Subgroups — C₅×#81885 #14457810

Order 1920.

896 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	C₅×#5766	C₂	1	2	yes	maximal, complemented
2	C₅×#5762	C₂	1	2	yes	maximal, complemented
3	C₃×C₅×#497	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5192	C₂	1	2	yes	maximal, complemented
5	C₅×#5177	C₂	1	2	yes	maximal, complemented
6	C₅×#5095	C₂	1	2	yes	maximal, complemented
7	C₅×#5062	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#5061	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#4717	C₂	1	2	yes	maximal, complemented
10	C₅×#3289	—	3	1	no	maximal, Hall
11	C₅×#1007	C₂²	1	2	yes	—
12	C₅×#1007	C₂²	1	1	yes	characteristic, complemented
13	C₅×#1004	C₂²	1	1	yes	characteristic
14	C₂×C₃×C₅×Q₁₆	C₂²	1	2	yes	complemented
15	C₂×C₃×C₅×SD₁₆	C₂²	1	2	yes	—
16	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
17	C₃×C₅×#124	C₂²	1	1	yes	characteristic
18	C₅×#942	C₂²	1	2	yes	—
19	C₅×#942	C₂²	1	2	yes	—
20	C₅×#942	C₂²	1	2	yes	complemented
21	C₅×#932	C₂²	1	2	yes	—
22	C₅×#919	—	2	2	no	—
23	C₅×#918	—	2	2	no	—
24	C₅×#918	—	2	2	no	—
25	C₅×D₃×Q₁₆	—	2	2	no	—
26	C₅×#916	—	2	2	no	—
27	C₅×#915	—	2	2	no	—
28	C₅×#914	—	2	2	no	—
29	C₅×D₃×SD₁₆	—	2	2	no	—
30	C₅×#904	C₂²	1	2	yes	—
31	C₅×#901	C₂²	1	2	yes	—
32	C₅×#901	C₂²	1	2	yes	complemented
33	C₃×C₅×#97	C₂²	1	1	yes	characteristic, complemented
34	C₅×#836	C₂²	1	2	yes	complemented
35	C₅×#836	C₂²	1	1	yes	characteristic, complemented
36	C₅×#833	C₂²	1	1	yes	characteristic
37	C₅×#819	C₂²	1	2	yes	complemented
38	C₅×#805	C₂²	1	2	yes	—
39	C₅×#805	C₂²	1	2	yes	complemented
40	#81885	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
41	C₅×#578	—	3	2	no	—
42	C₅×#577	—	3	2	no	—
43	C₅×#497	D₃	1	1	yes	characteristic, complemented
44	C₅×#473	—	3	2	no	—
45	C₅×#471	—	3	2	no	—
46	C₅×#456	—	3	2	no	—
47	C₅×#455	—	3	1	no	—
48	C₅×#454	—	3	1	no	—
49	C₅×#444	—	3	2	no	—
50	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
51	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
52	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
53	C₂×C₅×#67	—	4	1	no	—
54	C₅×#239	—	2	2	no	—
55	C₅×#239	—	2	2	no	—
56	C₅×#239	—	2	2	no	—
57	C₅×D₃×Q₈	—	2	2	no	—
58	C₅×D₃×Q₈	—	2	2	no	—
59	C₅×D₃×Q₈	—	2	2	no	—
60	C₅×#237	—	2	2	no	—
61	C₅×D₃×D₄	—	2	2	no	—
62	C₅×#235	—	4	2	no	—
63	C₅×#235	—	4	1	no	—
