Subgroups — C₅×#79893 #14458101

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×#5770	C₂	1	2	yes	maximal, complemented
2	C₅×#5751	C₂	1	2	yes	maximal, complemented
3	C₃×C₅×#443	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5141	C₂	1	2	yes	maximal, complemented
5	C₅×#4898	C₂	1	2	yes	maximal, complemented
6	C₅×#4826	C₂	1	2	yes	maximal, complemented
7	C₅×#4822	C₂	1	2	yes	maximal, complemented
8	C₅×#4700	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#4693	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#3291	—	3	1	no	maximal, Hall
11	C₅×#1010	C₂²	1	2	yes	—
12	C₅×#1009	C₂²	1	2	yes	complemented
13	C₃×C₅×#135	C₂²	1	1	yes	characteristic
14	C₃×C₅×#131	C₂²	1	2	yes	complemented
15	C₅×#951	C₂²	1	2	yes	complemented
16	C₅×#949	C₂²	1	2	yes	—
17	C₅×#918	—	2	2	no	—
18	C₅×#916	—	2	2	no	—
19	C₅×D₃×SD₁₆	—	2	2	no	—
20	C₅×#911	—	2	2	no	—
21	C₅×#909	—	2	2	no	—
22	C₅×#909	C₂²	1	2	yes	complemented
23	C₅×#908	—	2	2	no	—
24	C₅×#908	C₂²	1	2	yes	—
25	C₅×#904	—	2	2	no	—
26	C₅×#904	C₂²	1	1	yes	characteristic
27	C₂×C₅×#204	—	2	2	no	—
28	C₂×C₅×#204	C₂²	1	2	yes	complemented
29	C₂×C₅×#204	C₂²	1	2	yes	complemented
30	C₅×#901	C₂²	1	2	yes	complemented
31	C₅×#874	C₂²	1	1	yes	characteristic
32	C₅×#869	C₂²	1	1	yes	characteristic, complemented
33	C₃×C₅×#108	C₂²	1	1	yes	characteristic, complemented
34	C₃×C₅×#104	C₂²	1	2	yes	complemented
35	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic, complemented
36	C₅×#824	C₂²	1	2	yes	complemented
37	C₅×#823	C₂²	1	2	yes	complemented
38	C₅×#819	C₂²	1	1	yes	characteristic, complemented
39	C₅×#805	C₂²	1	2	yes	complemented
40	#79893	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	2	no	—
48	C₅×#443	—	3	1	no	—
49	C₅×#443	D₃	1	1	yes	characteristic, complemented
50	C₃×C₅×#41	C₂³	1	2	yes	—
51	C₅×#239	—	2	2	no	—
52	C₅×D₃×Q₈	—	2	2	no	—
53	C₅×#237	—	2	2	no	—
54	C₅×#237	—	4	2	no	—
55	C₅×D₃×D₄	—	2	2	no	—
56	C₅×D₃×D₄	—	4	2	no	—
57	C₅×#235	—	2	2	no	—
58	C₅×#235	—	2	2	no	—
59	C₅×#235	C₂³	1	2	yes	—
60	C₂×C₅×D₁₂	—	2	2	no	—
61	C₂×C₅×D₁₂	—	4	1	no	—
62	C₂×C₅×D₁₂	C₂³	1	2	yes	—
63	C₂×C₅×Dic₆	—	2	2	no	—
64	C₂×C₅×Dic₆	C₂³	1	2	yes	—
65	C₃×C₅×Q₁₆	D₄	1	1	yes	characteristic, complemented
66	C₃×C₅×SD₁₆	D₄	1	2	yes	complemented
67	C₃×C₅×D₈	D₄	1	1	yes	characteristic, complemented
68	C₃×C₅×M₁₆	—	2	2	no	—
69	C₃×C₅×M₁₆	C₂³	1	2	yes	—
70	C₂×C₃×C₅×C₈	—	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×#216	—	2	2	no	—
75	C₅×#215	—	2	2	no	—
