	no	—
268	#235	C₂³×C₅	1	2	yes	—
269	C₂×D₁₂	—	2	2	no	—
270	C₂×D₁₂	—	4	1	no	—
271	C₂×D₁₂	C₂³×C₅	1	2	yes	—
272	C₃×Q₁₆	—	2	2	no	—
273	C₃×SD₁₆	—	2	2	no	—
274	C₃×M₁₆	C₂³×C₅	1	2	yes	—
275	C₃×C₄⋊C₄	—	4	1	no	—
276	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
277	#216	—	2	2	no	—
278	#216	C₅×D₄	1	2	yes	complemented
279	#215	—	2	2	no	—
280	#215	—	2	2	no	—
281	#215	—	2	2	no	—
282	#215	—	2	2	no	—
283	#215	—	2	2	no	—
284	#215	—	2	2	no	—
285	#215	C₅×D₄	1	2	yes	complemented
286	#214	C₅×D₄	1	2	yes	complemented
287	#213	—	2	2	no	—
288	#213	C₅×D₄	1	2	yes	complemented
289	#208	—	2	2	no	—
290	#208	C₂³×C₅	1	2	yes	—
291	C₂×C₃⋊C₈	—	2	2	no	—
292	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
293	D₂₄	—	2	2	no	—
294	#204	—	2	2	no	—
295	ΓL(1,𝔽₂₅)	—	2	2	no	—
296	D₃×C₈	—	2	2	no	—
297	C₂³×C₅	—	6	2	no	—
298	C₂³×C₅	—	12	2	no	—
299	C₅×Q₈	—	2	2	no	—
300	C₅×Q₈	—	2	2	no	—
301	C₅×Q₈	—	3	2	no	—
302	C₅×Q₈	—	4	1	no	—
303	C₅×Q₈	—	12	1	no	—
304	C₅×Q₈	D₃×D₄	1	2	yes	—
305	C₅×D₄	—	2	2	no	—
306	C₅×D₄	—	3	2	no	—
307	C₅×D₄	—	4	1	no	—
308	C₅×D₄	—	6	2	no	—
309	C₅×D₄	—	6	2	no	—
310	C₅×D₄	—	6	2	no	—
311	C₅×D₄	—	12	2	no	—
312	C₅×D₄	—	12	1	no	—
313	C₅×D₄	—	12	2	no	—
314	C₅×D₄	—	24	2	no	—
315	C₅×D₄	D₃×D₄	1	2	yes	—
316	C₂×C₄×C₅	—	2	1	no	—
317	C₂×C₄×C₅	—	2	2	no	—
318	C₂×C₄×C₅	—	2	1	no	—
319	C₂×C₄×C₅	—	2	1	no	—
320	C₂×C₄×C₅	—	4	2	no	—
321	C₂×C₄×C₅	—	6	2	no	—
322	C₂×C₄×C₅	—	12	2	no	—
323	C₂×C₄×C₅	—	12	2	no	—
324	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
325	C₅×C₈	—	2	2	no	—
326	C₅×C₈	—	3	2	no	—
327	C₅×C₈	—	3	2	no	—
328	C₅×C₈	—	6	2	no	—
329	2₋¹⁺⁴	—	3	1	no	—
330	2₋¹⁺⁴	C₂×C₅×D₃	1	1	yes	characteristic
331	H(5,𝔽₂)	—	3	2	no	—
332	#137	—	3	2	no	—
333	#137	—	6	2	no	—
334	#137	—	6	2	no	—
335	#137	C₂×C₅×D₃	1	2	yes	complemented
336	AGL(1,ℤ/8)	—	3	2	no	—
337	AGL(1,ℤ/8)	—	3	2	no	—
338	AGL(1,ℤ/8)	—	6	2	no	—
339	AGL(1,ℤ/8)	—	6	2	no	—
340	#135	—	3	2	no	—
341	#135	—	6	2	no	—
342	#135	—	6	2	no	—
343	C₂×SD₁₆	—	3	2	no	—
344	C₂×SD₁₆	—	3	2	no	—
345	C₂×SD₁₆	—	6	2	no	—
346	C₂×SD₁₆	—	6	2	no	—
347	#131	—	3	2	no	—
348	#131	—	3	2	no	—
349	C₄⋊Q₈	C₂×C₅×D₃	1	1	yes	characteristic, complemented
350	#127	—	3	1	no	—
351	#108	—	3	2	no	—
352	#104	—	3	2	no	—
353	#104	C₂×C₅×D₃	1	2	yes	complemented