64	C₅×#235	C₂³	1	2	yes	—
65	C₅×#235	C₂³	1	2	yes	—
66	C₃×C₅×Q₁₆	—	2	2	no	—
67	C₃×C₅×Q₁₆	—	2	2	no	—
68	C₃×C₅×SD₁₆	—	2	2	no	—
69	C₃×C₅×SD₁₆	—	2	2	no	—
70	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
71	C₃×C₅×C₄⋊C₄	—	4	1	no	—
72	C₃×C₅×C₂²⋊C₄	—	4	1	no	—
73	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
74	C₅×#216	—	2	2	no	—
75	C₅×#216	—	2	2	no	—
76	C₅×#216	—	2	2	no	—
77	C₅×#215	—	2	2	no	—
78	C₅×#215	—	2	2	no	—
79	C₅×#215	—	2	2	no	—
80	C₅×#214	—	2	2	no	—
81	C₅×#213	—	2	2	no	—
82	C₅×#208	C₂³	1	2	yes	—
83	C₅×#208	C₂³	1	2	yes	—
84	C₅×Dic₁₂	D₄	1	2	yes	—
85	C₅×D₂₄	D₄	1	2	yes	—
86	C₅×#204	D₄	1	2	yes	—
87	C₅×#204	D₄	1	2	yes	—
88	C₅×ΓL(1,𝔽₂₅)	—	2	2	no	—
89	C₅×ΓL(1,𝔽₂₅)	—	2	2	no	—
90	C₅×D₃×C₈	—	2	2	no	—
91	C₅×D₃×C₈	—	2	2	no	—
92	#5766	C₂×C₅	1	2	yes	complemented
93	#5762	C₂×C₅	1	2	yes	complemented
94	C₃×#497	C₂×C₅	1	1	yes	characteristic, complemented
95	#5192	C₂×C₅	1	2	yes	complemented
96	#5177	C₂×C₅	1	2	yes	complemented
97	#5095	C₂×C₅	1	2	yes	complemented
98	#5062	C₂×C₅	1	1	yes	characteristic, complemented
99	#5061	C₂×C₅	1	1	yes	characteristic, complemented
100	#4717	C₂×C₅	1	2	yes	complemented
101	C₅×2₋¹⁺⁴	—	3	1	no	—
102	C₅×2₋¹⁺⁴	—	3	2	no	—
103	C₅×H(5,𝔽₂)	—	3	1	no	—
104	C₅×#137	—	3	2	no	—
105	C₅×#137	—	3	2	no	—
106	C₅×#137	—	3	2	no	—
107	C₅×#137	—	6	2	no	—
108	C₅×#137	—	6	2	no	—
109	C₅×#137	—	6	2	no	—
110	C₅×AGL(1,ℤ/8)	—	3	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×Q₁₆	—	6	2	no	—
116	C₂×C₅×Q₁₆	C₂×D₃	1	2	yes	complemented
117	C₂×C₅×SD₁₆	—	6	2	no	—
118	C₂×C₅×SD₁₆	C₂×D₃	1	2	yes	—
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×#124	C₂×D₃	1	1	yes	characteristic
123	C₅×#108	—	3	2	no	—
124	C₅×#104	—	3	2	no	—
125	C₅×#104	—	3	2	no	—
126	C₅×#101	—	3	1	no	—
127	C₅×#101	—	3	2	no	—
128	C₅×#100	—	3	1	no	—
129	C₅×#97	C₂×D₃	1	1	yes	characteristic, complemented
130	#3289	—	3	1	no	Sylow
131	C₂³×C₃×C₅	—	2	1	no	—
132	C₂²×C₅×D₃	—	4	1	no	—
133	C₃×C₅×Q₈	—	2	2	no	—
134	C₃×C₅×Q₈	—	2	2	no	—
135	C₃×C₅×Q₈	—	2	2	no	—
136	C₃×C₅×D₄	—	2	2	no	—
137	C₂×C₃×C₄×C₅	—	2	1	no	—
138	C₂×C₃×C₄×C₅	—	2	1	no	—
139	C₂×C₃×C₄×C₅	—	2	2	no	—
140	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
141	C₅×#67	—	2	2	no	—
142	C₅×#67	—	2	2	no	—
143	C₅×#67	—	4	2	no	—
144	C₂×C₅×Dic₃	—	4	1	no	—
145	C₅×D₁₂	—	4	1	no	—