76	C₅×#214	—	2	2	no	—
77	C₅×#213	—	2	2	no	—
78	C₅×C₄⋊Dic₃	—	4	1	no	—
79	C₅×#208	C₂³	1	2	yes	—
80	C₅×Dic₁₂	—	2	2	no	—
81	C₅×Dic₁₂	D₄	1	1	yes	characteristic, complemented
82	C₅×D₂₄	—	2	2	no	—
83	C₅×D₂₄	D₄	1	1	yes	characteristic, complemented
84	C₅×#204	—	2	2	no	—
85	C₅×#204	—	2	2	no	—
86	C₅×#204	—	2	2	no	—
87	C₅×#204	—	2	2	no	—
88	C₅×#204	—	2	2	no	—
89	C₅×#204	—	2	2	no	—
90	C₅×#204	D₄	1	2	yes	complemented
91	C₅×ΓL(1,𝔽₂₅)	—	2	2	no	—
92	C₅×D₃×C₈	—	2	2	no	—
93	#5770	C₂×C₅	1	2	yes	complemented
94	#5751	C₂×C₅	1	2	yes	complemented
95	C₃×#443	C₂×C₅	1	1	yes	characteristic, complemented
96	#5141	C₂×C₅	1	2	yes	complemented
97	#4898	C₂×C₅	1	2	yes	complemented
98	#4826	C₂×C₅	1	2	yes	complemented
99	#4822	C₂×C₅	1	2	yes	complemented
100	#4700	C₂×C₅	1	1	yes	characteristic, complemented
101	#4693	C₂×C₅	1	1	yes	characteristic, complemented
102	C₅×2₋¹⁺⁴	—	3	2	no	—
103	C₅×H(5,𝔽₂)	—	3	2	no	—
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)	—	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	1	no	—
113	C₅×#135	—	6	2	no	—
114	C₅×#135	—	6	2	no	—
115	C₅×#135	C₂×D₃	1	1	yes	characteristic
116	C₂×C₅×SD₁₆	—	3	2	no	—
117	C₂×C₅×SD₁₆	—	3	2	no	—
118	C₂×C₅×SD₁₆	—	6	2	no	—
119	C₂×C₅×SD₁₆	—	6	2	no	—
120	C₅×#131	—	3	2	no	—
121	C₅×#131	C₂×D₃	1	2	yes	complemented
122	C₅×C₄⋊Q₈	—	3	1	no	—
123	C₅×#127	—	3	1	no	—
124	C₅×#108	—	3	1	no	—
125	C₅×#108	C₂×D₃	1	1	yes	characteristic, complemented
126	C₅×#104	—	3	2	no	—
127	C₅×#104	C₂×D₃	1	2	yes	complemented
128	C₅×#101	—	3	2	no	—
129	C₅×#100	—	3	2	no	—
130	C₄×C₅×C₈	C₂×D₃	1	1	yes	characteristic, complemented
131	#3291	—	3	1	no	Sylow
132	C₂²×C₅×D₃	—	2	2	no	—
133	C₂²×C₅×D₃	—	4	2	no	—
134	C₃×C₅×Q₈	C₂×D₄	1	2	yes	—
135	C₃×C₅×D₄	—	2	2	no	—
136	C₃×C₅×D₄	C₂×D₄	1	2	yes	—
137	C₂×C₃×C₄×C₅	—	2	1	no	—
138	C₂×C₃×C₄×C₅	—	2	2	no	—
139	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
140	C₅×#67	—	2	2	no	—
141	C₅×#67	—	4	2	no	—
142	C₅×#67	—	4	2	no	—
143	C₂×C₅×Dic₃	—	2	2	no	—
144	C₂×C₅×Dic₃	—	4	2	no	—
145	C₅×D₁₂	—	2	2	no	—
146	C₅×D₁₂	—	2	2	no	—
147	C₅×D₁₂	—	4	2	no	—
148	C₅×D₁₂	—	8	2	no	—
149	C₅×D₁₂	C₂×D₄	1	2	yes	—
150	C₄×C₅×D₃	—	2	2	no	—
151	C₄×C₅×D₃	—	4	2	no	—
152	C₄×C₅×D₃	—	4	2	no	—
153	C₅×Dic₆	—	2	2	no	—
154	C₅×Dic₆	—	2	2	no	—
155	C₅×Dic₆	—	4	2	no	—
156	C₅×Dic₆	C₂×D₄	1	2	yes	—
157	C₃×C₅×C₈	—	2	2	no	—
158	C₃×C₅×C₈	C₂×D₄	1	1	yes	characteristic
159	C₃×C₅×C₈	C₂×D₄	1	1	yes	characteristic
160	C₃×C₅×C₈	C₂×D₄	1	1	yes	characteristic
161	C₃×C₅×C₈	C₂×D₄	1	1	yes	characteristic