354	#101	—	3	1	no	—
355	#101	C₂×C₅×D₃	1	1	yes	characteristic, complemented
356	#100	—	3	2	no	—
357	C₄×C₈	—	3	1	no	—
358	C₂×C₃×C₅	—	2	1	no	—
359	C₂×C₃×C₅	—	4	2	no	—
360	C₂×C₃×C₅	D₄²	1	1	yes	characteristic
361	C₅×D₃	—	4	2	no	—
362	C₅×D₃	—	8	2	no	—
363	C₂²×D₃	—	2	2	no	—
364	C₂²×D₃	—	4	2	no	—
365	C₃×Q₈	—	2	2	no	—
366	C₃×Q₈	—	2	2	no	—
367	C₃×Q₈	—	4	1	no	—
368	C₃×Q₈	C₂×C₅×D₄	1	2	yes	—
369	C₃×D₄	—	2	2	no	—
370	C₃×D₄	—	4	1	no	—
371	C₃×D₄	C₂×C₅×D₄	1	2	yes	—
372	C₂×C₃×C₄	—	2	1	no	—
373	C₂×C₃×C₄	—	2	2	no	—
374	C₂×C₃×C₄	—	2	1	no	—
375	C₂×C₃×C₄	—	2	1	no	—
376	C₂×C₃×C₄	—	4	2	no	—
377	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
378	#67	—	2	2	no	—
379	#67	—	4	2	no	—
380	D₁₂	—	2	2	no	—
381	D₁₂	—	2	2	no	—
382	D₁₂	—	4	2	no	—
383	D₁₂	—	4	1	no	—
384	D₁₂	—	8	2	no	—
385	D₁₂	C₂×C₅×D₄	1	2	yes	—
386	C₄×D₃	—	2	2	no	—
387	C₄×D₃	—	4	2	no	—
388	C₄×D₃	—	4	2	no	—
389	Dic₆	—	4	1	no	—
390	Dic₆	C₂×C₅×D₄	1	2	yes	—
391	C₃×C₈	—	2	2	no	—
392	C₃⋊C₈	—	2	2	no	—
393	C₃⋊C₈	C₂×C₅×D₄	1	2	yes	—
394	C₃⋊C₈	C₂×C₅×D₄	1	2	yes	—
395	C₂²×C₅	—	2	2	no	—
396	C₂²×C₅	—	6	2	no	—
397	C₂²×C₅	—	12	2	no	—
398	C₂²×C₅	—	24	2	no	—
399	C₂²×C₅	—	48	2	no	—
400	C₂²×C₅	#1004	1	1	yes	characteristic
401	C₄×C₅	—	2	2	no	—
402	C₄×C₅	—	2	2	no	—
403	C₄×C₅	—	4	1	no	—
404	C₄×C₅	—	4	1	no	—
405	C₄×C₅	—	6	2	no	—
406	C₄×C₅	C₂×D₃×D₄	1	2	yes	—
407	#41	—	2	2	no	—
408	#41	—	3	2	no	—
409	#41	—	4	1	no	—
410	#41	—	6	2	no	—
411	#41	—	6	2	no	—
412	#41	—	6	2	no	—
413	#41	—	12	1	no	—
414	#41	C₂²×C₅×D₃	1	2	yes	—
415	C₂×Q₈	—	2	2	no	—
416	C₂×Q₈	—	6	2	no	—
417	C₂×Q₈	C₂²×C₅×D₃	1	1	yes	characteristic
418	C₂×Q₈	C₂²×C₅×D₃	1	1	yes	characteristic
419	C₂×D₄	—	3	2	no	—
420	C₂×D₄	—	6	2	no	—
421	C₂×D₄	—	6	2	no	—
422	C₂×D₄	—	12	1	no	—
423	C₂×D₄	—	12	2	no	—
424	Q₁₆	—	2	2	no	—
425	Q₁₆	—	3	2	no	—
426	Q₁₆	—	6	2	no	—
427	SD₁₆	—	2	2	no	—
428	SD₁₆	—	3	2	no	—
429	SD₁₆	—	3	2	no	—
430	SD₁₆	—	6	2	no	—
431	SD₁₆	—	6	2	no	—
432	SD₁₆	—	6	2	no	—
433	SD₁₆	—	6	2	no	—
434	SD₁₆	—	6	2	no	—
435	SD₁₆	—	6	2	no	—
436	SD₁₆	—	6	2	no	—
437	D₈	—	3	2	no	—
438	D₈	—	6	2	no	—
439	D₈	—	6	2	no	—
440	M₁₆	—	3	2	no	—
441	M₁₆	—	6	2	no	—
442	M₁₆	—	6	2	no	—
443	M₁₆	C₂²×C₅×D₃	1	2	yes	—
444	C₂×C₈	—	3	2	no	—
445	C₂×C₈	—	6	2	no	—
446	C₂×C₈	—	6	2	no	—