146	C₅×D₁₂	—	4	2	no	—
147	C₅×D₁₂	C₂×D₄	1	2	yes	—
148	C₅×D₁₂	C₂×D₄	1	2	yes	—
149	C₄×C₅×D₃	—	2	2	no	—
150	C₄×C₅×D₃	—	2	2	no	—
151	C₄×C₅×D₃	—	4	2	no	—
152	C₄×C₅×D₃	—	4	2	no	—
153	C₄×C₅×D₃	—	4	2	no	—
154	C₅×Dic₆	—	4	1	no	—
155	C₅×Dic₆	—	4	2	no	—
156	C₅×Dic₆	C₂×D₄	1	2	yes	—
157	C₅×Dic₆	C₂×D₄	1	2	yes	—
158	C₃×C₅×C₈	C₂×D₄	1	2	yes	—
159	C₃×C₅×C₈	C₂×D₄	1	2	yes	—
160	C₅×C₃⋊C₈	—	2	2	no	—
161	C₅×C₃⋊C₈	—	2	2	no	—
162	#1007	C₂²×C₅	1	2	yes	—
163	#1007	C₂²×C₅	1	1	yes	characteristic, complemented
164	#1004	C₂²×C₅	1	1	yes	characteristic
165	C₂×C₃×Q₁₆	C₂²×C₅	1	2	yes	complemented
166	C₂×C₃×SD₁₆	C₂²×C₅	1	2	yes	—
167	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
168	C₃×#124	C₂²×C₅	1	1	yes	characteristic
169	#942	C₂²×C₅	1	2	yes	—
170	#942	C₂²×C₅	1	2	yes	—
171	#942	C₂²×C₅	1	2	yes	complemented
172	#932	C₂²×C₅	1	2	yes	—
173	#919	—	2	2	no	—
174	#918	—	2	2	no	—
175	#918	—	2	2	no	—
176	D₃×Q₁₆	—	2	2	no	—
177	#916	—	2	2	no	—
178	#915	—	2	2	no	—
179	#914	—	2	2	no	—
180	D₃×SD₁₆	—	2	2	no	—
181	#904	C₂²×C₅	1	2	yes	—
182	#901	C₂²×C₅	1	2	yes	—
183	#901	C₂²×C₅	1	2	yes	complemented
184	C₃×#97	C₂²×C₅	1	1	yes	characteristic, complemented
185	#836	C₂²×C₅	1	2	yes	complemented
186	#836	C₂²×C₅	1	1	yes	characteristic, complemented
187	#833	C₂²×C₅	1	1	yes	characteristic
188	#819	C₂²×C₅	1	2	yes	complemented
189	#805	C₂²×C₅	1	2	yes	—
190	#805	C₂²×C₅	1	2	yes	complemented
191	C₅×#41	—	3	2	no	—
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	1	no	—
198	C₅×#41	—	12	2	no	—
199	C₂×C₅×Q₈	—	6	2	no	—
200	C₂×C₅×Q₈	—	6	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	2	yes	—
204	C₂×C₅×D₄	—	6	2	no	—
205	C₂×C₅×D₄	—	12	1	no	—
206	C₂×C₅×D₄	C₂²×D₃	1	1	yes	characteristic
207	C₅×Q₁₆	—	2	2	no	—
208	C₅×Q₁₆	—	2	2	no	—
209	C₅×Q₁₆	—	3	2	no	—
210	C₅×Q₁₆	—	6	2	no	—
211	C₅×Q₁₆	—	6	2	no	—
212	C₅×Q₁₆	—	6	2	no	—
213	C₅×SD₁₆	—	2	2	no	—
214	C₅×SD₁₆	—	2	2	no	—
215	C₅×SD₁₆	—	3	2	no	—
216	C₅×SD₁₆	—	3	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×D₈	—	3	2	no	—
222	C₅×D₈	—	6	2	no	—
223	C₅×M₁₆	—	3	2	no	—
224	C₅×M₁₆	—	3	2	no	—
225	C₅×M₁₆	—	6	2	no	—
226	C₅×M₁₆	—	6	2	no	—
227	C₂×C₅×C₈	—	6	2	no	—
228	C₂×C₅×C₈	—	6	2	no	—
229	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
230	C₅×C₄⋊C₄	—	4	1	no	—
231	C₅×C₂²⋊C₄	—	4	1	no	—
232	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