162	C₅×C₃⋊C₈	—	2	2	no	—
163	#1010	C₂²×C₅	1	2	yes	—
164	#1009	C₂²×C₅	1	2	yes	complemented
165	C₃×#135	C₂²×C₅	1	1	yes	characteristic
166	C₃×#131	C₂²×C₅	1	2	yes	complemented
167	#951	C₂²×C₅	1	2	yes	complemented
168	#949	C₂²×C₅	1	2	yes	—
169	#918	—	2	2	no	—
170	#916	—	2	2	no	—
171	D₃×SD₁₆	—	2	2	no	—
172	#911	—	2	2	no	—
173	#909	—	2	2	no	—
174	#909	C₂²×C₅	1	2	yes	complemented
175	#908	—	2	2	no	—
176	#908	C₂²×C₅	1	2	yes	—
177	#904	—	2	2	no	—
178	#904	C₂²×C₅	1	1	yes	characteristic
179	C₂×#204	—	2	2	no	—
180	C₂×#204	C₂²×C₅	1	2	yes	complemented
181	C₂×#204	C₂²×C₅	1	2	yes	complemented
182	#901	C₂²×C₅	1	2	yes	complemented
183	#874	C₂²×C₅	1	1	yes	characteristic
184	#869	C₂²×C₅	1	1	yes	characteristic, complemented
185	C₃×#108	C₂²×C₅	1	1	yes	characteristic, complemented
186	C₃×#104	C₂²×C₅	1	2	yes	complemented
187	C₃×C₄×C₈	C₂²×C₅	1	1	yes	characteristic, complemented
188	#824	C₂²×C₅	1	2	yes	complemented
189	#823	C₂²×C₅	1	2	yes	complemented
190	#819	C₂²×C₅	1	1	yes	characteristic, complemented
191	#805	C₂²×C₅	1	2	yes	complemented
192	C₅×#41	—	3	2	no	—
193	C₅×#41	—	6	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	—	3	2	no	—
203	C₂×C₅×D₄	—	6	2	no	—
204	C₂×C₅×D₄	—	6	2	no	—
205	C₂×C₅×D₄	—	12	1	no	—
206	C₂×C₅×D₄	—	12	2	no	—
207	C₅×Q₁₆	—	3	1	no	—
208	C₅×Q₁₆	—	6	2	no	—
209	C₅×Q₁₆	—	6	2	no	—
210	C₅×Q₁₆	D₁₂	1	1	yes	characteristic, complemented
211	C₅×SD₁₆	—	3	2	no	—
212	C₅×SD₁₆	—	6	2	no	—
213	C₅×SD₁₆	—	6	2	no	—
214	C₅×SD₁₆	—	6	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	D₁₂	1	2	yes	complemented
221	C₅×D₈	—	3	1	no	—
222	C₅×D₈	—	6	2	no	—
223	C₅×D₈	—	6	2	no	—
224	C₅×D₈	D₁₂	1	1	yes	characteristic, complemented
225	C₅×M₁₆	—	2	2	no	—
226	C₅×M₁₆	—	3	2	no	—
227	C₅×M₁₆	—	6	2	no	—
228	C₅×M₁₆	C₂²×D₃	1	2	yes	—
229	C₂×C₅×C₈	—	2	2	no	—
230	C₂×C₅×C₈	—	6	2	no	—
231	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
232	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
233	C₅×C₄⋊C₄	—	12	1	no	—
234	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
235	#577	—	3	2	no	—
236	#577	—	3	2	no	—
237	#492	—	3	1	no	—
238	#471	—	3	2	no	—
239	#471	—	3	2	no	—
240	#456	—	3	2	no	—
241	#453	—	3	2	no	—
242	#443	—	3	1	no	—
243	#443	C₅×D₃	1	1	yes	characteristic, complemented
244	C₂²×C₃×C₅	—	2	2	no	—
245	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
246	C₂×C₅×D₃	—	2	2	no	—
247	C₂×C₅×D₃	—	4	2	no	—
248	C₂×C₅×D₃	—	8	2	no	—
249	C₂×C₅×D₃	—	16	2	no	—
250	C₃×C₄×C₅	—	2	2	no	—