447	C₄⋊C₄	—	4	1	no	—
448	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
449	C₃×C₅	#3291	1	1	yes	characteristic, complemented, Hall
450	C₂²×C₃	—	2	2	no	—
451	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
452	C₂×D₃	—	2	2	no	—
453	C₂×D₃	—	4	2	no	—
454	C₂×D₃	—	8	2	no	—
455	C₂×D₃	—	16	2	no	—
456	C₃×C₄	—	2	2	no	—
457	C₃×C₄	—	2	2	no	—
458	C₃×C₄	—	4	1	no	—
459	C₃×C₄	—	4	1	no	—
460	C₃×C₄	C₂²×C₅×D₄	1	2	yes	—
461	Dic₃	—	2	2	no	—
462	C₂×C₅	—	2	1	no	—
463	C₂×C₅	—	4	2	no	—
464	C₂×C₅	—	12	2	no	—
465	C₂×C₅	—	24	2	no	—
466	C₂×C₅	#5590	1	1	yes	characteristic
467	C₂³	—	6	2	no	—
468	C₂³	—	12	2	no	—
469	Q₈	—	2	2	no	—
470	Q₈	—	2	2	no	—
471	Q₈	—	3	2	no	—
472	Q₈	—	4	1	no	—
473	Q₈	—	12	1	no	—
474	Q₈	C₅×D₃×D₄	1	2	yes	—
475	D₄	—	2	2	no	—
476	D₄	—	3	2	no	—
477	D₄	—	4	1	no	—
478	D₄	—	6	2	no	—
479	D₄	—	6	2	no	—
480	D₄	—	6	2	no	—
481	D₄	—	12	2	no	—
482	D₄	—	12	1	no	—
483	D₄	—	12	2	no	—
484	D₄	—	24	2	no	—
485	D₄	C₅×D₃×D₄	1	2	yes	—
486	C₂×C₄	—	2	1	no	—
487	C₂×C₄	—	2	2	no	—
488	C₂×C₄	—	2	1	no	—
489	C₂×C₄	—	2	1	no	—
490	C₂×C₄	—	4	2	no	—
491	C₂×C₄	—	6	2	no	—
492	C₂×C₄	—	12	2	no	—
493	C₂×C₄	—	12	2	no	—
494	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
495	C₈	—	2	2	no	—
496	C₈	—	3	2	no	—
497	C₈	—	3	2	no	—
498	C₈	—	6	2	no	—
499	C₂×C₃	—	2	1	no	—
500	C₂×C₃	—	4	2	no	—
501	C₂×C₃	C₅×D₄²	1	1	yes	characteristic
502	D₃	—	4	2	no	—
503	D₃	—	8	2	no	—
504	C₅	#80302	1	1	yes	characteristic, direct product factor, Sylow
505	C₂²	—	2	2	no	—
506	C₂²	—	6	2	no	—
507	C₂²	—	12	2	no	—
508	C₂²	—	24	2	no	—
509	C₂²	—	48	2	no	—
510	C₂²	C₅×#1004	1	1	yes	characteristic
511	C₄	—	2	2	no	—
512	C₄	—	2	2	no	—
513	C₄	—	4	1	no	—
514	C₄	—	4	1	no	—
515	C₄	—	6	2	no	—
516	C₄	C₂×C₅×D₃×D₄	1	2	yes	—
517	C₃	C₅×#3291	1	1	yes	characteristic, complemented, Sylow
518	C₂	—	2	1	no	—
519	C₂	—	4	2	no	—
520	C₂	—	12	2	no	—
521	C₂	—	24	2	no	—
522	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×#456	C₂
socle	C₂×C₃×C₅	D₄²
hypercenter	C₅×#456	D₃
hypocenter	C₃	C₅×#3291
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₅ ◁ C₂×C₄×C₅ ◁ C₅×#456

Complements

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

N	H ≅ G/N	type
1. C₅×#5837	C₂	semidirect
2. C₅×#5778	C₂	semidirect
3. C₃×C₅×#456	C₂	semidirect