233	#578	—	3	2	no	—
234	#577	—	3	2	no	—
235	#497	C₅×D₃	1	1	yes	characteristic, complemented
236	#473	—	3	2	no	—
237	#471	—	3	2	no	—
238	#456	—	3	2	no	—
239	#455	—	3	1	no	—
240	#454	—	3	1	no	—
241	#444	—	3	2	no	—
242	C₂²×C₃×C₅	—	4	1	no	—
243	C₂²×C₃×C₅	—	8	1	no	—
244	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
245	C₂×C₅×D₃	—	2	2	no	—
246	C₂×C₅×D₃	—	2	2	no	—
247	C₂×C₅×D₃	—	16	1	no	—
248	C₃×C₄×C₅	—	4	1	no	—
249	C₃×C₄×C₅	—	4	1	no	—
250	C₃×C₄×C₅	—	4	2	no	—
251	C₃×C₄×C₅	C₂²×D₄	1	2	yes	—
252	C₅×Dic₃	—	2	2	no	—
253	C₅×Dic₃	—	2	2	no	—
254	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
255	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
256	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
257	C₂×#67	—	4	1	no	—
258	#239	—	2	2	no	—
259	#239	—	2	2	no	—
260	#239	—	2	2	no	—
261	D₃×Q₈	—	2	2	no	—
262	D₃×Q₈	—	2	2	no	—
263	D₃×Q₈	—	2	2	no	—
264	#237	—	2	2	no	—
265	D₃×D₄	—	2	2	no	—
266	#235	—	4	2	no	—
267	#235	—	4	1	no	—
268	#235	C₂³×C₅	1	2	yes	—
269	#235	C₂³×C₅	1	2	yes	—
270	C₃×Q₁₆	—	2	2	no	—
271	C₃×Q₁₆	—	2	2	no	—
272	C₃×SD₁₆	—	2	2	no	—
273	C₃×SD₁₆	—	2	2	no	—
274	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
275	C₃×C₄⋊C₄	—	4	1	no	—
276	C₃×C₂²⋊C₄	—	4	1	no	—
277	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
278	#216	—	2	2	no	—
279	#216	—	2	2	no	—
280	#216	—	2	2	no	—
281	#215	—	2	2	no	—
282	#215	—	2	2	no	—
283	#215	—	2	2	no	—
284	#214	—	2	2	no	—
285	#213	—	2	2	no	—
286	#208	C₂³×C₅	1	2	yes	—
287	#208	C₂³×C₅	1	2	yes	—
288	Dic₁₂	C₅×D₄	1	2	yes	—
289	D₂₄	C₅×D₄	1	2	yes	—
290	#204	C₅×D₄	1	2	yes	—
291	#204	C₅×D₄	1	2	yes	—
292	ΓL(1,𝔽₂₅)	—	2	2	no	—
293	ΓL(1,𝔽₂₅)	—	2	2	no	—
294	D₃×C₈	—	2	2	no	—
295	D₃×C₈	—	2	2	no	—
296	C₂³×C₅	—	2	1	no	—
297	C₂³×C₅	—	12	1	no	—
298	C₅×Q₈	—	2	2	no	—
299	C₅×Q₈	—	2	2	no	—
300	C₅×Q₈	—	2	2	no	—
301	C₅×Q₈	—	3	2	no	—
302	C₅×Q₈	—	3	2	no	—
303	C₅×Q₈	—	12	2	no	—
304	C₅×Q₈	—	12	1	no	—
305	C₅×D₄	—	2	2	no	—
306	C₅×D₄	—	3	2	no	—
307	C₅×D₄	—	3	2	no	—
308	C₅×D₄	—	6	2	no	—
309	C₅×D₄	—	6	2	no	—
310	C₅×D₄	—	12	1	no	—
311	C₅×D₄	—	12	2	no	—
312	C₅×D₄	—	12	2	no	—
313	C₂×C₄×C₅	—	2	1	no	—
314	C₂×C₄×C₅	—	2	1	no	—
315	C₂×C₄×C₅	—	2	2	no	—
316	C₂×C₄×C₅	—	6	2	no	—
317	C₂×C₄×C₅	—	6	2	no	—
318	C₂×C₄×C₅	—	12	2	no	—
319	C₂×C₄×C₅	—	12	2	no	—
320	C₂×C₄×C₅	—	12	2	no	—