251	C₃×C₄×C₅	—	2	2	no	—
252	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
253	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
254	C₅×Dic₃	—	2	2	no	—
255	C₅×Dic₃	—	4	2	no	—
256	C₃×#41	C₂³×C₅	1	2	yes	—
257	#239	—	2	2	no	—
258	D₃×Q₈	—	2	2	no	—
259	#237	—	2	2	no	—
260	#237	—	4	2	no	—
261	D₃×D₄	—	2	2	no	—
262	D₃×D₄	—	4	2	no	—
263	#235	—	2	2	no	—
264	#235	—	2	2	no	—
265	#235	C₂³×C₅	1	2	yes	—
266	C₂×D₁₂	—	2	2	no	—
267	C₂×D₁₂	—	4	1	no	—
268	C₂×D₁₂	C₂³×C₅	1	2	yes	—
269	C₂×Dic₆	—	2	2	no	—
270	C₂×Dic₆	C₂³×C₅	1	2	yes	—
271	C₃×Q₁₆	C₅×D₄	1	1	yes	characteristic, complemented
272	C₃×SD₁₆	C₅×D₄	1	2	yes	complemented
273	C₃×D₈	C₅×D₄	1	1	yes	characteristic, complemented
274	C₃×M₁₆	—	2	2	no	—
275	C₃×M₁₆	C₂³×C₅	1	2	yes	—
276	C₂×C₃×C₈	—	2	2	no	—
277	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
278	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
279	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
280	#216	—	2	2	no	—
281	#215	—	2	2	no	—
282	#214	—	2	2	no	—
283	#213	—	2	2	no	—
284	C₄⋊Dic₃	—	4	1	no	—
285	#208	C₂³×C₅	1	2	yes	—
286	Dic₁₂	—	2	2	no	—
287	Dic₁₂	C₅×D₄	1	1	yes	characteristic, complemented
288	D₂₄	—	2	2	no	—
289	D₂₄	C₅×D₄	1	1	yes	characteristic, complemented
290	#204	—	2	2	no	—
291	#204	—	2	2	no	—
292	#204	—	2	2	no	—
293	#204	—	2	2	no	—
294	#204	—	2	2	no	—
295	#204	—	2	2	no	—
296	#204	C₅×D₄	1	2	yes	complemented
297	ΓL(1,𝔽₂₅)	—	2	2	no	—
298	D₃×C₈	—	2	2	no	—
299	C₂³×C₅	—	6	2	no	—
300	C₂³×C₅	—	12	2	no	—
301	C₅×Q₈	—	3	2	no	—
302	C₅×Q₈	—	6	2	no	—
303	C₅×Q₈	—	6	2	no	—
304	C₅×Q₈	—	12	2	no	—
305	C₅×Q₈	C₂×D₁₂	1	2	yes	—
306	C₅×D₄	—	2	2	no	—
307	C₅×D₄	—	3	2	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	2	no	—
313	C₅×D₄	—	12	2	no	—
314	C₅×D₄	—	24	2	no	—
315	C₅×D₄	C₂×D₁₂	1	2	yes	—
316	C₂×C₄×C₅	—	2	1	no	—
317	C₂×C₄×C₅	—	2	2	no	—
318	C₂×C₄×C₅	—	6	2	no	—
319	C₂×C₄×C₅	—	6	2	no	—
320	C₂×C₄×C₅	—	12	2	no	—
321	C₂×C₄×C₅	—	12	2	no	—
322	C₂×C₄×C₅	—	12	2	no	—
323	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
324	C₅×C₈	—	2	2	no	—
325	C₅×C₈	—	6	2	no	—
326	C₅×C₈	C₂×D₁₂	1	1	yes	characteristic
327	C₅×C₈	C₂×D₁₂	1	1	yes	characteristic
328	C₅×C₈	D₃×D₄	1	1	yes	characteristic
329	C₅×C₈	D₃×D₄	1	1	yes	characteristic
330	2₋¹⁺⁴	—	3	2	no	—
331	H(5,𝔽₂)	—	3	2	no	—
332	#137	—	3	2	no	—
333	#137	—	3	2	no	—
334	#137	—	6	2	no	—
335	#137	—	6	2	no	—
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	1	no	—
341	#135	—	6	2	no	—
342	#135	—	6	2	no	—