4. C₅×#5203	C₂	semidirect
5. C₅×#5095	C₂	semidirect
6. C₅×#5085	C₂	semidirect
7. C₅×#4824	C₂	semidirect
8. C₅×#4822	C₂	semidirect
9. C₅×#4754	C₂	semidirect
12. C₅×#1009	C₂²	semidirect
14. C₃×C₅×#137	C₂²	semidirect
15. C₃×C₅×C₄⋊Q₈	C₂²	semidirect
20. C₅×#948	C₂²	semidirect
22. C₅×#942	C₂²	semidirect
24. C₂×C₅×#215	C₂²	semidirect
25. C₂×C₅×#215	C₂²	semidirect
31. C₅×#907	C₂²	semidirect
33. C₃×C₅×#104	C₂²	semidirect
34. C₃×C₅×#101	C₂²	semidirect
35. C₅×#836	C₂²	semidirect
36. C₅×#823	C₂²	semidirect
37. C₅×#822	C₂²	semidirect
38. C₅×#805	C₂²	semidirect
39. C₄×C₅×C₃⋊C₈	C₂²	semidirect
40. #80302	C₅	direct (N × H)
47. C₅×#456	D₃	semidirect
73. C₅×#216	D₄	semidirect
80. C₅×#215	D₄	semidirect
81. C₅×#214	D₄	semidirect
83. C₅×#213	D₄	semidirect
92. #5837	C₂×C₅	semidirect
93. #5778	C₂×C₅	semidirect
94. C₃×#456	C₂×C₅	semidirect
95. #5203	C₂×C₅	semidirect
96. #5095	C₂×C₅	semidirect
97. #5085	C₂×C₅	semidirect
98. #4824	C₂×C₅	semidirect
99. #4822	C₂×C₅	semidirect
100. #4754	C₂×C₅	semidirect
107. C₅×#137	C₂×D₃	semidirect
121. C₅×C₄⋊Q₈	C₂×D₃	semidirect
125. C₅×#104	C₂×D₃	semidirect
127. C₅×#101	C₂×D₃	semidirect
164. #1009	C₂²×C₅	semidirect
166. C₃×#137	C₂²×C₅	semidirect
167. C₃×C₄⋊Q₈	C₂²×C₅	semidirect
172. #948	C₂²×C₅	semidirect
174. #942	C₂²×C₅	semidirect
176. C₂×#215	C₂²×C₅	semidirect
177. C₂×#215	C₂²×C₅	semidirect
183. #907	C₂²×C₅	semidirect
185. C₃×#104	C₂²×C₅	semidirect
186. C₃×#101	C₂²×C₅	semidirect
187. #836	C₂²×C₅	semidirect
188. #823	C₂²×C₅	semidirect
189. #822	C₂²×C₅	semidirect
190. #805	C₂²×C₅	semidirect
191. C₄×C₃⋊C₈	C₂²×C₅	semidirect
240. #456	C₅×D₃	semidirect
278. #216	C₅×D₄	semidirect
285. #215	C₅×D₄	semidirect
286. #214	C₅×D₄	semidirect
288. #213	C₅×D₄	semidirect
335. #137	C₂×C₅×D₃	semidirect
349. C₄⋊Q₈	C₂×C₅×D₃	semidirect
353. #104	C₂×C₅×D₃	semidirect
355. #101	C₂×C₅×D₃	semidirect
449. C₃×C₅	#3291	semidirect
504. C₅	#80302	direct (N × H)
517. 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×#5837	2
C₅×#5778	2
C₃×C₅×#456	2
C₅×#5203	2
C₅×#5095	2
C₅×#5085	2
C₅×#4824	2
C₅×#4822	2
C₅×#4754	2
C₅×#3291	3
#80302	5

Subgroups — C5×#80302 #14458089

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#80302 #14458089