321	C₂×C₄×C₅	—	12	1	no	—
322	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
323	C₅×C₈	—	6	2	no	—
324	C₅×C₈	—	6	2	no	—
325	C₅×C₈	D₃×D₄	1	2	yes	—
326	C₅×C₈	D₃×D₄	1	2	yes	—
327	2₋¹⁺⁴	—	3	2	no	—
328	2₋¹⁺⁴	—	3	1	no	—
329	H(5,𝔽₂)	—	3	1	no	—
330	#137	—	3	2	no	—
331	#137	—	3	2	no	—
332	#137	—	3	2	no	—
333	#137	—	6	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)	—	6	2	no	—
338	#135	—	3	2	no	—
339	#135	—	6	2	no	—
340	#135	—	6	2	no	—
341	C₂×Q₁₆	—	6	2	no	—
342	C₂×Q₁₆	C₂×C₅×D₃	1	2	yes	complemented
343	C₂×SD₁₆	—	6	2	no	—
344	C₂×SD₁₆	C₂×C₅×D₃	1	2	yes	—
345	#131	—	3	2	no	—
346	#131	—	3	2	no	—
347	C₄⋊Q₈	C₂×C₅×D₃	1	1	yes	characteristic, complemented
348	#124	C₂×C₅×D₃	1	1	yes	characteristic
349	#108	—	3	2	no	—
350	#104	—	3	2	no	—
351	#104	—	3	2	no	—
352	#101	—	3	1	no	—
353	#101	—	3	2	no	—
354	#100	—	3	1	no	—
355	#97	C₂×C₅×D₃	1	1	yes	characteristic, complemented
356	C₂×C₃×C₅	—	2	1	no	—
357	C₂×C₃×C₅	—	8	1	no	—
358	C₂×C₃×C₅	D₄²	1	1	yes	characteristic
359	C₅×D₃	—	4	2	no	—
360	C₅×D₃	—	4	2	no	—
361	C₂³×C₃	—	2	1	no	—
362	C₂²×D₃	—	4	1	no	—
363	C₃×Q₈	—	2	2	no	—
364	C₃×Q₈	—	2	2	no	—
365	C₃×Q₈	—	2	2	no	—
366	C₃×D₄	—	2	2	no	—
367	C₂×C₃×C₄	—	2	1	no	—
368	C₂×C₃×C₄	—	2	1	no	—
369	C₂×C₃×C₄	—	2	2	no	—
370	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
371	#67	—	2	2	no	—
372	#67	—	2	2	no	—
373	#67	—	4	2	no	—
374	C₂×Dic₃	—	4	1	no	—
375	D₁₂	—	4	1	no	—
376	D₁₂	—	4	2	no	—
377	D₁₂	C₂×C₅×D₄	1	2	yes	—
378	D₁₂	C₂×C₅×D₄	1	2	yes	—
379	C₄×D₃	—	2	2	no	—
380	C₄×D₃	—	2	2	no	—
381	C₄×D₃	—	4	2	no	—
382	C₄×D₃	—	4	2	no	—
383	C₄×D₃	—	4	2	no	—
384	Dic₆	—	4	1	no	—
385	Dic₆	—	4	2	no	—
386	Dic₆	C₂×C₅×D₄	1	2	yes	—
387	Dic₆	C₂×C₅×D₄	1	2	yes	—
388	C₃×C₈	C₂×C₅×D₄	1	2	yes	—
389	C₃×C₈	C₂×C₅×D₄	1	2	yes	—
390	C₃⋊C₈	—	2	2	no	—
391	C₃⋊C₈	—	2	2	no	—
392	C₂²×C₅	—	4	1	no	—
393	C₂²×C₅	—	6	2	no	—
394	C₂²×C₅	—	6	2	no	—
395	C₂²×C₅	—	8	1	no	—
396	C₂²×C₅	—	48	1	no	—
397	C₂²×C₅	#1004	1	1	yes	characteristic
398	C₄×C₅	—	4	1	no	—
399	C₄×C₅	—	4	1	no	—
400	C₄×C₅	—	4	2	no	—
401	C₄×C₅	—	6	2	no	—
402	C₄×C₅	—	6	2	no	—
403	C₄×C₅	C₂×D₃×D₄	1	2	yes	—
404	#41	—	3	2	no	—
405	#41	—	3	2	no	—
406	#41	—	6	2	no	—
407	#41	—	6	2	no	—
408	#41	—	6	2	no	—
409	#41	—	6	2	no	—
410	#41	—	12	1	no	—
411	#41	—	12	2	no	—
412	C₂×Q₈	—	6	2	no	—
413	C₂×Q₈	—	6	2	no	—
414	C₂×Q₈	—	6	2	no	—