343	#135	C₂×C₅×D₃	1	1	yes	characteristic
344	C₂×SD₁₆	—	3	2	no	—
345	C₂×SD₁₆	—	3	2	no	—
346	C₂×SD₁₆	—	6	2	no	—
347	C₂×SD₁₆	—	6	2	no	—
348	#131	—	3	2	no	—
349	#131	C₂×C₅×D₃	1	2	yes	complemented
350	C₄⋊Q₈	—	3	1	no	—
351	#127	—	3	1	no	—
352	#108	—	3	1	no	—
353	#108	C₂×C₅×D₃	1	1	yes	characteristic, complemented
354	#104	—	3	2	no	—
355	#104	C₂×C₅×D₃	1	2	yes	complemented
356	#101	—	3	2	no	—
357	#100	—	3	2	no	—
358	C₄×C₈	C₂×C₅×D₃	1	1	yes	characteristic, complemented
359	C₂×C₃×C₅	—	2	1	no	—
360	C₂×C₃×C₅	—	4	2	no	—
361	C₂×C₃×C₅	D₄²	1	1	yes	characteristic
362	C₅×D₃	—	4	2	no	—
363	C₅×D₃	—	8	2	no	—
364	C₂²×D₃	—	2	2	no	—
365	C₂²×D₃	—	4	2	no	—
366	C₃×Q₈	C₂×C₅×D₄	1	2	yes	—
367	C₃×D₄	—	2	2	no	—
368	C₃×D₄	C₂×C₅×D₄	1	2	yes	—
369	C₂×C₃×C₄	—	2	1	no	—
370	C₂×C₃×C₄	—	2	2	no	—
371	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
372	#67	—	2	2	no	—
373	#67	—	4	2	no	—
374	#67	—	4	2	no	—
375	C₂×Dic₃	—	2	2	no	—
376	C₂×Dic₃	—	4	2	no	—
377	D₁₂	—	2	2	no	—
378	D₁₂	—	2	2	no	—
379	D₁₂	—	4	2	no	—
380	D₁₂	—	8	2	no	—
381	D₁₂	C₂×C₅×D₄	1	2	yes	—
382	C₄×D₃	—	2	2	no	—
383	C₄×D₃	—	4	2	no	—
384	C₄×D₃	—	4	2	no	—
385	Dic₆	—	2	2	no	—
386	Dic₆	—	2	2	no	—
387	Dic₆	—	4	2	no	—
388	Dic₆	C₂×C₅×D₄	1	2	yes	—
389	C₃×C₈	—	2	2	no	—
390	C₃×C₈	C₂×C₅×D₄	1	1	yes	characteristic
391	C₃×C₈	C₂×C₅×D₄	1	1	yes	characteristic
392	C₃×C₈	C₂×C₅×D₄	1	1	yes	characteristic
393	C₃×C₈	C₂×C₅×D₄	1	1	yes	characteristic
394	C₃⋊C₈	—	2	2	no	—
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	#1009	1	1	yes	characteristic
401	C₄×C₅	—	2	2	no	—
402	C₄×C₅	—	2	2	no	—
403	C₄×C₅	—	6	2	no	—
404	C₄×C₅	—	12	2	no	—
405	C₄×C₅	C₂²×D₁₂	1	1	yes	characteristic
406	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
407	#41	—	3	2	no	—
408	#41	—	6	2	no	—
409	#41	—	6	2	no	—
410	#41	—	6	2	no	—
411	#41	—	6	2	no	—
412	#41	—	12	2	no	—
413	#41	C₂²×C₅×D₃	1	2	yes	—
414	C₂×Q₈	—	3	2	no	—
415	C₂×Q₈	—	6	2	no	—
416	C₂×Q₈	—	6	2	no	—
417	C₂×D₄	—	3	2	no	—
418	C₂×D₄	—	6	2	no	—
419	C₂×D₄	—	6	2	no	—
420	C₂×D₄	—	12	1	no	—
421	C₂×D₄	—	12	2	no	—
422	Q₁₆	—	3	1	no	—
423	Q₁₆	—	6	2	no	—
424	Q₁₆	—	6	2	no	—
425	Q₁₆	C₅×D₁₂	1	1	yes	characteristic, complemented
426	SD₁₆	—	3	2	no	—
427	SD₁₆	—	6	2	no	—
428	SD₁₆	—	6	2	no	—
429	SD₁₆	—	6	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	C₅×D₁₂	1	2	yes	complemented
436	D₈	—	3	1	no	—
437	D₈	—	6	2	no	—
438	D₈	—	6	2	no	—
439	D₈	C₅×D₁₂	1	1	yes	characteristic, complemented
440	M₁₆	—	2	2	no	—
441	M₁₆	—	3	2	no	—
442	M₁₆	—	6	2	no	—
443	M₁₆	C₂²×C₅×D₃	1	2	yes	—
444	C₂×C₈	—	2	2	no	—
445	C₂×C₈	—	6	2	no	—
446	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
447	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
448	C₄⋊C₄	—	12	1	no	—
449	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
450	C₃×C₅	#3291	1	1	yes	characteristic, complemented, Hall
451	C₂²×C₃	—	2	2	no	—
452	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
453	C₂×D₃	—	2	2	no	—
454	C₂×D₃	—	4	2	no	—
455	C₂×D₃	—	8	2	no	—
456	C₂×D₃	—	16	2	no	—
457	C₃×C₄	—	2	2	no	—
458	C₃×C₄	—	2	2	no	—
459	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
460	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
461	Dic₃	—	2	2	no	—
462	Dic₃	—	4	2	no	—
463	C₂×C₅	—	2	1	no	—
464	C₂×C₅	—	4	2	no	—
465	C₂×C₅	—	12	2	no	—
466	C₂×C₅	—	24	2	no	—
467	C₂×C₅	D₄×D₁₂	1	1	yes	characteristic
468	C₂³	—	6	2	no	—
469	C₂³	—	12	2	no	—
470	Q₈	—	3	2	no	—
471	Q₈	—	6	2	no	—
472	Q₈	—	6	2	no	—
473	Q₈	—	12	2	no	—
474	Q₈	C₂×C₅×D₁₂	1	2	yes	—
475	D₄	—	2	2	no	—
476	D₄	—	3	2	no	—
477	D₄	—	6	2	no	—
478	D₄	—	6	2	no	—
479	D₄	—	6	2	no	—
480	D₄	—	12	2	no	—
481	D₄	—	12	2	no	—
482	D₄	—	12	2	no	—
483	D₄	—	24	2	no	—
484	D₄	C₂×C₅×D₁₂	1	2	yes	—
485	C₂×C₄	—	2	1	no	—
486	C₂×C₄	—	2	2	no	—
487	C₂×C₄	—	6	2	no	—
488	C₂×C₄	—	6	2	no	—
489	C₂×C₄	—	12	2	no	—
490	C₂×C₄	—	12	2	no	—
491	C₂×C₄	—	12	2	no	—
492	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
493	C₈	—	2	2	no	—
494	C₈	—	6	2	no	—
495	C₈	C₂×C₅×D₁₂	1	1	yes	characteristic
496	C₈	C₂×C₅×D₁₂	1	1	yes	characteristic
497	C₈	C₅×D₃×D₄	1	1	yes	characteristic
498	C₈	C₅×D₃×D₄	1	1	yes	characteristic
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	#79893	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×#1009	1	1	yes	characteristic
511	C₄	—	2	2	no	—
512	C₄	—	2	2	no	—
513	C₄	—	6	2	no	—
514	C₄	—	12	2	no	—
515	C₄	C₂²×C₅×D₁₂	1	1	yes	characteristic
516	C₄	C₂×C₅×D₃×D₄	1	1	yes	characteristic
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×D₄×D₁₂	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₅	D₄×D₁₂
commutator, cosocle	C₂×C₃×C₄	C₂⁴×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₃×C₅×#443	C₂
socle	C₂×C₃×C₅	D₄²
hypercenter	C₅×#443	D₃
hypocenter	C₃	C₅×#3291
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₅ ◁ C₂×C₄×C₅ ◁ C₅×#443

Complements

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

N	H ≅ G/N	type
1. C₅×#5770	C₂	semidirect
2. C₅×#5751	C₂	semidirect
3. C₃×C₅×#443	C₂	semidirect
4. C₅×#5141	C₂	semidirect