415	C₂×Q₈	C₂²×C₅×D₃	1	1	yes	characteristic
416	C₂×Q₈	C₂²×C₅×D₃	1	2	yes	—
417	C₂×D₄	—	6	2	no	—
418	C₂×D₄	—	12	1	no	—
419	C₂×D₄	C₂²×C₅×D₃	1	1	yes	characteristic
420	Q₁₆	—	2	2	no	—
421	Q₁₆	—	2	2	no	—
422	Q₁₆	—	3	2	no	—
423	Q₁₆	—	6	2	no	—
424	Q₁₆	—	6	2	no	—
425	Q₁₆	—	6	2	no	—
426	SD₁₆	—	2	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	D₈	—	3	2	no	—
435	D₈	—	6	2	no	—
436	M₁₆	—	3	2	no	—
437	M₁₆	—	3	2	no	—
438	M₁₆	—	6	2	no	—
439	M₁₆	—	6	2	no	—
440	C₂×C₈	—	6	2	no	—
441	C₂×C₈	—	6	2	no	—
442	C₂×C₈	C₂²×C₅×D₃	1	2	yes	—
443	C₄⋊C₄	—	4	1	no	—
444	C₂²⋊C₄	—	4	1	no	—
445	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
446	C₃×C₅	#3289	1	1	yes	characteristic, complemented, Hall
447	C₂²×C₃	—	4	1	no	—
448	C₂²×C₃	—	8	1	no	—
449	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
450	C₂×D₃	—	2	2	no	—
451	C₂×D₃	—	2	2	no	—
452	C₂×D₃	—	16	1	no	—
453	C₃×C₄	—	4	1	no	—
454	C₃×C₄	—	4	1	no	—
455	C₃×C₄	—	4	2	no	—
456	C₃×C₄	C₂²×C₅×D₄	1	2	yes	—
457	Dic₃	—	2	2	no	—
458	Dic₃	—	2	2	no	—
459	C₂×C₅	—	2	1	no	—
460	C₂×C₅	—	8	1	no	—
461	C₂×C₅	—	12	2	no	—
462	C₂×C₅	—	12	2	no	—
463	C₂×C₅	#5717	1	1	yes	characteristic
464	C₂³	—	2	1	no	—
465	C₂³	—	12	1	no	—
466	Q₈	—	2	2	no	—
467	Q₈	—	2	2	no	—
468	Q₈	—	2	2	no	—
469	Q₈	—	3	2	no	—
470	Q₈	—	3	2	no	—
471	Q₈	—	12	2	no	—
472	Q₈	—	12	1	no	—
473	D₄	—	2	2	no	—
474	D₄	—	3	2	no	—
475	D₄	—	3	2	no	—
476	D₄	—	6	2	no	—
477	D₄	—	6	2	no	—
478	D₄	—	12	1	no	—
479	D₄	—	12	2	no	—
480	D₄	—	12	2	no	—
481	C₂×C₄	—	2	1	no	—
482	C₂×C₄	—	2	1	no	—
483	C₂×C₄	—	2	2	no	—
484	C₂×C₄	—	6	2	no	—
485	C₂×C₄	—	6	2	no	—
486	C₂×C₄	—	12	2	no	—
487	C₂×C₄	—	12	2	no	—
488	C₂×C₄	—	12	2	no	—
489	C₂×C₄	—	12	1	no	—
490	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
491	C₈	—	6	2	no	—
492	C₈	—	6	2	no	—
493	C₈	C₅×D₃×D₄	1	2	yes	—
494	C₈	C₅×D₃×D₄	1	2	yes	—
495	C₂×C₃	—	2	1	no	—
496	C₂×C₃	—	8	1	no	—
497	C₂×C₃	C₅×D₄²	1	1	yes	characteristic
498	D₃	—	4	2	no	—
499	D₃	—	4	2	no	—
500	C₅	#81885	1	1	yes	characteristic, direct product factor, Sylow
501	C₂²	—	4	1	no	—
502	C₂²	—	6	2	no	—
503	C₂²	—	6	2	no	—
504	C₂²	—	8	1	no	—
505	C₂²	—	48	1	no	—
506	C₂²	C₅×#1004	1	1	yes	characteristic
507	C₄	—	4	1	no	—
508	C₄	—	4	1	no	—
509	C₄	—	4	2	no	—
510	C₄	—	6	2	no	—
511	C₄	—	6	2	no	—
512	C₄	C₂×C₅×D₃×D₄	1	2	yes	—