5. C₅×#4898	C₂	semidirect
6. C₅×#4826	C₂	semidirect
7. C₅×#4822	C₂	semidirect
8. C₅×#4700	C₂	semidirect
9. C₅×#4693	C₂	semidirect
12. C₅×#1009	C₂²	semidirect
14. C₃×C₅×#131	C₂²	semidirect
15. C₅×#951	C₂²	semidirect
22. C₅×#909	C₂²	semidirect
28. C₂×C₅×#204	C₂²	semidirect
29. C₂×C₅×#204	C₂²	semidirect
30. C₅×#901	C₂²	semidirect
32. C₅×#869	C₂²	semidirect
33. C₃×C₅×#108	C₂²	semidirect
34. C₃×C₅×#104	C₂²	semidirect
35. C₃×C₄×C₅×C₈	C₂²	semidirect
36. C₅×#824	C₂²	semidirect
37. C₅×#823	C₂²	semidirect
38. C₅×#819	C₂²	semidirect
39. C₅×#805	C₂²	semidirect
40. #79893	C₅	direct (N × H)
49. C₅×#443	D₃	semidirect
65. C₃×C₅×Q₁₆	D₄	semidirect
66. C₃×C₅×SD₁₆	D₄	semidirect
67. C₃×C₅×D₈	D₄	semidirect
81. C₅×Dic₁₂	D₄	semidirect
83. C₅×D₂₄	D₄	semidirect
90. C₅×#204	D₄	semidirect
93. #5770	C₂×C₅	semidirect
94. #5751	C₂×C₅	semidirect
95. C₃×#443	C₂×C₅	semidirect
96. #5141	C₂×C₅	semidirect
97. #4898	C₂×C₅	semidirect
98. #4826	C₂×C₅	semidirect
99. #4822	C₂×C₅	semidirect
100. #4700	C₂×C₅	semidirect
101. #4693	C₂×C₅	semidirect
121. C₅×#131	C₂×D₃	semidirect
125. C₅×#108	C₂×D₃	semidirect
127. C₅×#104	C₂×D₃	semidirect
130. C₄×C₅×C₈	C₂×D₃	semidirect
164. #1009	C₂²×C₅	semidirect
166. C₃×#131	C₂²×C₅	semidirect
167. #951	C₂²×C₅	semidirect
174. #909	C₂²×C₅	semidirect
180. C₂×#204	C₂²×C₅	semidirect
181. C₂×#204	C₂²×C₅	semidirect
182. #901	C₂²×C₅	semidirect
184. #869	C₂²×C₅	semidirect
185. C₃×#108	C₂²×C₅	semidirect
186. C₃×#104	C₂²×C₅	semidirect
187. C₃×C₄×C₈	C₂²×C₅	semidirect
188. #824	C₂²×C₅	semidirect
189. #823	C₂²×C₅	semidirect
190. #819	C₂²×C₅	semidirect
191. #805	C₂²×C₅	semidirect
210. C₅×Q₁₆	D₁₂	semidirect
220. C₅×SD₁₆	D₁₂	semidirect
224. C₅×D₈	D₁₂	semidirect
243. #443	C₅×D₃	semidirect
271. C₃×Q₁₆	C₅×D₄	semidirect
272. C₃×SD₁₆	C₅×D₄	semidirect
273. C₃×D₈	C₅×D₄	semidirect
287. Dic₁₂	C₅×D₄	semidirect
289. D₂₄	C₅×D₄	semidirect
296. #204	C₅×D₄	semidirect
349. #131	C₂×C₅×D₃	semidirect
353. #108	C₂×C₅×D₃	semidirect
355. #104	C₂×C₅×D₃	semidirect
358. C₄×C₈	C₂×C₅×D₃	semidirect
425. Q₁₆	C₅×D₁₂	semidirect
435. SD₁₆	C₅×D₁₂	semidirect
439. D₈	C₅×D₁₂	semidirect
450. C₃×C₅	#3291	semidirect
504. C₅	#79893	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×#5770	2
C₅×#5751	2
C₃×C₅×#443	2
C₅×#5141	2
C₅×#4898	2
C₅×#4826	2
C₅×#4822	2
C₅×#4700	2
C₅×#4693	2
C₅×#3291	3
#79893	5

Subgroups — C5×#79893 #14458101

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#79893 #14458101