513	C₃	C₅×#3289	1	1	yes	characteristic, complemented, Sylow
514	C₂	—	2	1	no	—
515	C₂	—	8	1	no	—
516	C₂	—	12	2	no	—
517	C₂	—	12	2	no	—
518	C₂	C₅×#5717	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₅	#5717
commutator, cosocle	C₂×C₃×C₄	C₂⁴×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₃×C₅×#497	C₂
socle	C₂×C₃×C₅	D₄²
hypercenter	C₅×#497	D₃
hypocenter	C₃	C₅×#3289
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₅ ◁ C₂×C₄×C₅ ◁ C₅×#497

Complements

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

N	H ≅ G/N	type
1. C₅×#5766	C₂	semidirect
2. C₅×#5762	C₂	semidirect
3. C₃×C₅×#497	C₂	semidirect
4. C₅×#5192	C₂	semidirect
5. C₅×#5177	C₂	semidirect
6. C₅×#5095	C₂	semidirect
7. C₅×#5062	C₂	semidirect
8. C₅×#5061	C₂	semidirect
9. C₅×#4717	C₂	semidirect
12. C₅×#1007	C₂²	semidirect
14. C₂×C₃×C₅×Q₁₆	C₂²	semidirect
16. C₃×C₅×C₄⋊Q₈	C₂²	semidirect
20. C₅×#942	C₂²	semidirect
32. C₅×#901	C₂²	semidirect
33. C₃×C₅×#97	C₂²	semidirect
34. C₅×#836	C₂²	semidirect
35. C₅×#836	C₂²	semidirect
37. C₅×#819	C₂²	semidirect
39. C₅×#805	C₂²	semidirect
40. #81885	C₅	direct (N × H)
43. C₅×#497	D₃	semidirect
92. #5766	C₂×C₅	semidirect
93. #5762	C₂×C₅	semidirect
94. C₃×#497	C₂×C₅	semidirect
95. #5192	C₂×C₅	semidirect
96. #5177	C₂×C₅	semidirect
97. #5095	C₂×C₅	semidirect
98. #5062	C₂×C₅	semidirect
99. #5061	C₂×C₅	semidirect
100. #4717	C₂×C₅	semidirect
116. C₂×C₅×Q₁₆	C₂×D₃	semidirect
121. C₅×C₄⋊Q₈	C₂×D₃	semidirect
129. C₅×#97	C₂×D₃	semidirect
163. #1007	C₂²×C₅	semidirect
165. C₂×C₃×Q₁₆	C₂²×C₅	semidirect
167. C₃×C₄⋊Q₈	C₂²×C₅	semidirect
171. #942	C₂²×C₅	semidirect
183. #901	C₂²×C₅	semidirect
184. C₃×#97	C₂²×C₅	semidirect
185. #836	C₂²×C₅	semidirect
186. #836	C₂²×C₅	semidirect
188. #819	C₂²×C₅	semidirect
190. #805	C₂²×C₅	semidirect
235. #497	C₅×D₃	semidirect
342. C₂×Q₁₆	C₂×C₅×D₃	semidirect
347. C₄⋊Q₈	C₂×C₅×D₃	semidirect
355. #97	C₂×C₅×D₃	semidirect
446. C₃×C₅	#3289	semidirect
500. C₅	#81885	direct (N × H)
513. C₃	C₅×#3289	semidirect

Maximal subgroups

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

subgroup	index
C₅×#5766	2
C₅×#5762	2
C₃×C₅×#497	2
C₅×#5192	2
C₅×#5177	2
C₅×#5095	2
C₅×#5062	2
C₅×#5061	2
C₅×#4717	2
C₅×#3289	3
#81885	5

Subgroups — C5×#81885 #14457810

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#81885 #14457810